A Tutorial on NYUSIM: Sub-Terahertz and Millimeter-Wave Channel Simulator for 5G, 6G, and Beyond

With the advancement of wireless communication to sub-terahertz (THz) and millimeter-wave (mmWave) bands, accurate channel models and simulation tools are becoming increasingly important for modeling a wide range of frequencies and scenarios. This paper provides a comprehensive tutorial on generating drop-based and spatial consistency-based channels using the open-source MATLAB-based NYU Channel Model Simulator (NYUSIM). NYUSIM is built on extensive real-world radio propagation measurements for the frequency range of 0.5–150 GHz, covering a variety of scenarios such as Urban Microcell (UMi), Urban Macrocell (UMa), Rural Macrocell (RMa), Indoor Hotspot (InH), and Indoor Factory (InF). Additionally, an overview of the evolution of simulators used to design and analyze wireless systems since the early days of cellular communication is also provided. We introduce the most popular types of simulators used in academia and industry, such as Channel Simulators (CSs), Link Level Simulators (LLSs), System Level Simulators (SLSs), and Network Simulators (NSs), to study wireless communication systems for 5G and beyond. Owing to the widespread adoption of the 3rd Generation Partnership Project (3GPP) Stochastic Channel Model (SCM) for channel generation in various simulators, we conduct a comparative analysis between the 3GPP SCM and NYUSIM channel model to highlight their differences. Moreover, NYUSIM’s versatility extends beyond its MATLAB implementation, as it can be implemented in various LLSs, SLSs, and NSs, enabling researchers to incorporate real-world measurement-based channels into their simulations. To illustrate this capability, we showcase NYUSIM’s implementation in ns-3, a widely used open-source discrete event network simulator. Additionally, we provide several applications of NYUSIM to highlight its potential uses.

SECTION I. Introduction

Wireless communication has fundamentally revolutionized how we live, communicate and conduct business. As smartphones, tablets, and IoT devices skyrocket in popularity and customers continue to demand greater data rates, cellular providers worldwide will continue to face the significant problem of bandwidth shortage [1], [2]. The key to alleviating the growing spectrum shortage is operating in higher frequencies, such as mmWave and sub-THz, where vast swaths of continuous bandwidths are available [3], [4]. Wireless researchers must understand and characterize the wireless medium in the mmWave and sub-THz bands to meet the growing demand for higher data rates and to enable technologies and applications of the future [5], [6], [7]. Understanding the wireless medium allows engineers to build the necessary infrastructure for the next-generation wireless networks, which will unify our experience across the physical and digital worlds [4], [8], [9], [10].

Channel models adequately capture the nature of wave propagation in a wireless medium, and engineers employ channel models to assist in designing, deploying, and comparing potential wireless technologies [11], [12]. Channel modeling is essential to advance state-of-the-art research, explore new promising frequency bands, and design power-efficient networks for the future. Channel models enable fair comparisons of different algorithms, designs, and performances in wireless networks to system and equipment design [11], [12], [13]. In addition, the choice of channel models significantly impacts spectrum efficiency, coverage, and hardware/signal processing requirements [13], [14], [15]. The performance of a wireless network ultimately depends on how accurately the channel models characterize the wireless medium in various propagation environments over different frequency bands [13], [14], [15]. As channel models are fundamental in characterizing a wireless medium and form the backbone of any wireless system [11], [12], various commercial organizations, academic institutions, and groups worldwide continue to analyze, compare and create channel models [12] as summarized in Table I. Furthermore, work in [11], [12], presents a summary of different channel models, radio propagation measurement campaigns, and the methodology used in creating the different types of channel models. The advent of new technologies and applications requires the use of various simulation tools which incorporate some of the channel models listed in Table I. The simulation tools then provide researchers and engineers an easy, efficient, accessible, cost-effective way to design, analyze and evaluate the performance of novel algorithms, protocols and wireless systems before deploying them in real-world scenarios.

TABLE I List of Popular Channel Models for 5G and Beyond (Part 2)

One such simulation tool is NYUSIM, which is an open-source sub-THz and mmWave Channel Simulator (CS) written in MATLAB1. It is free to download and use by both industry and academia. NYUSIM [31], [32], [33] was created using extensive field measurements and over a Terabyte of measurement data from 28 GHz to 140 GHz2 obtained during 2011–2022 in various scenarios such as UMi, UMa, RMa, InH, and InF [34], [37], [38], [39], [40], [41], [42], [43], [44], [45], [46], [47], [63], [64], [65], [150]. As of 2023, NYUSIM has been downloaded more than 100,000 times and is widely used by industry and academia as an alternative to 3GPP SCM and a surrogate for real-world channel measurements. The first version of NYUSIM was released in 2016 and since then, new features and channel model for higher frequency bands and different propagation scenarios have been incorporated in NYUSIM over the years by several generations of graduate students. As of 2023, NYUSIM is the world’s first CS capable of simulating wireless channels above 100 GHz for UMi, UMa, RMa, InH, and InF scenarios based on real-world radio propagation measurements conducted by NYU WIRELESS [48]. Moreover, NYUSIM’s versatility extends beyond its MATLAB implementation, as it can be implemented in various LLSs, SLSs, and NSs, enabling researchers to design, analyze, and optimize novel algorithms and protocols using real-world measurement-based channels.

The paper is organized as follows. Sections II and III provides an overview of simulations tools and some of the most popular simulators built since the early 1990s for cellular communications. A thorough comparison between the 3GPP SCM and NYUSIM channel model is presented in Section IV and the key differences between the mmWave and sub-THz channels is highlighted in Section V. Section VI introduces NYUSIM, a valuable alternative to the 3GPP SCM that can be implemented and used in various simulation tools to overcome the limitations of the 3GPP SCM. Then in Section VII, we present the details of the Graphical User Interface (GUI) for NYUSIM implementation in MATLAB. Section VIII provides an overview of the two modes of channel simulations supported by NYUSIM and the different types of output files generated by each mode of channel simulation. In Section IX, a deeper insight into the implementation details of NYUSIM is presented, which includes large-scale Path Loss (PL), small-scale PL models, the frequency dependence of large-scale and small-scale channel parameters, outdoor-to-indoor (O2I) penetration loss model, human blockage models, and polarization loss models. Additionally, Section X illustrates how NYUSIM can be used to obtain valuable insights about the mmWave and sub-THz channels. Furthermore, Section XI, showcases NYUSIM’s versatility extends beyond its MATLAB implementation, and we introduce the implementation of drop-based channel simulation mode of NYUSIM in ns-3. In Section XII we present some additional applications of using NYUSIM and in Section XIII we provide a brief survey of how researchers across the globe have used NYUSIM in their work over the years. Finally, we conclude this tutorial paper in Section XIV.

SECTION II. Overview of Simulation Tools

In general, simulation tools can be classified into four different categories: CSs, LLSs, SLSs, and NSs.

A CS is a software program that generates accurate and reliable Channel Impulse Response (CIR) for a particular frequency and environment [12] based on developed channel models (stochastic, deterministic or hybrid channel model [12]) thus, allowing researchers and engineers to skip expensive and time-consuming measurement campaigns. On the other hand, a Link Level Simulator (LLS) simulates the physical layer of a wireless network, including the Adaptive Modulation and Coding (AMC) schemes, channel estimation, prediction, tracking, Multiple Input Multiple Output (MIMO) and synchronization algorithms [49]. In general, a LLS is used to evaluate the performance of a single link in the network, typically between a Base Station (BS) and a User Terminal (UT) [49], [50]. LLSs provides the lowest level of abstraction and can be used to evaluate the impact of physical layer parameters on link-level performance. In contrast, a System Level Simulator (SLS) simulates the interaction between multiple links in a wireless network, including the impact of mobility, interference, and handover. It is used to evaluate the performance of a wireless network at the system level, including the network coverage, capacity, and quality of service [49], [50]. SLSs provide a higher level of abstraction than LLSs and can be used to evaluate the impact of various system configuration parameters on system-level performance. As opposed to a SLS, a Network Simulator (NS) simulates the entire wireless network, including multiple BS, UT, and the core network. It is used to evaluate the performance of the entire wireless network in various scenarios, including the impact of different network configurations, traffic patterns, and the investigation of applications and services that the network can support [51]. Generally, a NSs provides the highest level of abstraction and can be used to evaluate the overall end-to-end network performance of a wireless network. In summary, as shown in Fig. 1, the NSs provide the highest level of abstraction, SLSs provide a moderate level of abstraction, and LLSs simulators provide the lowest level of abstraction. The choice of the simulator depends on the specific requirements of the simulation, such as the level of detail needed, the complexity of the network, and the types of performance metrics to be evaluated.

Fig. 1.

Hierarchy of LLS, SLS and NS. In addition to 3GPP SCM, the wireless channel in all simulators, i.e., LLSs, SLSs and NSs can be modeled using NYUSIM channel model. NYUSIM channel model allows researchers and engineers to generate channels for the frequency range of 0.5-150 GHz based on real-world radio propagation measurements conducted by NYU WIRELESS in UMi, UMa, RMa, InH and InF scenarios.

SECTION III. Evolution of Simulators for Cellular Communications

A. Past Studies on Simulation Tools

Simulation tools have been developed and used since the very early days of cellular communication. Simulators were less prevalent in the early 1990s than they are today because the technologies used in 2G, such as Global System for Mobile Communications (GSM) and Enhanced Data rates for GSM Evolution (EDGE), were more easier to model analytically. Additionally, the computational power required to run complex wireless simulations was unavailable in the 2G era, making it challenging to develop and run complex simulators. Due to the technological limitations and the less critical role of wireless communications, only a few researchers who foresaw the potential of wireless communications as the next revolutionary technology were actively engaged in developing simulators. For instance, Smith [52] developed a simulation software that utilized Clarke’s two-ray Rayleigh fading channel model [53] for indoor and outdoor channels. The Simulation of Indoor Radio CIR Models (SIRCIM) model was developed by Rappaport and Seidel for the early development of WiFi [54]. SIRCIM was a measurement-based statistical indoor channel model that generated CIRs for indoor channels operating between 10 MHz and 60 GHz. In addition, another open-source Radio Frequency (RF) propagation simulator, Simulation of Mobile Radio CIR Models (SMRCIM) was developed for simulating outdoor channels [55], [56]. Fung et al. created Bit Error Rate (BER) Simulator (BERSIM) [57], a software simulation program that calculated the average BER and bit-by-bit error patterns for mobile radio communication links. This tool allowed real-time link quality evaluations without requiring RF hardware and was one of the earliest real-time wireless link-level simluators using realistic channel models with baseband hardware or computer software [205].

Beginning in the early 2000s, as 3G technology and wireless communication systems became complex, wireless simulators began to gain prominence. More complex modeling tools were required to build and optimize these systems as a result of the emergence of new wireless technologies like Wideband Code Division Multiple Access (WCDMA), High Speed Packet Access (HSPA), and later Long-Term Evolution (LTE). Moreover, another reason for the increased popularity of wireless simulators during this period was the growth in the importance of wireless communication in everyday life. With wireless simulators, testing and fine-tuning the cellular networks before deployment was possible, lowering the possibility of expensive delays or failures. In addition, wireless simulators became increasingly common as processing power and simulation technology improved. It became possible to model and simulate increasingly complicated wireless systems in greater detail as computers became more accessible, powerful, and cost-effective for developing simulation software. The work conducted by Gkonis et al. [49] provides a highly comprehensive and informative analysis of simulation tools. Their research highlights the remarkable evolution of simulators over the years, from the early days of 3G to 5G. The study effectively showcases the ever-growing sophistication and complexity of simulators that have accompanied the development of modern wireless communication technologies. In addition to providing a detailed overview of the evolution of simulators, [49] also presents a valuable resource for researchers and practitioners by listing the most commonly used LLSs, SLSs, NSs in 3G, 4G, and 5G era. Additionally, Mehlführer et al. [58] developed a downlink physical layer simulator (LLS) for LTE using the Parallel Computing Toolbox of MATLAB which could simulate single-downlink, single-cell Multi-user (MU), and multi-cell MU simulations. Furthermore, a SLS for LTE using MATLAB was built based on [58] for evaluating the performance of the downlink shared channel of LTE Single Input Single Output (SISO) and MIMO networks using open loop spatial multiplexing and transmission diversity transmit modes [59]. Furthermore, Mehlführer et al. [50] also developed a widely-recognized MATLAB-based LLS for UMTS LTE named “Vienna”. The “Vienna” simulator [50] had an open-source academic license, which promoted transparent and reproducible research in LTE. The simulator’s user-friendly interface, combined with MATLAB’s computational capabilities, enables effective simulation and analysis of diverse LTE scenarios. Moreover, Bouras et al. [51] conducted a comparative study on the most widely used NSs in both 4G and 5G and this work serves as a valuable resource for researchers seeking insights on selecting the most appropriate NS for their specific use case. The study also comprehensively analyzes the strengths and weaknesses of various NS options. Additionally, a study by Bonati et al. [60] provides the first unified and exhaustive synthesis of contemporary open-source software and frameworks for 5G cellular networks with a full-stack end-to-end perspective. The authors in [60] underscore the different open-source software’s capabilities, functions, and relationships and describe how these different software’s fit in the 5G ecosystem. Moreover, a detailed discussion on the hardware and testbeds that support these open-source software’s is provided in [60]. Furthermore, a critical assessment of the shortcomings of the state-of-the-art open-source software’s and suggestions to improve, support, and feasibly advance them are also discussed [60].

B. Focus of the Current Study on Simulation Tools

On the other hand, this article provides an overview of the most popular CSs, LLSs, SLSs, and NSs used by industry and academia for 5G and beyond cellular communications since 20133, 4. In particular, this article emphasizes the channel models supported by popularly used simulators, which are critical in accurately modeling wireless communication systems. This study is unique because it presents the first comprehensive review of simulators in the context of the channel models supported by them. While numerous CSs, LLSs, SLSs, and NSs have been created by academia and industry, our study focuses only on those developed by academia. This is because the simulators developed by the industry are often proprietary, costly, and not available for public use. However, we do make an exception and include CSs, LLSs, SLSs, and NSs developed by the industry only if they are free for public use, which typically occurs when the industry develops open-source software. There are many available options for choosing among CSs, LLSs, SLSs, and NSs, and each type of simulator has distinct features and capabilities. A non-exhaustive list of the popular CSs, LLSs, SLSs, and NSs created across the globe, along with the channel models they support, are listed in Table II. The second column in Table II contains the link in the citations to download the publicly available simulators. However, for simulators that are not accessible to the public, readers can contact the creators directly to obtain instructions to use the simulator. Furthermore, the third column in Table II mentions the developers and provides the link in the citations to important papers related to the development of the simulator.

TABLE II Non-Exhaustive List of Popular CSs, LLSs, SLSs, and NSs Developed Across the Globe for 5G and Beyond and the Channel Models Supported by Them. the Links to Download the Simulator and the Associated Papers Are Provided in Citations of Column II and Column III, Respectively

TABLE III Comparison of Key Channel Parameters for UMi and InH Scenarios Using the 3GPP SCM and NYUSIM Channel Model in the mmWave Band

TABLE IV Major Developments in NYUSIM Since 2016

TABLE V List of Default Values Used in NYUSIM

TABLE VI Received Omnidirectional $(P_{r,omni})$ and Directional $(P_{r,dir})$ Power at a Fixed Distance (100 m) for a CW Signal for Different Frequencies in UMi LOS and NLOS Channel Conditions

TABLE VII Distributions Used in NYUSIM From 0.5–150 GHz in 3GPP-Listed Scenarios (UMi, UMa, RMa, InH and InF)

TABLE VIII Channel Parameters for NYUSIM at 28 GHz in All 3GPP-Listed Scenarios (UMi, UMa, RMa, InH and InF)

TABLE IX Channel Parameters for NYUSIM at 142 GHz in All 3GPP-Listed Scenarios (UMi, UMa, RMa, InH and InF)

From Table II we see that most LLSs, SLSs, and NSs use the 3GPP SCM for modeling the wireless channel. This involves either implementing the 3GPP SCM directly or using the 3GPP TDL or CDL models derived from the 3GPP SCM. However, it is important to note that the 3GPP SCM has some limitations (discussed in Section IV) that may affect its accuracy. Additionally, as most simulation tools utilized by researchers and engineers rely heavily on the 3GPP SCM, it results in limited comprehension of the influence of the wireless channel model on algorithms, protocols, and system design [13], [14], [15]. Furthermore, Table X provides further examples of how channel model selection impacts design of wireless systems. Therefore, it is imperative for engineers to carefully choose appropriate channel models to ensure accurate design, performance, and evaluation of their work.

TABLE X Summary of Research Work on 5G and Beyond Using NYUSIM (PART 1)

SECTION IV. Comparison of 3GPP SCM and NYUSIM Channel Model

Prior work in [14] investigated and analyzed NYUSIM channel model and 3GPP SCM at mmWave bands. Based on measurements conducted in New York City [14], [41], [61] in UMi and UMa scenarios it was concluded that 3GPP SCM has a higher chance of predicting Line of Sight (LOS) compared to NYUSIM channel model at larger distances (several hundred meters) in UMi and UMa scenarios [14]. In addition, the cell radius can differ by as much as 50 m; 3GPP SCM predicts LOS distances to be larger than NYUSIM channel model because of the difference in LOS probability and PL models of 3GPP SCM and NYUSIM channel model. Furthermore, [14] has demonstrated that, in outdoor scenarios, NYUSIM channel model provides a more realistic characterization of the wireless channel than 3GPP SCM. For a single-cell, three-user MIMO scenario, the hybrid precoding and analog combining method proposed in [142] and the digital block diagonalization (BD) approach presented in [143] were used. By using these approaches, the Spectral Efficiency (SE) per user (averaged over three users) produced by NYUSIM channel model and 3GPP SCM was 18 bits/Hz and 12 bits/Hz [14], respectively.

Work in [13] compared the 3GPP SCM with NYUSIM channel model and showed that the number of clusters in the 3GPP SCM5 are much higher compared to the measured number of Time Cluster (TC) and Spatial Lobe (SL) 6 in NYUSIM channel model, resulting in different levels of channel sparsity in both the models. The 3GPP SCM are advantageous for spatial multiplexing as they have larger number of clusters, resulting in more multipaths and power distributed uniformly across all the multipaths. In NYUSIM channel model, the channels are sparse and have few strong multipaths. When the few strong multipaths are exploited with different beamforming approaches, it leads to higher SE than 3GPP SCM. For instance, even with the highest number of RF chains, the average SE produced by the 3GPP SCM for the one-stream situation in a Single-user (SU)-MIMO system using the Hybrid Beamforming (HBF) algorithm in [13] is still lower than the NYUSIM SE with the smallest number of RF chains.

In addition, from Table III we can see that for the outdoor and indoor scenarios 3GPP SCM has an unrealistically large number of clusters and rays per cluster compared to NYUSIM channel model which is not observed in real-world measurements at mmWave bands [1], [38], [39], [40].

Furthermore, for the InF scenario, the 3GPP SCM TR 38.901 document assumes the number of clusters for both LOS and Non Line of Sight (NLOS) environments is 25 [16] whereas, in NYUSIM channel model, the average number of time clusters (TC) from empirical channel measurements at 142 GHz are 3.4 and 3 for the LOS and NLOS channel conditions respectively [47]. Note that for the InF scenario, the observations are at 142 GHz for NYUSIM channel model, whereas the 3GPP SCM observations are for mmWave frequencies. However, based on past observation in mmWave frequencies for outdoor and indoor scenarios between 3GPP SCM and NYUSIM channel model as stated above, it is fair to say that the number of clusters observed in 3GPP SCM for InF is higher, and in the real-world, the observation will be lower than what is stated in 3GPP SCM. The higher number of clusters in the 3GPP SCM in outdoor and indoor scenarios is likely to result in a higher rank of mmWave channels, unrealistic eigen-channel distributions, and thereby inaccurate SE prediction for 5G mmWave channels [13], [14], [62].

Additionally, a direct comparison between NYUSIM channel model and the 3GPP SCM for frequencies exceeding 100 GHz is unfeasible due to the latter’s limitations. Moreover, with the emergence of sub-THz bands, encompassing frequencies ranging from 100-300 GHz, the wireless channel’s propagation characteristics are significantly different from those observed in the mmWave band. Consequently, it is crucial to ensure accurate characterization of the wireless channel at these sub-THz frequencies to harness their full potential. Thus, in the following section, we list some key observations that were made based on radio propagation measurements conducted by NYU WIRELESS and NYUSIM channel model above 100 GHz across all 3GPP-listed scenarios.

SECTION V. Key Differences Between mmWave and Sub-THz Channels

• As we go higher in frequency, the wavelength reduces. The reduction in wavelength at sub-THz bands compared to mmWave bands allows the development of more compact directional antennas in the same form factor. We can fit more antennas with an antenna spacing of $\lambda $ /2 in the sub-THz bands compared to mmWave bands. This facilitates the formation of a pencil-like beam and enables double-directional channels with steerable antennas at both the BS and UT [47], [63], [64], [65], [66], [145].

• Atmospheric absorption and rain impair mmWave and sub-THz frequencies much more than frequencies below 6 GHz. Additionally, the attenuation due to atmosphere and rain in sub-THz bands is higher compared to mmWave bands. But the high directional antennas at both Transmitter (Tx) and Rx in sub-THz bands and mmWave bands can easily compensate for the atmospheric loss and attenuation due to rain [47], [63], [64], [65], [66], [145].

• Things are much opaquer and are hard to penetrate in sub-THz bands when compared to mmWave bands. As we go higher in frequency, i.e., from mmWave band to sub-THz bands the loss due to reflection, penetration and scattering increases. But the good thing is we still observe a few strong dominant multipaths in sub-THz bands which can be exploited to create a link between the BS and UT [47], [63], [64], [65], [66], [145].

• There is generally more channel sparsity in time and space (fewer numbers of AOA, AOD and TC are observed) in sub-THz bands compared to mmWave bands. This is mainly because the materials in the environment become more lossy as we go higher in frequency and we observe only a few strong dominant multipaths [47], [63], [64], [65], [66], [145].

• The Root Mean Square (RMS) delay spread and RMS angular spread reduce when we go to higher frequency due to channel sparsity. The channel is much more sparser in sub-THz bands compared to mmWave bands which leads to a lower RMS delay spread and RMS angular spread in sub-THz bands [47], [63], [64], [65], [66], [145].

Using NYUSIM researchers and engineers can generate channels that exhibit the above key characteristic to build wireless systems above 100 GHz. Furthermore, detailed insights about mmWave and sub-THz channels that can be obtained via NYUSIM is presented in Section X. NYUSIM can be downloaded from https://wireless.engineering.nyu.edu/5g-millimeter-wave-channel-modeling-software/ and the steps to run simulations using NYUSIM can be found in the NYUSIM user manual available with the software.

SECTION VI. NYUSIM Overview

To overcome the limitations of the 3GPP SCM mentioned in Section IV and to generate mmWave and sub-THz channels, the existing and future LLSs, SLSs, and NSs can leverage NYUSIM. NYUSIM is based on real-world measurement data and can support a wide frequency range of 0.5-150 GHz for all 3GPP-listed scenarios such as UMi, UMa, RMa, InH and InF scenarios and provide a more comprehensive and accurate realization of the wireless channel [13], [14], [15] compared to the 3GPP SCM. Moreover, NYUSIM is an active open-source project which has been continuously maintained and upgraded by several generations of graduate students at NYU WIRELESS. Table IV summarizes the major developments in NYUSIM over the past seven years since its first release in 2016 [32].

NYUSIM uses Monte Carlo simulations to generate samples of CIR at specific Tx-Receiver (Rx) (T-R) separation distances. The user specifies the range of T-R separations, and NYUSIM uniformly selects a distance from this range. NYUSIM offers two simulation modes namely drop-based and spatial consistency-based modes for UMi, UMa, RMa, InH and InF scenarios. When the spatial consistency mode is enabled, NYUSIM generates correlated CIRs along the UT trajectory. When disabled, NYUSIM operates in drop-based mode and generates independent CIRs for different T-R distances. The human blockage module works in both modes. The simulator can support RF bandwidth up to 800 MHz for frequencies less than 100 GHz because it was built using measurements made in the real world at an RF bandwidth of 800 MHz for frequencies below 100 GHz. On the other hand, the simulator can support RF bandwidths from 0 to 1 GHz for frequencies above 100 GHz because measurements at 142 GHz conducted in office [46], [63], [66], outdoor [64], [65], [67], [68], [69], and factory [45], [47], [70], [71] environments used wideband probing signals with 1 GHz RF bandwidth.

SECTION VII. GUI of MATLAB Based NYUSIM

The GUI for the MATLAB-based implementation of NYUSIM is shown in Fig. 2 and is divided into four categories: channel parameters [32], antenna properties [32], spatial consistency parameters [33], and human blockage parameters [33]. There are fifty-one input parameters in NYUSIM which are self explanatory and the details of each of these parameters can be found in the NYUSIM user manual available with the software. The channel parameters, antenna properties, spatial consistency, and human blockage parameters have twenty-one, twelve, eleven, and seven input parameters, respectively. The user can independently set all the input parameters according to their needs. If an input parameter is set incorrectly, an error prompt will appear to guide the user to set the correct value. Furthermore, if the user does not specify any input parameters, the default value of the input parameters will be used during the simulation as specified in Table V.

Fig. 2.

GUI of NYUSIM 4.0 with four panels: channel parameters, antenna properties, spatial consistency parameters, human blockage parameters. All parameters in the GUI can be customized as per user requirement.

SECTION VIII. Types of Channel Simulations Supported by NYUSIM

NYUSIM offers two simulation modes: the drop-based mode and the spatial consistency mode (details of the implementation of each mode can be found in the NYUSIM user manual available with the software). Subsequent subsections offer brief overviews of these two simulation modes and the output figures and files they produce. The detailed procedure to generate the channel using the drop-based mode in NYUSIM is shown in Fig. 3 and explained in [32], [35]. Similarly, the detailed procedure to generate the channel using the spatial consistency mode in NYUSIM is shown in Fig. 10 and explained in [33], [139], [140], [141].

Fig. 3.

Flowchart illustrating the channel generation procedure for drop-based mode in NYUSIM.

Fig. 4.

Sample 3D AOD power angular spectrum generated from NYUSIM at a T-R separation distance of 39.7 m for 142 GHz UMi NLOS.

Fig. 5.

Sample 3D AOA power angular spectrum generated from NYUSIM at a T-R separation distance of 39.7 m for 142 GHz UMi NLOS.

Fig. 6.

Sample omnidirectional PDP generated from NYUSIM at a T-R separation distance of 39.7 m for 142 GHz UMi NLOS.

Fig. 7.

Sample directional PDP generated from NYUSIM at a T-R separation distance of 39.7 m for 142 GHz UMi NLOS.

Fig. 8.

Sample omnidirectional PDP over different receive antenna elements generated from NYUSIM at a T-R separation distance of 39.7 m for 142 GHz UMi NLOS.

Fig. 9.

Sample omnidirectional and directional PL plot generated from NYUSIM for 142 GHz UMi NLOS.

Fig. 10.

Flowchart illustrating the channel generation procedure for spatial consistency mode in NYUSIM (the text in red in the blocks underscore the major differences in channel generation procedure between the drop-based and spatial-consistency based simulation modes in NYUSIM).

A. Drop-Based Mode in NYUSIM

For any given simulation run, i.e., for a specific T-R separation distance, the drop-based mode produces random and independent channel realizations [32]. Fig. 3 shows the procedure to generate drop-based channels in NYUSIM.

1) Output Figures:

Six figures are generated by running drop-based simulations for a given set of input parameters which are as follows:

• 3D AOD power spectrum: Indicates the multipath profile on the Tx side in the spatial domain over the azimuth and elevation plane, as shown in Fig. 4.

• 3D AOA power spectrum: Indicates the multipath profile on the Rx side in the spatial domain over the azimuth and elevation plane, as shown in Fig. 5.

• Omnidirectional Power Delay Profile (PDP): Denotes the omnidirectional multipath profile in the time domain. The omnidirectional PDP plot in Fig. 6 shows a few key pieces of data, including the frequency, environment, T-R separation distance, Root Mean Square (RMS) delay spread $(\sigma _{\tau })$ , omnidirectional received power $(\mathrm {P_{omni_{r}}})$ , omnidirectional Path Loss (PL), and Path Loss Exponent (PLE). The transmit power, the measurement system’s dynamic range (180 dB), and a 10 dB SNR are used to calculate the noise threshold, equal to the transmit power in logarithmic scale minus 170 dB. This is shown as the lower limit of the y-axis in Fig. 6.

• Directional PDP: Represent the directional multipath profile in the time domain. A sample directional PDP generated using a particular antenna pattern (the details of the antenna pattern used in NYUSIM can be found in the NYUSIM user manual available with the software) antenna pattern is shown in Fig. 7. The directional PDP in Fig. 7 shows proper channel and antenna parameters, including the frequency, environment, T-R separation distance, directional RMS delay spread $(\sigma _{\tau })$ , directional received power $(\mathrm {P_{dir_{r}}})$ , directional PL, directional Path Loss Exponent (PLE), and Tx and Rx antenna Half Power Beamwidth (HPBW)s and gains in degrees and dBi, respectively.

• Small-scale PDP: As seen in Fig. 8, a series of PDPs over each receive antenna element were obtained using [146, eq. (4)], by utilizing the user-specified type of antenna array, the number of antenna elements, and the spacing between the antenna elements.

• PL: As shown in Fig. 9, a PL scatter plot is produced after N (${N}\geq $ 1) continuous simulation runs with the same input parameters. The values for omnidirectional and directional PL over the entire distance range are shown in this figure, along with the fitted PLE and standard deviation for shadow fading using the minimum-mean-square-error (MMSE) method [41], [43]. In the legend of the figure “PathLossPlot,” n denotes the PLE, $\sigma $ is the shadow fading standard deviation, “omni” denotes omnidirectional, “dir” represents directional, and “dir-best” means the direction with the strongest received power. When no antenna gains are considered, the directional PLE is larger than the omnidirectional PLE. A directional antenna will spatially filter out more multipath components because of its directional pattern, resulting in the Rx receiving fewer multipath components and less energy.

When ${N}\geq $ 1 (i.e., the number of simulation runs entered greater than 1), the T-R separation distance is randomly chosen for each simulation run. The value of the T-R separation distance chosen in each run is randomly generated within the upper and lower bound of the T-R separation distance (the upper bound and lower bound of T-R separation distance are specified by the user). Regardless of the value of N, the first five figures are always generated from the first simulation run, and the sixth figure (omnidirectional and directional path loss plot) is generated for the $N^{th}$ simulation run.

2) Output Files:

For each simulation, based on the type of output file selected, NYUSIM can either generate.txt files or.mat files, or both. The list of files that can be produced as output is as follows:

• Text files (.txt)

  1. AOALobePowerSpectrumn_yy_Lobex.txt

  2. AODLobePowerSpectrumn_yy_Lobex.txt

  3. OmniPDPn_yy.txt

  4. DirectionalPDPn_yy.txt

  5. SmallScalePDPn_yy.txt

  6. BasicParam.txt

  7. OmniPDPInfo.txt

  8. DirPDPInfo.txt

• MATLAB files (.mat)

  1. AOALobePowerSpectrumn_yy.mat

  2. AODLobePowerSpectrumn_yy.mat

  3. OmniPDPn_yy.mat

  4. DirectionalPDPn_yy.mat

  5. SmallScalePDPn_yy.mat

  6. BasicParam.mat

  7. OmniPDPInfo.mat

  8. DirPDPInfo.mat

• Both Text and MATLAB files (.txt and.mat): Upon choosing this option, all the files (sixteen in total) mentioned above in Text files (.txt) and MATLAB files (.mat) are produced in the output.

In all the files mentioned above n denotes the $n^{th}$ Rx location (i.e., $n^{th}$ simulation run), x represents the $x^{th}$ SL and yy denotes the type of polarization, i.e., Co-Pol, X-Pol, Co/X-Pol, All-Pol.

(i) and (ii) in.txt files, have five columns, namely multipath delay (ns), multipath power (mW), multipath phase (rad), azimuth Angle of Arrival (AOA) (degree) (in (i)) or azimuth Angle of Departure (AOD) (degree) (in (ii)) and elevation AOA (degree) (in (i)) or elevation AOD (degree) (in (ii)). The multipath delay (ns), multipath power (mW), and multipath phase (rad) represent the absolute propagation time delays, received power, and phases of distinct multipath components, respectively. In addition, files (i) and (ii) in.mat files contain a structure of the number of SL. For instance, if there are three AOA SL, then (i) will contain three structures, one for each SL. Each structure has five columns as described above, depending on whether the.mat file is for AOA or AOD. (iii) in.txt and.mat file indicates omnidirectional PDP, whereas file (iv) in.txt and.mat file is generated by applying directional antenna gain patterns to the omnidirectional PDP. The files (iii) and (iv) in.txt and.mat files have two columns: the first shows the propagation time delay in nanoseconds, and the second shows the received power in dBm. (v) in.txt and.mat file captures the omnidirectional PDPs seen over each Rx antenna element. It comprises three columns, where the first column indicates the separation between antenna elements in terms of wavelengths, the second column the delay in propagation time in nanoseconds, and the third column the received power in dBm. For visual purposes, the noise power is set to –150 dBm. (vi) in.txt and.mat file stores all the fifty-one input parameters for running a simulation. (vii) in.txt and.mat file comprised five columns, each of which represents a critical variable for one of the $n^{th}$ omnidirectional PDPs from the N continuous simulation runs. The five columns are T-R separation distance (m), omnidirectional received power in dBm, omnidirectional PL in dB, omnidirectional RMS delay spread in ns, and the Ricean K-factor in dB. The Ricean K-factor is the ratio of the strongest power of the multipath to the sum of the powers of the other multipath components [40]. (viii) in.txt and.mat file consists of 11 columns, each representing a variable for one of the $n^{th}$ directional PDPs from the N continuous simulation runs. The columns denote the simulation run number, T-R separation distance (m), absolute time delay (ns), received power (dBm), Phase (rad), Azimuth AOD (degree), Elevation AOD (degree), Azimuth AOA (degree), Elevation AOA (degree) of each resolvable multipath component respectively. In addition, there is directional PL (dB) and directional RMS delay spread (ns). The directional PL is measured by lining up the Tx and Rx antenna boresights with the AOD and AOA of each resolvable multipath component. The transmit power plus the Tx/Rx antenna boresight gains, less the directional received power, is equal to the directional PL.

B. Spatial Consistency Mode in NYUSIM

Spatial consistency refers to the correlation of channel characteristics over time and space, which is crucial for accurately predicting the behavior of wireless signals as they propagate through different environments [33], [73], [74]. Without spatial consistency, the predicted channel characteristics could be inaccurate, leading to suboptimal system performance [1], [147].

In mobile communication systems, where UTs are either moving or are closely spaced (within 10–15m), the scattering environment remains consistent. This implies that the CIRs for such proximate locations are highly correlated. Spatial consistency in a channel model enables the generation of correlated, time-variant channel coefficients based on the UT’s trajectory. When incorporated into a channel simulator, this allows for a continuous and realistic simulation of angular power spectrums and PDPs based on the UT movement in the vicinity. Spatial consistency, essentially, ensures that the wireless channel behaves in a predictable manner across nearby locations [1], [74], [147]. For instance, if a UT is moving along a path, the received signal strength does not drastically change from one location to the next but varies smoothly.

The implementation of spatial consistency in NYUSIM is a multi-step process, as illustrated in Fig. 10. In the subsequent discourse, we offer a comprehensive overview of the essential steps required to achieve spatial consistency in NYUSIM:

1. Spatial-Correlated Propagation Assignment: Determining the propagation condition (LOS or NLOS) using spatial correlation is fundamental for ensuring spatial consistency. NYUSIM derives its spatially-correlated large-scale parameters (factors like shadow fading and LOS/NLOS conditions) by leveraging an exponential spatial filter. This filter is applied to independent random values produced from drop-based simulation, paralleling the methodology employed in WINNER II [148].

2. Integration of Shadow Fading Map Generation: This procedure is pivotal for actualizing the spatial correlation in the propagation conditions.

   1. Initialization of Shadow Fading Map: A 2-D grid map is generated to contain values of spatially correlated shadow fading in a simulated area. The granularity of the map is set to be 1 m, which means the distance between two neighboring grid points is 1 m. Shadow fading is modeled as a log-normal random variable with zero mean and $\sigma $ dB standard deviation. The map of shadow fading is initialized by assigning an independent and identically distributed (i.i.d) normal distributed random variable at each grid point [74].

   2. Application of 2-D Exponential Filter: A 2-D exponential filter is applied to the map, whose filter response is given by the following equation [33], [73]:\begin{equation*} h(p, q) {=} \exp \left ({-\frac {\sqrt {p^{2} + q^{2}}}{d_{co}}}\right),\tag{1}\end{equation*} where p and q are coordinates with respect to the center of the filter, $\sqrt {p^{2} + q^{2}}$ represents the distance to the center of the filter, and $d_{co}$ is the correlation distance of shadow fading.

   3. Generation of Correlated Values: The correlated values in the map are calculated by [33], [140]:\begin{align*} \!\!\! M_{c}(i, j) {=} \sum _{p}\sum _{q} h(p, q)M\left ({i - p + 1, j - q + 1}\right),\!\!\!\! \tag{2}\end{align*} where $M_{c}$ is the correlated map and M is the initialized independent map. i and j are the coordinates of grid points in the map.

3. Power Update: The power of each multipath component is updated by redistributing cluster powers and multipath component powers in each cluster [145]. This redistribution, considers the time-variant large-scale path loss, ensuring that signal power levels are consistent with the spatial characteristics of the environment.

4. Smooth Transitions: NYUSIM ensures spatial consistency by managing the birth and death of clusters as the user moves. This cluster birth and death process, modeled as a Poisson process, allows for smooth transitions between different channel segments. If the number of time clusters differs between segments, the power of a single cluster ramps up or down individually, ensuring no abrupt changes in channel characteristics. This dynamic nature of clusters, crucial for simulating mobile users in motion or multiple users in proximity, contributes significantly to the spatial consistency of the channel model [33], [73], [74]. For a clearer understanding, consider a scenario where a user is moving along a path in an urban environment. As the user moves, new clusters may be born due to new buildings or other obstacles coming into the LOS. Similarly, existing clusters may die as buildings or obstacles move out of the LOS.

5. Dynamic Parameter Updates: In NYUSIM, as the UT moves every 1 m along its path, channel coefficients are dynamically updated to mirror evolving propagation conditions and maintain spatial consistency. Key time-variant parameters per cluster include: 1) Path loss, derived from the UT’s position, with localized shadow fading standard deviation adaptable to LOS or NLOS shifts; 2) Cluster and subpath excess delays, initially set by NYUSIM but adjusted for UT motion, incorporating velocity, direction, and varying AOAs and AODs; 3) Cluster and subpath powers, reallocated due to variable path loss, using correlated shadowing factors; and 4) Efficiently computed subpath AODs and AOAs, leveraging linear approximations for complex NLOS angles.

1) Output Figures:

Five figures are generated by running drop-based simulations for a given set of input parameters which are as follows:

1. Map of spatially correlated shadow fading: As shown in Fig. 11, this map indicates the BS and UT locations along with the UT. In addition, the frequency, environment, T-R separation distance, the standard deviation of shadow fading, track distance, and velocity is also displayed.

2. Map of spatially correlated LOS/NLOS condition: It shows all locations in a local area with the same propagation condition (LOS or NLOS), as seen in Fig. 12. The figure also shows fundamental data such as frequency, environment, T-R separation distance, the standard deviation of shadowing fading, track distance, and velocity.

3. User track: Fig 13 indicates the region of the spatially correlated shadow fading map that the UT travels along. This figure displays the track distance and traveling direction.

4. Consecutive omnidirectional PDPs along the user trajectory: Fig. 14 illustrates the power variation and delay drifting of multipath components when directional antenna gain patterns are used at the Tx and Rx and synthesized to create an omnidirectional PDP. The PDP plot displays specific fundamental data, including frequency, environment, T-R separation distance, track distance, and velocity.

5. Consecutive directional PDPs with strongest received power along the user trajectory: Fig. 15 illustrates the power variation and delay drifting of multipath components when directional antenna gain patterns are used at the Tx and Rx. The PDP plot displays specific fundamental data, including frequency, environment, T-R separation distance, track distance, and velocity.

Fig. 11.

A map of spatially correlated shadow fading with the BS and UT locations generated using NYUSIM at T-R distance of 42.7 m for 142 GHz UMi NLOS.

Fig. 12.

A sample map of spatially correlated LOS/NLOS condition generated using NYUSIM at T-R distance of 42.7 m for 142 GHz UMi NLOS.

Fig. 13.

A sample user track generated using NYUSIM at T-R distance of 42.7 m for 142 GHz UMi NLOS.

Fig. 14.

A sample consecutive omnidirectional PDPs generated using NYUSIM at T-R distance of 42.7 m for 142 GHz UMi NLOS.

Fig. 15.

A sample consecutive directional PDPs generated using NYUSIM at T-R distance of 42.7 m for 142 GHz UMi NLOS.

2) Output Files:

For each simulation, based on the type of output file selected, NYUSIM can either generate.txt files or.mat files, or both. The list of files that can be produced as output is as follows:

• Text files (.txt)

  1. OmniPDP_snapx.txt

  2. DirectionalPDP_snapx.txt

  3. OmniPDPInfo.txt

  4. DirPDPInfo.txt

  5. BasicParam.txt

• MATLAB files (.mat)

  1. OmniPDP_snapx.mat

  2. DirectionalPDP_snapx.mat

  3. OmniPDPInfo.mat

  4. DirPDPInfo.mat

  5. BasicParam.mat

  6. CIR_MIMO_EVO.mat

• Both Text and MATLAB files (.txt and.mat): Upon choosing this option, all the files (eleven in total) mentioned above in Text files (.txt) and MATLAB files (.mat) are produced in the output.

In all the files mentioned above, x denotes the index of the channel snapshot. Note that when spatial consistency is selected, it is recommended to set the value of N as 1. When ${N}\geq $ 1, the files stored in the output location will be for the $N^{th}$ run. This is done because each run in the spatial consistency mode generates a large number of output files, and to prevent the memory of the user’s device from getting exhausted, only the files from the $N^{th}$ run is saved.

(i) and (ii) in.txt files and.mat files have seven columns, namely multipath delay (ns), multipath power (dBm), multipath phase (rad), Angel of Depature (AOD) (degree), ZOD (degree), Angel of Arrival (AOA) (degree) and ZOA (degree). The multipath delay (ns), multipath power (dBm), and multipath phase (rad) represent the absolute propagation time delays, received power, and phases of distinct multipath components, respectively. The AOD and AOA represent the azimuth AOD and azimuth AOA of the multipath components, whereas ZOD and ZOA denote the elevation AOD and elevation AOA of the multipath component. (iii) in.txt and.mat file comprises of five columns, namely T-R separation distance (m), omnidirectional received power (dBm), omnidirectional PL (dB), omnidirectional Root Mean Square (RMS) delay spread (ns) and Ricean K-factor (dB), and each row corresponds to a channel snapshot. On the other hand, (iv) in.txt and.mat file also has five columns, namely Snapshot index, T-R separation distance (m), directional received power (dBm), omnidirectional PL (dB) and omnidirectional RMS delay spread (ns) and each row represents a channel snapshot. The file (v) in.txt and.mat format saves the input parameters of the simulation run, and file (vi), which is a.mat file, contains the MIMO channel matrix generated by NYUSIM for each snapshot of the channel, where inside each snapshot of the channel, the field “H_ensemble” contains the MIMO channel matrix.

SECTION IX. Implementation Details of NYUSIM

NYU’s broadband Stochastic Channel Model (SCM) [66], [75] is used as a foundation in NYUSIM. As additional characteristics, the NYU-developed spatial consistency process [72], [73], [74], the human blockage model [76], [150], and the outdoor-to-indoor (O2I) penetration loss model [151], [152] are also employed in NYUSIM.

A. Large-Scale Path Loss Model

NYUSIM utilizes large-scale Path Loss (PL) models to estimate the received power based on the distance from the Tx. These models have parameters like Path Loss Exponent (PLE) and shadowing that reflect the wireless channel’s slowly varying characteristics over time and space. The Close-in (CI) PL model, which assumes a 1 m reference distance, is used for calculating PL in Urban Microcell (UMi), Urban Macrocell (UMa), Indoor Hotspot (InH) and Indoor Factory (InF) except Rural Macrocell (RMa) scenario due to its superior accuracy and reduced sensitivity to measurement error [41]. For the RMa scenario, the CIH PL model (CI model with a height-dependent PLE) is adopted, as given by [44, eqs. (21) and (22)]. For RMa scenario, the BS height provided by the user on the GUI is used for the CIH PL model, while other scenarios do not use BS height at all for PL computation. In our implementation of NYUSIM, the CI PL model extended with BS height (CIH) and CI PL model accounts for additional attenuation terms such as atmospheric attenuation (AT), O2I loss, and foliage loss (FL). For instance, the CI PL model with additional attenuation terms can be expressed as (3)\begin{align*} \mathrm {PL^{CI}}(f,d) \left [{\mathrm {dB}}\right ]=&\mathrm {FSPL} \left ({f,1 \; \mathrm {m}}\right) \left [{\mathrm {dB}}\right ] + 10 \eta \log _{10}(d) + \\&\mathrm {AT}\left [{\mathrm {dB}}\right ] + \mathrm {O2I} \left [{\mathrm {dB}}\right ] + \mathrm {FL} \left [{\mathrm {dB}}\right ] + \chi _{\sigma }^{CI} \left [{\mathrm {dB}}\right ], \tag{3}\end{align*} where f is the frequency in GHz, d denotes the 2D T-R separation distance, and $d \geq 1$ m, FSPL(f, 1 m) represents the free space PL at a T-R separation of 1 m at carrier frequency f, $\eta $ denotes the PLE. O2I loss is caused due to the propagation of the signal from the outdoor to the indoor environment. O2I loss is implemented using the high and low loss parabolic models for building penetration loss [152], [153]. $\chi _{\sigma }^{CI}$ is a zero-mean Gaussian random variable with $\sigma $ as the standard deviation in dB to represent shadow fading about the distant-dependent mean PL value. The definition of the terms $\mathrm {FSPL}(f,1 \; \mathrm {m})$ , AT and FL can be found in [32, eqs. (2) and (4)] and [15, eq. (5)].

Fig. 16 illustrates the propagation attenuation values due to dry air, vapor, haze, and rain at mmWave and sub-THz frequencies from 1 GHz to 150 GHz, with a barometric pressure of 1013.25 mbar, relative humidity of 80%, a temperature of 20°C, and a rain rate of 5 mm/hr, while the collective attenuation effects of these four main natural absorbers are displayed in Fig. 17. These results were obtained and reproduced from five reported controlled experiments on atmospheric attenuation [154].

Fig. 16.

Individual propagation attenuation due to dry air, vapor, haze, and rain for the frequency range of 0.5-150 GHz, with a barometric pressure of 1013.25 mbar, a relative humidity of 80%, a temperature of 20°C, and a rain rate of 5 mm/hr generated using NYUSIM [154].

Fig. 17.

Collective attenuation effects of dry air, vapor, haze, and rain for the frequency range of 0.5-150 GHz, with a barometric pressure of 1013.25 mbar, a relative humidity of 80%, a temperature of 20°C, and a rain rate of 5 mm/hr generated using NYUSIM [145], [154].

Measurements at 28, 73, and 142 GHz in indoor and outdoor environments [63], [67] demonstrate that the CI and CIF (an extension of the CI PL model that includes a frequency-dependent correction factor) PL models produce highly similar PLEs, indicating that a single PLE can accurately represent PL across a wide frequency range. The only frequency-dependent effect is PL in the first meter of propagation as energy spreads into the far field [63], [67], [68]. As a result, NYUSIM uses a consistent PLE for UMi, UMa, InH, and InF scenarios across all frequencies.

It is worth noting that the CI model contains an inherent frequency dependency of PL already included in the FSPL term. A unique property of (3) is that $10\eta $ expresses PL in dB in terms of decades of distances beginning at 1 m (making it very straightforward to compute power over distance in one’s head). The CI PL model is rooted in wireless propagation principles dating back to Friis [155] and Bullington [156]. The PLE parameters, which reflect the PL based on the environment, have a value of 2 in free space (as demonstrated by Friis) and a value of 4 for the asymptotic two-ray ground bounce propagation model (as demonstrated by Bullington). By standardizing to a reference distance of 1 meter, measurements and models can be easily compared, and the PLE can be defined consistently, allowing for quick computation of PL and intuitive understanding of the results [41]. The CI PL model has the same mathematical structure as the existing ABG model used in 3GPP SCM/ITU channel models [16], [41], [43]. However, it outperforms it in terms of stability of model parameters, prediction accuracy across a wide range of frequencies, distances, and scenarios, and intuitive appeal. Additionally, it achieves these results using fewer parameters [41].

When analyzing large-scale PL, it is commonly believed that higher-frequency channels experience more loss due to the consideration of only the free space PL with omnidirectional antennas. However, this belief is a general misconception. It is crucial to note that antennas can be highly directional at higher frequencies and provide higher gain, resulting in less loss. The friis free space PL can be expressed as follows:\begin{equation*} P_{r}(d) {=} \frac {P_{t} G_{t} G_{r}}{\left ({\frac {4 \pi d}{\lambda }}\right)^{2}},\tag{4}\end{equation*} where, $P_{r}$ and $P_{t}$ are the received and transmitted power in mW, respectively. d is the 3D distance between the Tx and Rx and ${d} \geq $ 1 m, $\lambda $ is the wavelength in m and can be expressed as $\lambda = {}{}\frac {c}{f_{c}}$ where $c = 3\times 10^{8} m/s$ and $f_{c}$ is the center frequency in Hz. $G_{t}$ and $G_{r}$ denote the gains of the Tx and Rx antennas, respectively. In general, the gain of an antenna can be expressed as \begin{equation*} G {=} \frac {A_{e}4\pi }{\lambda ^{2}},\tag{5}\end{equation*} where, $A_{e}$ is the effective aperture area (m₂) of the antenna. Substituting $\lambda $ in (5) we get \begin{equation*} G {=} \frac {A_{e}4\pi f_{c}^{2}}{c^{2}},\tag{6}\end{equation*} Thus, for a fixed $A_{e}$ (6) can be expressed as follows:\begin{align*}&G {=} k_{1} f_{c}^{2}, \tag{7}\\&G \propto f_{c}^{2},\tag{8}\end{align*} where $k_{1} = {}{}\frac {A_{e}4\pi }{c^{2}}$ . Thus, (7) shows that at higher frequencies (mmWave and above), the antennas (for a given physical size) are highly directional and have higher gains (gain is proportional to the square of frequency (8)) when compared to the antenna at sub-6 GHz.

Similarly, on substituting $\lambda $ and (6) in (4) we can express (4) as \begin{equation*} P_{r}(d) {=} \frac {P_{t} A_{et} A_{er} f_{c}^{2}}{d^{2} c^{2}},\tag{9}\end{equation*} where, $A_{et}$ and $A_{er}$ are the effective aperture area (in m₂) of the Tx and Rx antennas, respectively. For a given $P_{t}$ , $A_{et}$ and $A_{er}$ we can further express (9) as follows \begin{align*} P_{r}(d)=&k_{2}\frac {f_{c}^{2}}{d^{2}}, \tag{10}\\ P_{r}(d)\propto&\frac {f_{c}^{2}}{d^{2}},\tag{11}\end{align*} where $k_{2} {=}{}{}\frac {P_{t} A_{et} A_{er}}{c^{2}}$ . Thus, (10) demonstrates that when high gain directional antennas are used at both the Tx and Rx, higher frequency links have less loss than lower frequencies as for a fixed distance d the received power grows as the square of frequency (11) [4], [42].

To illustrate the above concept consider a continuous wave signal with a bandwidth of 0 Hz, transmitted with a power $(P_{t})$ of 1 mW (or –30 dBW) using an antenna with an efficiency of 0.6 (antenna efficiency is defined as the ratio of power radiated by the antenna to the power supplied to the antenna). The Tx antenna has an area $(A_{et})$ of 0.5 m² (0.5 m x 1 m), and the Rx antenna has an area $(A_{er})$ of 0.0005 m² (0.022 m x 0.022 m). The distance between the Tx and Rx is 100 meters, and we are considering frequencies of 3, 10, 30, 100, and 300 GHz. We will evaluate this configuration for the UMi scenario in two different channel conditions: LOS and NLOS, with PLEs of 2 and 3.2, respectively [63].

The received power for the above configuration in dB is calculated using:\begin{align*} P_{r}(d) \mathrm {(dBW)} {=} P_{t} \mathrm {(dBW)} + G_{t} + G_{r} - PL^{CI}(f,d) \mathrm {(dB)}, \tag{12}\end{align*} where, $G_{t}$ and $G_{r}$ given the $A_{et}$ and $A_{er}$ for each frequency mentioned above can be computed by (6). On the other hand, when omnidirectional antennas are considered at both Tx and Rx, $G_{t}$ and $G_{r}$ is equal to 0 dBi. To compute $PL^{CI}(f,d)$ in LOS and NLOS channel conditions for the UMi scenario for different frequencies we use (3) without the terms AT[dB], O2I[dB], FL[dB] and $\chi _{\sigma }^{CI}$ . The $P_{r}$ for directional and omnidirectional antennas in LOS and NLOS channel conditions is calculated using (12) and presented in Table VI. Additionally, from Table VI we can conclude the following:

1. In LOS and NLOS channel conditions if we use omnidirectional antennas at both Tx and Rx and go up in frequency from 3 to 300 GHz the $P_{r,omni}$ decreases. This is because as we go higher up in frequency the Path Loss (PL) increases and the omnidirectional antennas cannot compensate for the increase in PL.

2. In LOS and NLOS channel conditions for a particular frequency the $P_{r,dir}$ is higher for a directional antenna when compared to an omnidirectional antenna. This is because directional antennas focus more energy in a particular direction which can compensate for the PL much more than an omnidirectional antenna which radiates in all directions.

3. In LOS and NLOS channel conditions if we use directional antennas at both Tx and Rx and go up in frequency from 3 to 300 GHz the $P_{r,dir}$ increases. This is because as we go higher up in frequency the PL increases and the gains of the Tx and Rx antenna also increase as the square of frequency as shown in (6). The higher gain directional antennas used at Tx and Rx can easily compensate for the increase in PL.

Thus, Table VI shows that the received power increases as we increase the carrier frequency when directional antennas are used at both Tx and Rx [4].

Similarly, we can compute the SNR from the received power using the expression \begin{equation*} SNR \mathrm {(dB)} {=} P_{r}(d) - 10 log_{10}(KTB) - NF,\tag{13}\end{equation*} where K is the Boltzmann constant, T is temperature in Kelvin, B is the bandwidth in Hz and NF is the noise figure in dB. For illustration purposes, we set the NF as 10 dB, and B is set as 100 MHz, 500 MHz, 1 GHz, 5 GHz, and 10 GHz. Fig. 18 shows the plot of frequency vs SNR for different B. From Fig. 18 we can see that for a given bandwidth, the SNR increases as we go higher up in frequency.

Fig. 18.

Plot of SNR calculations (in dB) at different frequencies (fc) and bandwidths in UMi LOS/NLOS. This demonstrates that as we ascend to higher frequencies for a given bandwidth, the SNR increases due to the increase in received power resulting from higher antenna gains at higher frequencies.

B. Small-Scale Multipath Model

Small-scale parameters are wireless channel characteristics that change rapidly in time and space. Small-scale multipath models are required to accurately model the variations in the wireless channel over short distances and periods. These models help statistically reproduce the CIR by capturing the multipath components present in the time-varying wireless channel. The approach used by NYUSIM to generate the temporal and spatial characteristics of the channel is called Time Cluster Spatial Lobe (TCSL) [39], [75].

The TCSL approach [39], [75] is based on extensive measurement campaigns conducted by NYU WIRELESS from 2011–2022. The TCSL approach in NYUSIM separates the time and space dimensions by calculating temporal and spatial statistics independently. The TCSL approach defines two key terms: Time Cluster (TC) and Spatial Lobe (SL). A Time Cluster (TC) has multipath components that are close in time but may come from distinct spatial directions [39], [75]. Whereas, the SL can comprise of many multipath components arriving (or departing) from a particular direction in space but with different time delays [39], [75] which can be spread over hundreds of nanoseconds. Real world measurements revealed that multipath components in the same TC can arrive from different spatial pointing angles and multipaths arriving or departing in a specific pointing direction can have a propagation delay of hundreds or thousands of nanoseconds.

The TCSL approach implements a physics-based clustering scheme based on field observations and can be used to extract TC and SL statistics for any ray-tracing or measurement data sets [39], [75]. To find the number of TC and SL, we partition the omnidirection PDP and Power Angular Spectrum (PAS), respectively, using minimum inter-cluster time void interval (MTI) and SL threshold (SLT) as described in [39], [75]. Fig. 19 provides a comprehensive representation of the multipath components in both the temporal and spatial dimensions. These components are derived from a sample Tx and Rx location in the UMi scenario at 142 GHz simulated using the drop-based channel simulation mode in NYUSIM. Fig. 19 adeptly illustrates the TCSL concept by visually demonstrating the behavior of multipath components from both a temporal and spatial standpoint. Focusing on the upper right-hand section of Fig. 19, the temporal perspective is emphasized. This view showcases the omnidirectional PDP, which comprises a total of six distinct multipath components. These multipath components exhibit variations in arrival times, angular directions, and power levels. Crucially, they can be categorized into three distinct TC based on the MTI. Each TC accommodates a varying number of multipath components (TC1 contains two, TC2 contains three and TC3 contains only 1 multipath component respectively), and these multipath components in a TC can emerge from varying spatial/angular direction. On the other hand, from the spatial domain perspective the six multipath components are grouped into two SL. These SLs collectively encompass all three TCs mentioned earlier. Specifically, SL1 is composed of TC2, incorporating three multipath components. Meanwhile, SL2 encompasses TC1 and TC2, resulting in a combined total of three multipath components (two from TC1 and one from TC3). Thus, in each SL we observe that multipaths arrive over several tens to hundreds of nanoseconds.

Fig. 19.

Spatio-temporal/TCSL visualization of multipaths components arriving at the Rx and forming two distinct SLs and three TCs. The Z-axis represents the received power; The XY-plane plots the AOA where along the radius the absolute propagation delay in nanoseconds is represented. The top-right corner illustrates the omnidirectional PDP and the three distinct TCs within the PDP.

Probabilistic distributions are created after processing the measurement data using the TCSL approach and doing curve fitting [46], [65], [75]. A complete list of the channel parameters at 28 GHz and 142 GHz can be found in Table VIII and Table IX, respectively. The outdoor, indoor, and factory scenarios exhibit distinct probabilistic distributions for several channel parameters, such as the number of TCs, cluster subpaths, and SL. For instance, the number of TCs, and cluster subpaths are Uniformly distributed for the UMi scenario, whereas they are Poisson distributed for the InH and InF scenarios. Table VII summarizes the distributions employed to model various channel parameters. The values for the parameters used to characterize these random variables are collated in the fetchChanParams.m file in the folder /“NYUSIM Base Code” for the outdoor, indoor, and factory scenarios, encompassing both LOS and NLOS environments. These parameter values are readily accessible to users, who can modify them according to their needs and preferences.

C. Frequency Dependence of Large-Scale and Small-Scale Channel Parameters

NYU WIRELESS has conducted outdoor and indoor radio propagation measurements at four different frequency bands: 28, 38, 73, and 142 GHz, but not all scenarios were measured at all frequency bands, except for the 28 GHz and 142 GHz bands where UMi and InH scenarios were measured. The UMa and RMa scenarios were measured at 38 GHz and 73 GHz only. Due to limited measurements in UMa and RMa scenarios at 28 GHz and 142 GHz, channel parameters for these scenarios have been primarily derived from UMi scenario measurements at the same frequencies, as presented in Tables VIII and IX. Moreover, deploying base stations at 25m for UMa measurements in New York City is impractical due to regulatory hurdles. Additionally, the dense urban environment in New York City, with an average building height exceeding 30m, renders the difference between 10m (UMi) and 25m (UMa) base station heights negligible. Both scenarios would experience similar channel propagation. The InF measurements were conducted only at 142 GHz, and thus the derived channel parameters for InF at 142 GHz are used for the entire simulation frequency range, i.e., from 0.5-150 GHz. Further measurements might be necessary to accurately characterize frequency-dependent channel parameters for the UMa, RMa and InF scenarios across the entire frequency range of 0.5-150 GHz.

To accurately model the wireless channel at any arbitrary frequency band for any scenario of interest, we need to interpolate the large-scale and small-scale parameters values based on measurements in two specific bands using a linear interpolation technique. This approach ensures that our channel model is accurate and consistent across the entire frequency range of interest, covering the allowable user-specified carrier frequency range of NYUSIM from 0.5-150 GHz. For frequencies below 28 GHz, the large-scale and small-scale channel parameters are set to the values at 28 GHz, and for frequencies above 140 GHz, they are set to the values at 140 GHz.In the future we will extend NYUSIMs capability to the FR3 frequency band (7 – 24 GHz). for all 3GPP-listed scenarios. The current linear interpolation implemented in NYUSIM is expressed as:\begin{align*} p(f)=\begin{cases} p(28),&~~f \leq 28, \\ {}{}\frac {p(140)-p(28)}{140-28}f+{}{}\frac {5p(28)-p(140)}{4},&~~ 28 < f < 140, \\ p(140), &~~ f \geq 140, \end{cases} \tag{14}\end{align*} where p(f) denotes the large-scale or small-scale parameters which needs to be estimated at frequency f (GHz), p(28) and p(140) represent the large-scale or small-scale parameters value at 28 GHz and 140 GHz, respectively. In summary, the method of linear interpolation makes NYUSIM a reliable and efficient tool for predicting channel characteristics across a wide range of frequencies in diverse 3GPP-listed scenarios.

D. O2I Penetration Loss Model

Outdoor-to-indoor (O2I) penetration loss refers to the attenuation or reduction of RF signal power as it travels from an outdoor to an indoor environment. O2I penetration loss can be affected by various factors such as the signal frequency, the distance between the transmitting and receiving antennas, the type and thickness of the building materials, and the presence of other obstructions in the environment. O2I penetration loss is particularly important in mmWave and sub-THz wireless communication because these frequency bands have shorter wavelengths and higher frequencies than traditional wireless bands, such as 2.4 GHz and 5 GHz used in Wi-Fi. As a result, the signal propagation characteristics are different, and the signals have more difficulty penetrating through obstacles like walls and buildings, leading to higher attenuation and penetration loss. O2I loss for building penetration loss is implemented in NYUSIM using the high and low loss parabolic models in [33], [152], which fits the measured building penetration loss with standard glass and IRR glass. The current O2I loss models implemented in NYUSIM [33], [152] are based on frequencies upto 100 GHz. However, we plan to extend the current O2I loss model upto 150 GHz in the near future.

E. Human Blockage Loss Models

The human blockage loss model is a mathematical model that characterizes the effects of human bodies on the propagation of radio signals. This model helps to predict the attenuation or signal loss caused by the presence of people in the communication path. Human blockage can lead to temporary signal disruptions and degradation, particularly in areas with high human traffic, such as crowded urban environments, stadiums, and transportation hubs. In situations with a temporary blockage, there is typically a signal loss for several hundred milliseconds. A four-stage Markov model has been proposed based on field measurements [76], [150] to characterize these blockage events, including unshadowed, decay, shadowed, and rising stages and implemented in NYUSIM [33]. The current human blockage model is based on measurements conducted at 73 GHz and may be used upto 150 GHz. However, further validation is required to asses the accuracy to the human blockage models upto 150 GHz.

F. Polarization Model

Dual-polarized Tx and Rx antenna arrays can transmit and receive signals with two different polarization’s simultaneously. In other words, each antenna in the array has two separate elements oriented in different polarizations, such as vertical and horizontal. This enables increased data throughput as two signals can be transmitted and received simultaneously without interfering with each other and can help mitigate the effects of polarization fading. Dual-polarized antennas can also increase the channel rank for higher-order MIMO diversity and multiplexing. Hence, a Channel Simulator (CS) like NYUSIM must generate the CIR under different polarization to understand the impact of polarization and further optimize the performance of the wireless system. In NYUSIM, polarization’s effect is considered to generate CIRs for any scenario of interest in the frequency range of 0.5-150 GHz. NYUSIM supports four types of polarization and allows users to select the desired polarization type to generate CIRs. For example, if the user selects polarization type as “Co-Pol” (Tx and Rx antennas are V-V/H-H polarized), the CIRs generated will include the effect of polarization loss due to “Co-Pol” antennas along with losses due to large-scale PL, atmospheric loss, etc.

To model the effect of polarization in NYUSIM, the Cross-Polarization (Cross-Pol) Discriminator (XPD) and Co-Polarization (Co-Pol) Discrimination (CPD) metrics are used. XPD is expressed in dB and represents the attenuation in signal power, which is calculated as the ratio of the power of the cross-polarized signal (when the transmit antenna is vertically/horizontally polarized and the receive antenna is horizontal/vertically polarized) to the power of the co-polarized signal (both transmit and receive antennas are vertically or horizontally polarize). In contrast, CPD is defined as the ratio of the power of the co-polarized component of the received signal to the power of the total received signal, including both the co-polarized and cross-polarized components and is also expressed in dB.

The literature reports XPD values for various indoor and outdoor environments at microwave and mmWave frequencies [38], [43], [66], [77], [157], [158], [159], [160], [161], [162], [163], [164], showing that XPD tends to increase as the carrier frequency increases. To model XPD over the NYUSIM-supported frequency range of 0.5-150 GHz, a linear function of frequency is used, which is given by \begin{equation*} \mathrm {XPD}\: \left ({\mathrm {dB}}\right) {=} k\cdot f\: \left ({\mathrm {GHz}}\right) + b,\tag{15}\end{equation*} where k and b are the slope and intercept, respectively. Research has shown that XPD values tend to be larger in LOS environments compared to NLOS environments, as the boresight path in LOS typically experiences less depolarization. Therefore, in NYUSIM, two different linear functions which comprise of different k and b values are used to model XPD values in LOS and NLOS environments as shown in Fig. 20. To simplify the polarization model while ensuring validity, a single XPD value is applied to the total omnidirectional received power computed in CIR instead of applying different XPD values to different multipath components. This is because there is limited available literature on multipath-wise XPD values. This approach allows for a succinct yet accurate modeling of polarization effects in NYUSIM.

Fig. 20.

The measured XPDs with linear fits for the LOS and NLOS channel condition for the frequency range of 0.5-150 GHz.

The studies on the CPD are very limited [157], [160], [165], [166], showing that the V-V polarization usually has a slightly larger received power than the H-H polarization when walls are the primary reflectors in the environment. However, the difference in the overall received power is typically negligible (within 1 dB) [157], [160], [165], [166] for V-V and H-V polarization. One exception is the tunnel scenario, where the particular confined waveguide shape causes the CPD variation between -20 dB and 80 dB with a mean of 5.4 dB [165] for V-V and H-H polarization. NYUSIM focuses on the common indoor and outdoor environments. Thus the CPD is modeled as a zero-mean Gaussian random variable with a small standard deviation (1.6 dB) between V-V and H-H polarization [157], [160], [165], [166].

SECTION X. Analyzing mmWave and Sub-THz Channels Using NYUSIM

NYUSIM can be used to generate channels for the mmWave and sub-THz bands in drop-based and spatial-consistency mode for different 3GPP-listed scenarios. This provides the user with the ability to perform diverse research work to design, build and analyze systems and algorithms for the mmWave and sub-THz bands as shown in Sections XII and XIII. Moreover, using NYUSIM one can determine the fundamental characteristics of the wireless channel such as RMS delay spread and RMS angular spread. RMS delay spread represents the temporal dispersion and frequency selectivity of the channel. Whereas, RMS angular spread characterizes the angular dispersion of the channel. RMS angular spread is essential for designing and evaluating MIMO communications systems with beamforming and spatial multiplexing capabilities. NYUSIM can be used to obtain insights on the RMS delay spread and RMS angular spread for mmWave and sub-THz bands for different scenarios such as UMi, UMa, RMa, InH and InF. For example, from Fig. 21 we can see that the omnidirectional RMS delay spread obtained via NYUSIM for 28 GHz LOS and NLOS in the InH scenario is 10.8 ns and 16.7 ns respectively. In contrast, the omnidirectional RMS delay spread obtained via NYUSIM for 142 GHz LOS and NLOS in the InH scenario is 2.6 ns and 6.7 ns respectively. Similarly, from Fig. 22 we can see that the RMS angular spread obtained via NYUSIM for 28 GHz LOS and NLOS in the InH scenario is 23.6° and 24.6° respectively. In contrast, the RMS delay spread obtained via NYUSIM for 142 GHz LOS and NLOS in the InH scenario is 4.4° and 6.4° respectively. Thus, as we go higher in frequency from 28 GHz to 142 GHz we see a reduction in omnidirectional RMS delay spread and RMS angular spread in LOS and NLOS channel conditions in the InH scenario. In general, a smaller value of RMS delay spread in the InH scenario in sub-THz bands compared to mmWave bands indicates that the coherence bandwidth is larger in the sub-THz bands thus, a wider subcarrier spacing can be used in the sub-THz bands compared to mmWave bands. A wider subcarrier spacing results in a shorter symbol duration since the symbol duration is inversely proportional to the subcarrier spacing. Similarly, a lower value of RMS angular spread in the sub-THz band compared to the mmWave band in the InH scenario indicates that the spatial correlation between multipaths increases leading to lesser spatial streams. Similar comparisons can be made for other scenarios and between different scenarios in mmWave and sub-THz bands [47].

Fig. 21.

Measured and simulated omnidirectional RMS delay spread for InH scenario in LOS/NLOS for 28 GHz and 142 GHz.

Fig. 22.

Measured and simulated omnidirectional RMS angular spread for InH scenario in LOS/NLOS for 28 GHz and 142 GHz.

Additionally, as shown in Fig. 21 and Fig. 22 to verify the accuracy of NYUSIM, we conduct a comparison between the RMS delay spread and RMS angular spread obtained from real-world channel measurements and those generated after the implementation of the channel model in NYUSIM (the channel models implemented in NYUSIM are derived from the post processing of the real-world channel measurement data).

SECTION XI. NYUSIM in NS-3

Researchers worldwide frequently use discrete-event NS, like ns-3, to study and evaluate intricate wireless networks, create new protocols, and for cross-layer optimization. The mmWave [107] and New Radio (NR) [109] modules in ns-3 are the most popular and widely used full-stack end-to-end simulation modules for simulating 5G mmWave networks using the 3GPP SCM [16], [167]. Intensive computational power is required to simulate a complicated network with several UT and BSs (gNBs), each with a fully developed protocol stack implementation. As SCM offer the best balance between accuracy and complexity, SCM are utilized for system-level simulations in ns-3.

As stated earlier in Section IV there are key differences between the channels generated by 3GPP SCM and NYUSIM, which inspired us to implement NYUSIM in ns-3. For instance, using NYUSIM in ns-3 researchers can understand the effects of lower-layer inconsistencies, like SE discovered in [14], on the end-to-end throughput, latency, and packet drop [15], [206] and create, design, evaluate novel protocols and algorithms using a realistic channels generated by NYUSIM in ns-3 to improve the performance of wireless systems. In addition, ns-3 currently uses the 3GPP SCM for simulations which limits researchers to the frequency range of 0.5-100 GHz. Whereas NYUSIM can support a frequency range of 0.5-150 GHz, thus allowing researchers to investigate, analyze and build future wireless networks above 100 GHz. Moreover, a detailed information about the implementation of drop-based NYUSIM in ns-3 is provided in [34], [35].

, Poddar et al. [15], [206] presents a study of the impact of lower layer discrepancy, i.e., Signal to Interference and Noise Ratio (SINR), on the end-to-end throughput, latency, and packet drop in a wireless network operating at 28 and 140 GHZ with a RF bandwidth of 100 MHz and 1 GHz, respectively. The study conducted in [15], [206] indicates that to analyze, improve, and design the protocol stack for future wireless devices, we must choose the channel model wisely because it affects the SINR, drastically impacting end-to-end throughput, latency, and packet drops.

SECTION XII. NYUSIM: Applications

NYUSIM can be used in a multitude of different ways. For instance, work in [32] shows an example of two different applications for NYUSIM. In one of the applications, NYUSIM is used to determine the MIMO channel condition number and in the second application the SE between the NYUSIM channel model and 3GPP SCM is compared. Moreover, [33] demonstrates that NYUSIM can be used to generate time-variant large-scale PL based on UT trajectory and shows that PL varies smoothly with correlated shadow fading values as compared to the drop-based models (in the drop-based models, the showing fading values are independently generated and not correlated to each other). Additionally, in [33], the impact of human blockage on directional channels using NYUSIM is studied. Results in [33] showed that UT using narrow HPBW have a higher likelihood of severe blockage shadowing loss and 31% of UT equipped with 7° HPBW antenna experience more than 15 dB shadowing loss. Furthermore, NYUSIM can be used to generate synthetic channel data for training and testing various AI/ML algorithms for 5G and beyond. In addition to the applications mentioned above, in this section, we present two more applications to illustrate the capabilities of NYUSIM.

A. Prediction of Indoor Coverage

When deploying WiFi networks in indoor scenarios, it is essential to forecast how much of an area a WiFi hotspot will cover indoors. At sub-THz frequencies, the PL increases within the first meter of propagation distance, reducing the cell size and necessitating an ultra-dense network to maintain an adequate link margin. Here, we demonstrate a method for predicting a sub-THz indoor wireless system’s average coverage using the drop-based channel simulation mode in NYUSIM. The following values are used as input parameters:

• Frequency: 140 GHz

• RF bandwidth: 800 MHz

• Scenario: InH

• Distance Range Option: Indoor (5-50 m)

• Environment: LOS and NLOS

• Lower Bound of T-R Separation Distance: 5 m

• Upper Bound of T-R Separation Distance: 50 m

• Tx Power: 10 dBm

• BS Height: 2.5 m

• Polarization: Co-Pol

• Number of Rx Locations: 100 in LOS and 100 in NLOS

• Tx Array Type: URA

• Rx Array Type: URA

• Number of Tx Antenna Elements $N_{t}$ : 16

• Number of Rx Antenna Elements $N_{r}$ : 4

• Tx Antenna Spacing: 0.5 wavelength

• Rx Antenna Spacing: 0.5 wavelength

• Number of Tx Antenna Elements Per Row $W_{t}$ : 4

• Number of Rx Antenna Elements Per Row $W_{r}$ : 2

• Tx Antenna Azimuth HPBW: 10°

• Tx Antenna Elevation HPBW: 10°

• Rx Antenna Azimuth HPBW: 30°

• Rx Antenna Elevation HPBW: 30°

We presume that a mobile Rx’s sensitivity is -82 dBm following WLAN compliance. For indoor directional channels in both LOS and NLOS situations, the scatter plot of the received powers and the average power level of the received signals are shown in Fig. 23 for distances between 5 m and 50 m. The Tx and Rx use antenna arrays that produce narrow beams with HPBW of 10° and 30°, which can offer strong directional gains and are not prone to interference from communication links of other hotspots or mobile devices. In a LOS environment, the Tx and Rx beams are oriented in the direction of boresight, while in an NLOS environment, the beams are pointed in the direction of strongest reflection. Figure 23 indicates that in a LOS scenario, the Rx keeps an adequate SNR level for distances beyond 50 m. However, when the Tx and Rx antennas are pointed in the strongest reflection direction in an NLOS environment, the received power drops below the Rx sensitivity (−82 dBm) at the separation distance of 35.8 m, indicating the potential use of multi-beam antenna combing [168] and reconfigurable intelligent surfaces (RISs) [169] to increase the signal coverage.

Fig. 23.

Scatter plot of the received powers and the average power level of the received signals at distances from 5 to 50 m for LOS and NLOS InH directional channels. For the NLOS environment, the average power level of received signals drops below the Rx sensitivity beyond 35.8 m.

B. Continuous Wave (CW) Fading Channel at Sub-THz Frequencies

In the spatial consistency mode, NYUSIM may produce small-scale fading channels depending on user-specified channel characteristics (such as frequency, scenario, and environment) and movement parameters (such as Rx moving direction and velocity). The following values are used as input parameters:

• Frequency: 142 GHz

• RF bandwidth: 800 MHz

• Scenario: UMi

• Distance Range Option: Standard (10-500 m)

• Environment: NLOS

• Lower Bound of T-R Separation Distance: 10 m

• Upper Bound of T-R Separation Distance: 100 m

• Tx Power: 10 dBm

• BS Height: 3 m

• Polarization: Co-Pol

• Moving distance: 1 m

• Update distance: 0.001 m

• User track type: Linear

• Moving direction: 45°

• Velocity: 10 m/s

• Tx Array Type: URA

• Rx Array Type: URA

• Number of Tx Antenna Elements $N_{t}$ : 16

• Number of Rx Antenna Elements $N_{r}$ : 4

• Tx Antenna Spacing: 0.5 wavelength

• Rx Antenna Spacing: 0.5 wavelength

• Number of Tx Antenna Elements Per Row $W_{t}$ : 4

• Number of Rx Antenna Elements Per Row $W_{r}$ : 2

• Tx Antenna Azimuth HPBW: 10°

• Tx Antenna Elevation HPBW: 10°

• Rx Antenna Azimuth HPBW: 30°

• Rx Antenna Elevation HPBW: 30°

Fig. 24 depicts a sample of CW fading at 142 GHz across a moving distance of 1 m at a speed of 10 m/s. Due to the mm-level wavelength (2 mm at 142 GHz), significant signal change (also known as fading) can be seen over a tiny local area of 1 m. There are 19 multipaths in this example simulated channel, spread over different TCs. On the other hand, Fig. 25 shows another example of simulated CW fading in a multipath channel with four multipaths, and shows that sparse channels may exhibit smaller but faster signal fluctuation than multipath-rich channels. In general, fading envelopes that represent Rayleigh and Rician distributions or random fading envelopes (other than Rayleigh and Rician) can be produced using the spatial consistency of NYUSIM. In the sub-THz channels, for instance, there might be a dearth of multipaths, making it likely to produce random fading envelopes that are neither Rayleigh distributions nor Rician distributions.

Fig. 24.

A sample CW fading of a simulated UMi channel with 19 multipath components over a 1 m moving distance with a velocity of 10 m/s at 142 GHz generated using NYUSIM.

Fig. 25.

A sample CW fading of a simulated UMi channel with four multipath components over a 1 m moving distance with a velocity of 10 m/s at 142 GHz generated using NYUSIM.

SECTION XIII. Studies Conducted Using NYUSIM

Besides the aforementioned applications in Section XII that highlight NYUSIM’s potential usage, Table X provides an

overview of how NYUSIM has been utilized in various works since its initial release in 2016. From Table X we can see that researchers across the globe use NYUSIM for analyzing and investigating the impact of different channel models on the physical layer and network layer performance. In addition, NYUSIM has also been used to evaluate novel beamforming algorithms, power allocation algorithms, etc., and in studies involving propagation, coverage, and blockage in different mmWave frequency bands. Furthermore, new use cases such as UAV and V2X communications, which exploit the mmWave spectrum, have also been explored using NYUSIM [13], [14], [149], [170], [171], [172], [173], [174], [175], [176], [177], [178], [179], [180], [181], [182], [183], [184], [185], [186], [187], [188], [189], [190], [191], [192], [193], [194], [195], [196], [197], [198], [199], [200], [201], [202], [203], [204].

SECTION XIV. Conclusion

In this tutorial paper, we have presented how simulation tools for cellular communications have proliferated with the increase in complexity of wireless systems and computing power since the early 1990s and provided a list of the most widely used LLSs, SLSs and NSs by researchers and engineers for 5G and beyond. Moreover, we have highlighted the limitations of 3GPP SCM used to model the wireless channel in the LLSs, SLSs, and NSs and signify the importance of using accurate real-world measurement based channel models like NYUSIM for the frequency range of 0.5-150 GHz for UMi, UMa, RMa, InH and InF scenarios. Using ns-3 as an example, we showed how easy it is to implement NYUSIM in various LLSs, SLSs, and NSs, which will enable the research community to simulate channels above 100 GHz and enable researchers to use realistic channels in their simulations. In addition to the implementation details of MATLAB based NYUSIM, we have also presented details on the drop-based and spatial-consistency-based modes of channel simulations, and the output figures, and files generated for each mode in NYUSIM. The capability to generate real-world measurement based channels in the mmWave and sub-THz bands using NYUSIM is essential to obtain more accurate and realistic results from the different simulation tools. Furthermore, by leveraging the world’s first sub-THz CS “NYUSIM”, which can generate channels above 100 GHz, researchers can explore possibilities for future developments in the sub-THz bands.

ACKNOWLEDGMENT

The authors thank Michael G. Cotton at the National Telecommunications and Information Administration (NTIA) for providing them with the reference material and code for the atmospheric attenuation characteristics at frequencies below 1000 GHz. The development and support of NYUSIM has also been made possible through the help of the NYU WIRELESS Industrial Affiliates and the National Science Foundation (with award numbers: 1302336, 1320472, 15502967, 1731290, 1909206, and 2037845). The authors also thank Shu Sun, Yunchou Xing, Ojas Kanhere, and George R. MacCartney for contributing to NYUSIM. Moreover, the authors would like to thank Mingjun Ying, Valentina Fambri, Tomoki Yoshimura, and Akhileshwar Chowdary for reviewing the paper and suggesting valuable edits to improve the quality of the paper. Finally, the authors would like to acknowledge the global community of NYUSIM beta testers and users for running extensive simulations and providing insights on making the simulator more beneficial for the entire research community.

AbbreviationExpansion

List of Acronyms
3GPP	3rd Generation Partnership Project
AMC	Adaptive Modulation and Coding
AWGN	Additive White Gaussian Noise
AOD	Angle of Departure
AOA	Angle of Arrival
BS	Base Station
BER	Bit Error Rate
CIR	Channel Impulse Response
CS	Channel Simulator
CI	Close-in
CDL	Cluster Delay Line
Co-Pol	Co-Polarization
CIH	CI PL model extended with BS height
Cross-Pol	Cross-Polarization
CW	Continuous Wave
EDGE	Enhanced Data rates for GSM Evolution
ETSI	European Telecommunications Standards Institute
GSM	Global System for Mobile Communications
GUI	Graphical User Interface
HPBW	Half Power Beamwidth
HSPA	High Speed Packet Access
HST	High Speed Train
H-H	Horizontal-Horizontal
HBF	Hybrid Beamforming
InH	Indoor Hotspot
InF	Indoor Factory
ITU	International Telecommunication Union
LSP	Large-Scale Parameter
LOS	Line of Sight
LLS	Link Level Simulator
LTE	Long-Term Evolution
MIMO	Multiple Input Multiple Output
MU	Multi-user
NS	Network Simulator
NR	New Radio
NLOS	Non Line of Sight
NTN	Non Terrestrial Networks
NOMA	Non-Orthogonal Multiple Access
NYUSIM	NYU Channel Model Simulator
O2I	Outdoor-to-Indoor
PL	Path Loss
PLE	Path Loss Exponent
RF	Radio Frequency
Rx	Receiver
RMS	Root Mean Square
RMa	Rural Macrocell
SL	Spatial Lobe
SINR	Signal to Interference and Noise Ratio
SCM	Stochastic Channel Model
SLS	System Level Simulator
SE	Spectral Efficiency
SU	Single-user
SISO	Single Input Single Output
TC	Time Cluster
T-R	Tx-Rx
Tx	Transmitter
TR	Technical Report
TDL	Tapped Delay Line
TS	Technical Specification
UMi	Urban Microcell
UMa	Urban Macrocell
UAV	Unmanned Aerial Vehicle
UT	User Terminal
ULA	Uniform Linear Array
URA	Uniform Rectangular Array
UM	Ultra Massive
V2X	Vehicle-to-everything
V-V	Vertical-Vertical
V-H	Vertical-Horizontal
WCDMA	Wideband Code Division Multiple Access
XPD	Cross-Pol Discriminator