Design and Analysis of In-Band Full-Duplex Private 5G Networks Using FR2 Band

This paper studies a solution for efficient industrial Internet of things (IIoT) communications through a in-band full-duplex (IBFD) enabled private 5G network in frequency range 2 (FR2) band (≥24.250 GHz), where ultra-reliable low-latency communications (URLLC) and enhanced mobile broadband (eMBB) devices can be simultaneously served. Large-scale antenna array and RF beamforming are applied, and a self-interference cancellation (SIC) scheme is proposed under such architecture. Particularly, the proposed RF cancellation scheme addressed two key issues of extending current technologies to wideband operations in FR2 band: limited operational bandwidth and the requirement for a large number of cancellers. Then, a frequency domain-based digital canceller is proposed to process with the residual self-interference (RSI) with short processing latency. A game theoretic user allocation algorithm is proposed to minimise co-channel interference (CCI) in a heterogeneous environment. Given a typical IIoT scenario, the performance of such IBFD private 5G network is evaluated in terms of bit-error rate (BER) and spectral efficiency (SE) through simulations and analysed based on numerical results and theoretical calculations. It is demonstrated that the latency of uplink eMBB devices can be reduced by 54% through IBFD radios, and the latency of downlink URLLC devices can be reduced to 0.5 ms with the help of flexible numerology, mini-slot, and self-contained sub-frames introduced in 5G NR. IBFD radios can enhance the SE by 92% compared to HD radios with our SIC and user allocation policy. The high SE in conjunction with abundant resources in FR2 band provide multi-Gbps peak data rates, high reliability, and massive connectivity.


I. INTRODUCTION
5 G and beyond is particularly attractive for industrial communications due to its unified wireless interface, guaranteed quality of service, mobility, security, and positioning [1]. Different from traditional human-centric communication networks, industrial Internet of things (IIoT) need to serve multi-type devices for diverse applications, e.g., ultra-reliable low-latency communications (URLLC) devices for control applications, enhanced mobile broadband (eMBB) devices for bandwidth-hungry applications, and massive machinetype communications (mMTC) devices for monitoring applications [2], [3]. In order to cope up with such a heterogeneous environment, various requirements are introduced in 5G new radio (NR) such as ultra-high reliability, low latency, high connection density, high energy and spectral efficiency, and high flexibility [3]. In particular, the URLLC service is the most challenging due to simultaneous requirements on ultrahigh reliability and low latency with limited resources.
To meet the stringent demand of huge capacities and low latency in 5G and beyond IIoT networks, the in-band fullduplex (IBFD) radios and frequency range 2 (FR2) spectrum (≥ 24.250 GHz), i.e., millimeter wave (mmWave), are investigated as promising techniques [4]- [7]. IBFD is a novel paradigm that allows simultaneous transmission and reception in the same frequency band, so it has the potential to enhance the spectrum efficiency and reduce the latency of current time division duplex (TDD) or frequency division duplex (FDD) systems [8]. FR2 provides much more unused The processing latency for SIC, which is a significant part of the end-to-end latency, is minimised with considerable reliability in [14] for URLLC. As for the CCI, it is not as significant as the SI due to nature propagation attenuation and can be mitigated simply through interference alignment [15], resource allocation [16] or beamforming [11], [17].
However, these implementations mainly focus on FR1 band within operational bandwidth below 100 MHz, while lacking analysis of extending to FR2 band with wider bandwidth. Besides, since the private 5G network for IIoT works in a heterogeneous environment, the solutions must be flexible to support a mixture of multi-type devices. In this paper, we propose solutions to solve these challenges under IIoT scenarios. Particularly, a self-interference cancellation (SIC) scheme is proposed to efficiently suppress the significant SI in the analog and digital domain, and a user allocation algorithm is proposed to minimise the CCI. Our solutions are given based on the system model in FR2 band, where large-scale antenna arrays with RF beamforming are utilised to compensate for the high path loss while saving the financial cost and energy consumption. Our contributions are summarised as • We evaluate the performance of a private 5G NR network equipped with IBFD base station that provides simultaneous URLLC and eMBB services based on FR2 channel models. We utilise 5G NR 4× scaled numerology (60 kHz of subcarrier spacing), self-contained sub-frames, and mini-slot for URLLC devices, which could reduce the latency by half while remaining high throughput with the help of abundant resources provided by FR2 band, large-scale antenna array, and IBFD radios. Based on the numerical results of bit-errorrate (BER) and spectral efficiency (SE) and theoretical analysis, the performance of this private 5G network is evaluated in terms of throughput, latency, reliability, and device density. • We adopt large-scale antenna array to compensate for the high path loss in FR2 band and RF beamforming to save the cost and energy through significantly reducing the number of RF chains. Taking advantage of such architecture, we propose to tap the reference signals for RF cancellation from RF chains instead of antennas to reduce the number of RF cancellers, making it practically feasible with large-scale antenna arrays. The effect of the RF beamforming on the SIC with such architecture is firstly analysed in this paper in terms of delay spread. • We explore optical components to construct a multitap RF canceller for a sufficient number of taps and wideband RF signal processing properties at 28 GHz. Compared with existing designs (see [10] and references therein), we considered the processing properties of components for FR2 band and investigated a method to provide sufficient delay lines using normal components instead of elaborate components (e.g., fiber Bragg gratings) to save the cost, which gives a costfriendly efficient RF cancellation scheme for FR2 band scenarios. • We investigate a digital canceller that operates in the frequency domain. It captures the effective channel effects by a single coefficient on each subcarrier. Compared with conventional polynomial cancellers as in [14], such canceller has ultra-low processing latency with the help of self-contained sub-frames but lack the ability to deal with nonlinear distortions. The effects of these transceiver and canceller nonlinear distortions on the digital cancellation are analysed. • The performance of the SIC scheme is analysed and evaluated in terms of cancellation depth, channel estimation accuracy, and overall noise and distortion floor after SIC. This theoretical analysis gives further insights into the SIC under such structure (i.e., large antenna array with RF beamforming). • We propose a user allocation algorithm to minimise the CCI and maximise the IBFD gain for higher spectral efficiency. Compared with existing methods [16], we consider the gains of antenna arrays and support for heterogeneous environment (i.e., multi-type devices with different antenna array sizes and bandwidths), which is more flexible than the existing one and supports antenna arrays. It is analysed that such algorithm can always achieve the optimal allocation policy to minimise the CCI from the perspective of user allocation. The rest of this paper is organised as follows: Section II gives models of a general FR2 full-duplex private 5G network and a transceiver architecture with RF beamforming, followed by FR2 channel models and end-to-end latency analysis. In Section III, the signal processing for self-interference cancellation in the analog and digital domain is proposed. Then, a user allocation algorithm is proposed to minimise the CCI in Section IV. Section V demonstrates and analyses numerical results of our simulations under a typical IIoT scenario. Finally, conclusions are drawn in Section VI.

II. SYSTEM MODEL
Consider a private 5G network for IIoT as Fig. 1, where K BS IBFD enabled 5G NR base stations (gNB) service K DL DL user equipments (UEs) and K UL UL UEs in FR2 band. To compensate for the high path loss in FR2 band, which is always an obstacle to provide reliable communications [4], [9], large-scale antenna array is leveraged to provide effective links by exploiting the beamforming gain to form highly directional narrow beams. In order to make largescale antenna array practically feasible, a novel transceiver architecture is utilised as Fig. 2 shows, where RF beamforming is introduced to connect a small amount of RF chains to the large-scale antenna array [5] A tabular form for the notation used in this paper is given in Appendix A for readers to easily follow this paper.

A. TRANSMITTED SIGNALS
The IBFD base station transmits N Tx sym independent data symbols to DL users and receives N Rx sym independent data symbols from UL users, respectively. We have N Tx sym = N Tx RF N Tx ant and N Rx sym = N Rx RF N Rx ant to allow the fully-digital beamforming being decomposed into the digital beamfoming followed by RF beamforming without penalty [18]. At the BS, the N Tx sym modulated data symbols (either by PSK or QAM) at k th subcarrier s BS [k] are first converted into the time domain by leveraging N FFT -point IFFT followed by addition cyclic prefix. It is then converted into the RF domain by the N Tx RF independent RF chains followed by the RF precoder F BS RF . The transmitted complex symbol from the BS at the k th subcarrier in the discrete frequency-domain is denoted as represents the transmitter distortion caused by RF chains, which can be modelled by a zero mean complex Gaussian distribution as [7] t Lastly, ω BS is the scaling factor used to meet the power constraints such that tr E Similarly, the transmitted complex symbol from the j th UL users at the k th subcarrier in the discrete frequency-domain can be denoted as where , and the transmitter distortion t UL j [k] is also described by the Gaussian model as Equation (2) (we assume identical transmitter distortion factor σ 2 t at the BS and UEs for simplicity).

B. RECEIVED SIGNALS
The received signal by BS g at the k th subcarrier can be described as b, the SI channel matrix at BS g, and the UL channel matrix from UL user j k to BS g, respectively. UL user j k is the user that occupies the k th subcarrier and transmits the signal of interest, and n BS g [k] represents all interference and noise terms except the desired signal. The indexes of RF precoder and combiner are omitted here since it is frequency-flat. There is no intra-user interference since we consider all UEs are orthogonal to each other through appropriate modulations (either by baseband modulation or OFDM). n BS g [k] is the additive white Gaussian noise (AWGN) at BS g that n BS g [k] ∼ CN 0, σ 2 BS I N Rx RF , and n qtz g [k] denotes the quantisation noise due to limited ADC dynamic range, which will be detailed later. r BS g [k] represents the receiver distortions induced by receiver RF chains except the quantisation noise, which can be described by the complex Gaussian model as [7] where y[k] = y[k] − r[k] denotes the received signal without receiver distortion. The received signal by DL user i k at the k th subcarrier is given as where is the DL channel coefficients matrix at the k th subcarrier from BS b to the DL user i k , H DU i k ,j k [k] is the channel coefficients matrix from UL user j k to DL user represents all the interference and noise terms, and r DL i k [k] represents the receiver distortion at the DL user i k , which can also be described by Equation (5). It should be noted that the quantisation noise is not specially described here since the received signals at UEs are usually within the dynamic range of ADCs, so its effect is included in . The intended signal for DL user i k is transmitted by BS b i , i.e., the first term on the right hand side is the signal of interest.

C. QUANTISATION NOISE
denote input signals of ADCs at these RF chains, the quantisation noise can be described by the Gaussian model as [19] n qtz where ρ = π √ 3 2 · 2 −2b if b > 5, for the case b ≤ 5, the value of ρ can be found in Table 1 in [19].

D. FR2 CHANNEL MODEL
Let H(τ ) denote the time-domain channel matrix between the transmit and receive antenna arrays. Each element of H(τ ) at delay τ consists of line of sight (LOS) and non-line of sight (NLOS) components and is given as [20] [H] r,s (τ ) = where r and s represent the r th receive and s th transmit antenna respectively, L is the number of clusters, M n is the number of rays in n th cluster, τ n is the delay of the n th cluster, τ mn is the delay of m th n ray in the n th cluster, and K is the Rician factor. h LOS rs and h NLOS rs,n,mn denote the complex channel gains for LOS and NLOS paths given as h NLOS rs,n,mn λ (er(θ A n,mn ,φ A n,mn ) T dr) · e j 2π λ (er(θ D n,mn ,φ D n,mn ) T ds) where F θ,GCS,r , F φ,GCS,r , F θ,GCS,s , and F φ,GCS,s are the radiation field patterns in the direction of the spherical basis vectors e θ and e φ of the s th transmit antenna and r th receive antenna, respectively. θ A and φ A represent the elevation and azimuth angle of arrival (AoA) for associated LOS path or the m th n NLOS ray in n th cluster respectively, and θ D and φ D represent the elevation and azimuth angle of departure (AoD) for associated LOS path or the m th n NLOS ray in n th cluster respectively. d r and d s are the position vectors of the receive antenna r and transmit antenna s given in the global coordinate system (GCS) respectively. λ denotes the wavelength of the carrier frequency. Specifically, the NLOS component of SI channels is the same as given in Equations (8) and (10), while the complex gain of the LOS component of SI channels is given as [21] h LOS,SI where d rs is the distance between the s th transmit antenna and r th receive antenna.

E. END-TO-END LATENCY
The total end-to-end latency can be described as [3], [22] T total = T ttt + T ppg + T buff + T pcs (12) • T ttt is the time-to-transmit latency.
• T ppg is the propagation latency determined by the signal travel distance. • T buff is the buffering latency associated with receiving the signal at the receiver. • T pcs is the processing latency that the transceiver encodes and decodes the signal and estimates the channel, etc. T pcs can be reduced by self-contained sub-frames and new physical layer design as in [3], while T ppg is determined only by the travel distance and is small. We focus on reducing T ttt and T buff , which depend on the slot length and can be reduced by advanced frame structures inspired by IBFD radios, 5G NR numerology and mini-slot supported by FR2 band.
IBFD radios allow UL eMBB devices and DL URLLC devices to simultaneously use any time slot and subcarrier. So there is no need to reserve time slots for URLLC devices as in TDD systems and double the number of available subcarriers than FDD systems. FR2 band provides enormous frequency resources for signalling, redundancy, and parity to provide ultra-low latency with high reliability. 5G NR introduces multiple types of numerology, i.e., 15 kHz, 30 kHz, 60 kHz, 120 kHz, and 240 kHz of subcarrier spacing, to reduce the symbol duration time [23]. For an instance, expanding the subcarrier spacing from 15 kHz to 60 kHz can reduce the symbol duration time from 72 µs to 18 µs. Utilising FR2 band, we have to reduce the cell radius and densely deploy base stations due to the high path loss. Thus, the channel delay spread will be smaller than FR1 band channels. This indicates that FR2 band can support higher numerology. It should be noted that there can still be a large number of subcarriers with expanded subcarrier spacing to deliver high throughput in FR2 due to the ultra-wide bandwidth provided by FR2 spectrum. To reduce the processing latency, we put all the reference and control signals, e.g., physical data shared channel-demodulation reference signal (PDSCH-DMRS), at the first few symbols of the 14 symbols in a slot, known as VOLUME 4, 2016 self-contained sub-frames. Thus, the PDSCH-DMRS have been decoded and the channel estimation has been done when the DL payload is received, and the receiver can start decoding the DL payload immediately. Besides, mini-slot (e.g., 7 symbols in a slot) is especially introduced to be a remedy of latency reduction for URLLC at the cost of achievable rate reduction due to the fact that URLLC service usually does not require a huge data throughput [3]. With all these technologies, the slot length for URLLC devices can be reduced to 125 µs, i.e., T ttt = 125 µs and T buff ≤ 125 µs, resulting the end-to-end latency T total ≤ 0.5 ms with the propagation and processing latencies, and later simulation results in Section V demonstrate ≥ 99.999% reliability can be achieved with such low latency.

III. SIGNAL PROCESSING FOR FULL-DUPLEX
IBFD introduces significant self-interference, which could be 100 dB higher than the received signal of interest (SoI) due to the proximity of the transmit and receive antenna arrays at the IBFD base station [24]. Thus, it has to be efficiently suppressed, otherwise, the SoI will be swamped and the UL communications will be invalidated [4], [18]. Typically, the significant SI is suppressed through three steps, where antenna isolation and active RF cancellation are essential to prevent the receiver from saturation [8] and digital cancellation processes the residual self-interference (RSI) due to imperfect analog cancellation. In this section, we propose active signal processing methods in the analog and digital domain (i.e., RF and digital cancellation) to efficiently suppress the SI over a wide band with low latency. In contrast, the CCI will experience natural propagation loss and will not exceed the receiver dynamic range. In this section, we propose a user allocation policy to minimise the CCI in the propagation domain, so it can be efficiently managed through appropriate digital beamforming, such as the weighted sum rate beamforming in [7].

A. ANTENNA ISOLATION
There are usually three passive antenna isolation methods, i.e., spatial separation, non-reciprocity of circulators, and antenna polarisations for single-input and single-output (SISO) cases. These basic techniques provide about 10-20 dB of isolation level, while it can be improved to 30 dB with the help of further decoupling network or reflection control circuit [25]. All the three methods can be combined for antenna arrays, but only the spatial separation method can be used multiple times. It should be noted that the spatial separation method is not bandwidth limited, while the decoupling network and the reflection control circuit are bandwidth limited [25]. So, we consider a combination of spatial separation and non-reciprocity of circulators without decoupling networks or reflection control circuits for our design throughout this paper, offering a total of 15 dB of passive cancellation. This can be viewed as additional path loss of the SI channel without loss of generality, i.e., the complex gains of SI channel described as Equation (10) and (11) are reduced by 15 dB.

B. RF CANCELLATION
Typically, there are Stanford architecture and Rice architecture for RF cancellation [26]. The Stanford architecture taps the reference signal at transmit antennas, so that the reference signal contains the transmitter nonlinearity and distortions. It leads the RF canceller to only mimic the linear wireless SI channel. However, there are two limiting factors to extend such architecture to FR2 band: • The first one is the operational bandwidth, which is usually limited by the insertion loss and poor frequency flatness of RF components utilised to construct the canceller [10]. • The second one is the huge number of required cancellers to match the antenna pairs with large-scale antenna array, i.e., N TX ant × N RX ant cancellers are required for the IBFD base station. Such a number is physically prohibitive with large-scale antenna array. To address these issues, we propose a novel RF cancellation scheme, which explores optical components to break the bandwidth limitation due to hardware imperfections and takes advantages of the RF beamforming to reduce the number of required cancellers. Compared with previous studies, this design avoids using auxiliary transmitters and complex digital signal pre-processing as in [27], and can enlarge the operational bandwidth which is difficult in RF domain [28].
We tap the reference signal from each transmitter RF chain and insert the nulling signal, which is generated by an optical domain based canceller as Fig. 3, into associated receiver RF chain instead of TX and RX antennas as Fig. 2 shows. It should be noted that although the hybrid beamforming architecture is commonly used in FR2 band communications, taking advantages of such architecture for feasible RF cancellation is still rare and valuable. By doing this, the number of required cancellers reduces from N Tx ant × N Rx ant to N Tx RF × N Rx RF , which is a significant gain since N Tx RF N Tx ant and N Rx RF N Rx ant , e.g., from 256 × 256 to 4 × 4. However, such operation also changes the characteristics of the SI channel that the canceller needs to mimic. Conventionally, the canceller between a specific TX and RX antennas pair mimics the linear wireless SI channel between the two antennas, which can be described by the tapped delay line (TDL) model. In our design, we have to consider the effects of RF beamforming. Focus on a specific transmitter and receiver RF chains pair, e.g., the u th transmitter RF chain and the v th receiver RF chain, the output RF signal of the u th transmitter RF chain is x u (t), then the v th receiver RF chain receives signal caused by this transmitter RF chain as where N ant,u and N ant,v denote the number of transmit and receive antennas connected to the u th transmitter RF chain and v th receiver RF chain, a i (t) and a j (t) are the complex  coefficient introduced by the time-variant frequency-flat RF precoder and combiner at the i th transmit antenna and j th receive antenna, respectively, and h ij (t) is the wireless channel between the two antennas described by Equation (8) and can be denoted in an alternative way as where α ij (t) and t ij are the channel coefficient and delay of associated path (e.g., α ij,l = 1 K+1 h NLOS rs,n,mn and t ij,l = τ n + τ mn if l = n · m n ), L ij = L · M n . Then, we can rewrite Equation (13) as To suppress the SI from the u th transmitter RF chain at the v th receiver RF chain, we insert a canceller between the two RF chains to generate a nulling signal as . First, we tap the output RF signal x u (t) via a 90 • hybrid coupler with coupling factor α 1 , which equally splits the RF reference signal with a resultant 90 • phase shift between two output ports as so the top two branches represent the I-channel and the bottom two branches represent the Q-channel. Then we equally splits the two signals via a 180 • hybrid coupler with coupling factor α 2 , which introduces 180 • phase shift between two output ports as Then the phase-shifted reference signals are converted into the optical domain through intensity modulation by the dual-parallel Mach-Zehnder modulator (DPMZM). The laser source generates the carrier with frequency f c and amplitude VOLUME 4, 2016 A c such that c(t) = A c · cos(2πf c t). The modulated optical signal can be given as where l MZM is the insertion loss of the DPMZM. We only model the I+ branch since other 3 branches have identical architecture and can be similarly described, e.g., The modulated optical signal will be equally splitted by the splitter, and each output port of the splitter can be described as where l sp is the insertion loss of the splitter. Then these signals are propagated into different-lengths independent fiber associated with VOAs and photo-diodes, which we call as fiber array. These signals will be delayed due to the natural propagation delay and be weighted by the VOA, which can be described as where l fb (m) is the propagation loss and t m is the propagation delay, which are determined by the fiber length of corresponding tap m, l IL = 1 M l VOA l sp l MZM describes the fix hardware insertion loss, and α 0 = α 1 α 2 captures the total coupling factor. Finally, these signals are converted back by photo-diodes through direct detection and combined together to form the output as where R pd is the reponsivity of the photo-diode. This suggests that we get an accumulation of multiple phase-shifted, delayed and weighted versions of the input reference signal x u (t) at the output of each branch. In practice, hardware imperfections will introduce amplitude and phase imbalance to the 4 branches. So we use different subscripts to capture the practical insertion losses and phase shifting of corresponding branches, and the canceller can be described as . As explained in , designing the canceller in the time domain will loss the adaptability to environmental changes, so we convert it to the frequency domain via Fourier transformation as T , and p is the placeholder for associated branch. The target of RF cancellation is to tune the canceller to be as close to the inverse effective SI channel as possible within the band of interest, which can be described as where the constraints come from passive VOAs to minimise the canceller's nonlinearity. Assume the effective SI channel can be well characterised by K s + 1 samples within the band of interest [ω 0 , ω s ] (e.g., can accurately describe the effective SI channel within the band of interest, and the canceller at corresponding frequency components can be denoted as Then, we can derive the optimal solution of the tuneable weights according to the minimum mean-square error (MMSE) criterion as It should be noted that the W * MMSE gives the optimal performance that can be achieved with M taps (i.e., M tuneable variables).

1) Practical Implementation
The fiber length depends on the access delay spread of the effective RF SI channel between specific RF chain pair, e.g., between the v th receiver RF chain and the u th transmitter RF chain. Assume τ NLOS vu,max is the maximum delay of the significant NLOS paths (above the noise floor) and τ LOS vu denotes the delay of the LOS path, then the access delay spread of this channel is τ access vu = τ NLOS vu,max − τ LOS vu and the length of the m th fiber is where c is the light speed. This makes the propagation delays of the M taps uniformly distributed within the delay spread of the effective SI channel, such that τ vu,m = τ LOS vu + τ access vu m−1 M −1 . As for tuning the weights, we can have the matrix L in Equation (27) once the canceller is built, while H eff is usually unviable since the channel estimation happens after the RF cancellation stage. However, if the statistics of the effective SI channel can be explored, this problem can still be solved by the common Wiener solution as in [8] or the gradient descent search algorithm with the residual signal strength indicator as in [29].

2) Canceller Nonlinearity & Noise
In addition to the desired nulling signal, the canceller will also introduce additional noise and nonlinear distortions. The noise consists of the AWGN introduced by laser sources and the shot noise from photo-diodes, while the nonlinearities come form the DPMZM and VOAs. The nonlinearity introduced by the modulation profile can be suppressed to the noise floor by filters and appropriate bias voltages of the DPMZM. These noise and nonlinearities can be described by the complex Gaussian model, so that the SI term in the received signal model (i.e., where σ 2 canc captures the amount of in-band noise and nonlinearities introduced by the canceller.

3) Key Affecting Factors
This canceller does not rely on specific SI channel conditions, although more complex channels call for more taps for efficient performance. The important SI channel parameters associated with RF cancellation are excess delay and root mean square (RMS) delay. The RMS delay determines the coherence bandwidth, i.e., frequency-selectivity, of the SI channel, so affects the number of required taps. The excess delay determines the delays of canceller's taps. The excess delay is the delay difference between the LOS path and the last significant NLOS path, while the RMS delay τ RM S is the second moment of the power delay profile of the SI channel, which can be described as where χ ij,l = |a j α ij,l a i | 2 captures the power profile of associated rays and τ 0 represents the mean delay of the SI channel that can be described as The RF beamformer reduces the number of paths between any two nodes since it leads the transmitted beam to a specific direction, but it will increase the RMS delay of the SI channel. This suggests that the coherence bandwidth of the effective SI channel is smaller than the wireless SI channel (i.e., without RF beamforming effects), so more number of taps are needed to well characterise the effective SI channel within a specific band. It is demonstrated that the insertion loss is the obstacle to create sufficient taps [8]. The proposed design solves this problem from two aspects: • Optical components have much smaller insertion and propagation losses than RF components; • Improving the power of optical carriers can compensate for the insertion loss as Equation (22) suggests. Thus, it can provide much more taps than conventional RF domain based cancellers (e.g., up to 100 taps in theory).
Remark: It should be noted that the number of taps is mostly proportional to the operational bandwidth and delay spread of the SI channel for specific cancellation depths [8], but more taps created in the canceller results in more VOAs, photo-diodes, and fibers, which increases the area and financial cost of RF cancellers. This suggests that a trade-off between the implementation cost and the cancellation depth must be made; otherwise, we would like to create as many taps as possible to minimise the SI effects at the IBFD node. Furthermore, the noise and nonlinearities of cancellers can be reduced by more elaborate components, but also results in higher financial cost.

4) Performance Analysis
For a specific subcarrier, the RF cancellation performance can be described by the average cancellation depth of all N Rx RF × N Tx RF cancellers as

C. DIGITAL CANCELLATION
The digital cancellation also follows the subtractive idea that a nulling signal is generated with the knowledge of the transmit SI signal and the estimated channel state information (CSI) from pilot signals. Different from previous studies which operate in the time domain [12], we operate in the frequency domain to reduce the processing latency in conjunction with the self-contained sub-frames as introduced above. The physical data shared channel-demodulation reference signal (PDSCH-DMRS) is used as pilot signal at specified subcarrier index in the first N plt t OFDM symbols in a slot. After the analog SIC, the received SI can be digitised with trivial quantisation noise. The frequency-domain digital residual self-interference (RSI) signal at the pilot subcarrier k p is given as: where represents the effective RSI channel coefficients at the k th p subcarrier that includes the effects of RF precoder, RF combiner, and RF cancellers at the k th p subcarrier, and n BS,g RSI [k p ] represents all residual terms except the received SI. Interference from other nodes are not present here since an interference-free period is usually provided by the MAC protocol via carrier sense to achieve accurate channel estimation. The estimated channel coefficients at pilot subcarrier k p is given as: Then, the RSI can be subtracted from the received signal and the intended UL payload can be decoded with only selfinterference effects come from imperfect channel estimation.

1) Complexity
The effective channel coefficients are estimated through the PDSCH-DMRS pilot signal at the initial N plt t symbols within a slot. Assume the pilot signal is inserted into N plt f subcarriers at the first symbols, the total coefficients need to be estimated, i.e., computational complexity, is given as . This indicates the complexity of such digital canceller is not affected by the antenna array size as [12] does, so it is suitable for large antenna arrays.

2) Performance Analysis
The estimated and actual effective RSI channels at subcarrier k can be related as where canc +σ 2 BS PBS as given in Appendix C. The digital SIC depth is given as which indicates the hybrid architecture, i.e., the number of transmitter RF chains and number of subarrays at the receiver, will affect the digital cancellation performance. Besides, too deep RF cancellation (i.e., η RF g is large) will also degrade the digital cancellation performance. The degradation comes from the fact that the RF cancellation decreases the SNR of the SI signal for channel estimation in digital cancellation.
Remark: The advantage of our proposed frequencydomain based method is the significantly-reduced processing time to reduce the end-to-end latency, but the performance will be degraded if the nonlinearities of the transceiver or cancellers is large as Equation (38) suggests. In contrast, there are polynomial cancellers [12] and neural networkbased cancellers [13] that can deal with these nonlinear distortions and achieve deeper cancellation with larger processing latency. This means we have to make a trade-off between the cancellation depth and the latency and then decide which kind of digital canceller to use. Besides, Equation (38) also indicates that more RF chains and subarrays help with minimising SI effects, while results in higher energy and financial cost. So we still need to make trade-offs between the cost and performance.

1) Noise floor
We can describe the noise floor (include AWGN, transceiver distortions, canceller's noise and nonlinearities, and residual self-interference after digital cancellation) as

2) Achievable UL Rate
After all stages of SIC applied, the received signal by BS g at the k th subcarrier can be described as which yields the achievable rate of intended UL user j k as where Θ j [k] and Ψ j [k] are the signal power and interferenceplus-noise power at subcarrier k given as Equations (31) and (32), and K j is the number of indexes of subcarriers occupied by this user.

IV. SIGNAL PROCESSING FOR REDUCED CCI
IBFD radios also make DL users be interfered by UL users which have over-lapping frequency bands, which is known as co-channel interference. The CCI is not as strong as the SI to invalidate the communication due to the nature propagation loss, but will still degrade the DL throughput. To combat the CCI and obtain the maximum IBFD gain, we propose a user allocation algorithm through a game-theoretic approach. Assume the whole communication bandwidth is separated into T DL and T UL orthogonal sub-bands for DL and UL users respectively as Fig. 4, where the sub-band can have different bandwidths to provide different performance profiles for a variety of user needs in IIoT networks. Let X = x DL , x UL denote user allocation policy which is the collections of all DL and UL indicators. x DL and x UL have dimension of if DL user k d is allocated into the t th d DL sub-band sub DL t , and 0 otherwise. Similarly, [x UL ] tu,ku = 1 if UL user k u is allocated into the t th u UL sub-band sub UL t , and 0 otherwise. There will be co-channel interference as long as the DL sub-bands and UL sub-bands overlap. The essence of user allocation is to allocate the DL and UL user pairs that may cause significant CCI to orthogonal sub-bands while leave the user pairs with small CCI in the overlapping sub-bands. According to Equations (4) and (6), the achievable sum rate of DL user i and UL user j served by BS g can be described as where h DL i,g , h UL g,j , h DU i,j , and h BS g,b represent the path losses form BS g to DL user i, form UL user j to BS g, from UL user j to DL user i, and between BS b and BS g, respectively. P DL i , P UL j , and P BS b represent the transmit power for DL user i, transmit power by UL user j, and total transmit power at BS b respectively. P RSI,g is the RSI power after SIC at BS g to capture our SIC effects. P DL n,i and P BS n,g are AWGN power at DL user i and BS g. K ol ji is the number of UL users which have overlapping with DL user i. η DL i , η UL j , and η ol i,ji capture the ratio of the sub-band of DL user i in the whole bandwidth, the ratio of the sub-band of UL user j in the whole bandwidth, and the ratio of the overlapping portion of sub-bands of DL user i and UL user j i in the sub-band of DL user i. The optimal user allocation policy is achieved if the sum rate of the network is maximised, which can be cast as where the two constraints force each UE to be allocated to only one sub-band. This problem can be solved by a game theoretic approach [16], where the sum utility of all UEs in this network is given as The sum rate is used as the sum utility instead of the SINR to capture the gain of antenna arrays. The user allocation game is a characteristic formation game with non-transferable utility, which can be solved based on a preference relation as where x ≺ x | t←i means that UE i is preferred to be allocated into sub-band t instead of its current sub-band. The moving operation will be done if the sum utility increases after UE i moves to sub-band t. We consider each sub-band for UL users will only be occupied by a single user to maximise its capacity since UL eMBB devices require high data throughput. Hence, the UL users can be randomly allocated to these sub-bands at first. Then, each DL users compares the preference with being allocated into all other sub-bands, and executes the moving operation if the condition in Equation (41) is satisfied. It should be noted that the indicator of subband only determines the order of these sub-bands, while its bandwidth varies with associated users. Performing the compare-and-moving operation for all DL users, the optimal user allocation policyS is obtained. The user allocation algorithm is illustrated as Algorithm 1.

Remark:
The user allocation policy mainly depends on the channel strengths, which are strongly dependent on user allocations, so it will be affected by the mobility of users, especially when users move extremely fast. For IIoT scenarios, it is reasonable to assume that users are mostly static or move very slowly that their locations do not change rapidly. Otherwise, the path losses h † * , * must be time-variant to include the effects of user mobbility, and some statistical knowledge will be required to calculate the mean sum rate of users.

A. COMPLEXITY
The algorithm is based on the compare-and-moving operations of each DL UE. There is one time of computations when each DL UE compares the sum utility and determines whether the user is moving. In order to obtain the optimal policy, each of the all K DL DL users should move to all other T DL − 1 sub-bands and executes the compare-and-moving operation, which results in a total of K DL (T DL − 1) computation times in one cycle. Given a number of cycle times C, the computational complexity of the proposed algorithm is O UA (CK DL (T DL − 1)). DL UE i moves into all other sub-band except its current sub-band. 6: Record the new allocation policy after the UE moves as X . 7: Calculate the sum utilities under the two policy U (X ) and U (X ).

8:
Compare the preference of the i th DL UE based on the preference relation in Equation (41). 9: if the preference relation is satisfied then 10: Update the current policy as X ← X . Let X 0 denote the initial user allocation policy, and X f is the final policy. During the game, the policy is changed as follows: Algorithm 1 indicates that the user allocation policy X will only be changed if the sum utility increases, which suggests that the sum utility is strictly increased with the policy changes in sequence (42) such that As the number of user allocation policies is finite due to the finite number of sub-bands and UEs, the policy in sequence (42) is guaranteed to converge to the local optimal policy.

V. SIMULATION RESULTS
Consider a typical industrial scenario with 4 eMBB devices as UL users, 8 URLLC devices as DL users, and an IBFD enabled 5G NR access point (AP) as shown in Fig. 5. The simulation parameters are taken from 5G NR [30] as shown in Table. 1.

A. LATENCY REDUCTION FOR EMBB DEVICES
In this section, we will do a simple calculation of transmission time (this does not include propagation time, processing time at 5G NR access point, etc.) of eMBB payload shows the advantage of IBFD in terms of reducing latency. For HD systems, the data transmission and reception in FR2 band is based on TDD. It means some part of the slot is used for UL users and the rest is used for DL users. The partition of resources is based on the amount of payload and priority of services. In a typical industry scenario, where sensors and robotics arms are very critical in terms of reliability and latency which act as DL users (URLLC devices), on the other hand, the UL users are CCTV cameras which have a huge amount of data to be transmitted to access point (eMBB devices). Since the payload of URLLC devices is very critical, some part in each slot is reserved even if there is no payload for any slot. These reserved resources tends to increase the latency of eMBB devices. The IBFD enabled 5G NR access point reduces the latency of eMBB devices by simultaneously transmit and receive data to URLLC and from eMBB, respectively. In 5G NR, a slot is consists of 14 OFDM symbols of duration 0.25ms for 60 kHz subcarrier spacing and a mini-slot concept for URLLC transmission which consists of 2, 4, and 7 OFDM symbols. Let us assume that eMBB has 7.68×10 6 samples which is to be transmitted to 5G NR access point with 60 kHz subcarrier spacing, 1920 data subcarriers for 100 MHz bandwidth. Table 2 shows the comparison of IBFD and HD in terms of the number of slots and transmission time of 7.68×10 6 samples with 1920 data subcarriers which require 4000 OFDM symbols. In Table 2, HD (12) represents 12 OFDM symbol (out of which 1 OFDM symbol is used for PDSCH-DMRS) is used by eMBB and 2 OFDM symbol is used by URLLC. Similarly, HD (10) and HD (7) represents 10 and 7 OFDM symbols are used by eMBB, respectively. While IBFD used the whole slot (14 OFDM symbols) for eMBB payload. As observed from Table  2, IBFD reduces the latency (by 54%) by using fewer slots to deliver the same amount of symbols due to the significantlyimproved spectral efficiency and always-available time slots.

B. SELF-INTERFERENCE CANCELLATION
Consider a 12-bits ADC at each RF chain, which provides about 67 dB of dynamic range, assuming 10 dB of PAPR of the input signal. The thermal noise density is -174 dBm/Hz,   and the noise figure of the access point is 13 dB, which yields a total of -75 dBm noise power with 400 MHz bandwidth. This suggests that the received SI power at the access point has to be suppressed to be at or below -8 dBm to prevent ADC saturation. Assume an access point transmit power of 24 dBm and 15 dB of antenna isolation, 17 dB of RF cancellation is required to be provided by each canceller in theory. Table  3 shows the required number of constructed delay lines, i.e., taps, to achieve near 20 dB of RF cancellation amount for various bandwidths in FR2 band. The hardware impairments are included in the simulation, where the parameters are taken from some off-the-shelf products available at the "Thorlabs". The VOAs have the tuneable range of 30 dB and a tuning step of 0.1 dB. It is not comprehensive to analyse the effects of RF beamformers on SIC and the relationship between RF and digital cancellation via the channel coefficients estimation error or solely digital cancellation depth, so we demonstrate the total cancellation (antenna isolation, RF and digital cancellation) depth and overall noise floor after SIC in Fig. 6. It illustrates that more subarrays at the receiver may degrade the total cancellation depth, but such degradation is only obvious when the RF cancellation depth is too large (i.e., 90 dB). In contrast, the number of RF chains at the transmitter is more influential on the total cancellation depth, especially when the transceiver distortion is significant. More RF chains at the transmitter can improve the total cancellation performance. We can also see that total cancellation depth does not benefit from further RF cancellation as long as the transceiver distortion is not too large (≤ 50 dB). Although we have concluded that too deep RF cancellation will degrade the digital cancellation performance, it does not degrade the total cancellation performance. From the perspective of overall residual noise, more subarrays at receiver and more RF chains at transmitter will be preferred as they can reduce the overall noise floor at access points, so provide a better quality of eMBB services. It also illustrates the importance of sufficient RF cancellation. With 0 dB of RF cancellation, even a total of 80 dB of SIC (contributed by about 65 dB of digital cancellation and 15 dB of antenna isolation) can be achieved, there will be about -40 dBm of residual noise left due to the significant quantisation noise. It should also be noted that at least 30 dB of RF cancellation is required to achieve desired overall SIC (i.e., the total noise floor after SIC is close to the receiver noise floor), while our previous theoretical analysis shows 20 dB of RF cancellation is sufficient. This difference comes from the fact the digital cancellation is not perfect and suffers from channel estimation inaccuracy, which will also be affected by the quantisation noise. Therefore, an 80-taps canceller is utilised to achieve about 30 dB of RF cancellation for later simulations.

C. USER ALLOCATION
We assume all UEs and the AP are equipped with an identical number of transmit and receive antennas, and the number of antennas at 5G NR access point, eMBB devices and URLCC devices are 256, 16 and 8, respectively. The access point transmits signals with a total power of 24 dBm averagely allocated to the 8 DL users, and the transmit power at the UL users is 23 dBm. The whole bandwidth is equally divided into 4 orthogonal sub-bands for both DL and UL users. The path loss model is taken from [31]. After performing the proposed user allocation algorithm, the UEs are allocated to sub-bands as Table 4 shows. It actually allocated the UL users and DL users farthest away from this UL user to the identical subband in this simple case. Fig. 7 shows the sum rate variation of this network during the user allocation algorithm with three different random initial user allocation policies, which proves the convergence behaviour. Different initial policies may result in different policy changing sequences but will converge to the same final optimal policy.

D. BER AND SE EVALUATION
In this section, we evaluate the system level performance of this network in terms of average BER and SE through practical simulations. It should be noted that the performance will be similar in the 4 sub-bands since they have identical configurations, so the performance for URLCC devices can be evaluated by the pair on a single sub-band, e.g., pair 1 (DL users 1 and 2) on sub-band 1. Antennas at 5G NR access points are divided into 4 subarrays, and each subarray has an equal number (64) of non-overlap antenna elements   Fig. 8(a) shows the average BER vs SNR of pair 1 of URLCC devices with and without interference. The interference to the pair of URLCC devices is the CCI from corresponding eMBB devices. Only RF precoding and combining are used, and their weights are pre-calculated according to their known coordinates. It is observed from the figure that there is error floor in BER in the presence of interference, i.e., there is no significant difference for scenarios with and without CCI when SNR< 12 dB. The reason is that the CCI has been mitigated by the user allocation policy and highly directional beams due to RF beamforming, so the CCI is below the receiver noise floor when SNR is low (i.e., transmit power is small). It shows that ≥ 99.99999% reliability can be achieved with SNR ≥ 16 dB with the minimised CCI in our network, while about 20 dB of SNR can be achieved as long as the URLLC devices are within 50 m of the access point. Fig. 8(b) shows the SE vs SNR of pair 1 of URLCC devices with and without interference. The achievable SE of the HD radios is half of the blue curve (without interference), while the red curve (with interference) is the achievable SE of the IBFD radios with the optimal user allocation policy and RF beamformers (i.e., mitigated CCI). With SNR > 10 dB (> 45 bps/Hz SE), 56 kHz bandwidth is sufficient to deliver 2.5 Mbps of throughput, while 103 kHz is needed for HD radios. This indicates that the IBFD can almost double the connection density for specific throughput. The interference can be further mitigated by transmitting a pencil beam to the desired user using more number of antennas, digital beamforming as in [7] and [11], or advanced signal processing such as interference alignment in [15], thus, further improve the quality of URLLC service. Fig. 9 shows the average BER vs SNR of pair 1 of eMBB devices with various quantisation and modulation conditions in the presence of all noise and distortions (i.e., AWGN, transceiver distortion, canceller distortions and RSI), where the x-axis of Fig. 9(a) and Fig. 9(c) means the RSI after RF cancellation is x dB higher than the received SoI. Fig. 9(b) and Fig. 9(d) are derived with 14 dB and 20 dB of SNR respectively, and Fig. 9(b) and Fig. 9(d) are derived with received SI 35 dB higher than the received SoI. Fig. 9(a) and Fig. 9(b) show results for QPSK modulation, while Fig. 9(c) and Fig. 9(d) show results for 16QAM modulation. It can be seen that high quantisation resolution (more effective bits of ADCs) is essential to deliver highly reliable services if the RF cancellation is not deep enough (e.g., the RSI is 30 dB higher than the received signal of interest due to insufficient RF cancellation). Typically, 20 dB of RF cancellation will be required to eliminate the effects of dynamic range of ADCs (12 bits) for QPSK, and this value increases to 30 dB for 16-QAM. Also, this value increases with decreasing number of effect bits of ADCs. ≥ 99.9999% reliability can be achieved with SNR ≥ 13 dB for QPSK, and SNR ≥ 20 dB for 16-QAM. Fig. 10 shows the SE vs SNR of eMBB devices in the presence of all noise and distortions with 12-bits ADCs and RSI 35 dB higher than the received SoI. It demonstrates that 2.5 Gbps data rate can be achieved with 400 MHz communication bandwidth even with SNR = 0 dB for eMBB devices due to the enormous resources provided by the FR2 band, IBFD radios, and large antenna arrays. Furthermore, the effects of the limited dynamic range of ADCs on the SE is not as significant as on the BER that it is almost invisible at low SNR. This suggests that too deep RF cancellation is not extremely critical for eMBB service, which does not have stringent requirements to the reliability. Besides, Fig.  8(b) and Fig. 10 in conjunction with the reduction of 4 dB SNR of UL signals indicate that IBFD radios achieve about 1.92 times SE of HD radios with our SIC scheme and user allocation policy.

VI. CONCLUSION
In this paper, we proposed signal processing techniques to reduce the SI and CCI for full-duplex private 5G networks 23    in FR2 band and evaluated its performance in terms of throughput, latency, reliability, and device density under a typical industrial scenario. Large antenna array is essential to compensate for the large path loss in FR2 band, and RF beamforming is applied to save the cost. RF cancellation also benefited from the RF beamforming to reduce the number of cancellers, but each canceller will need more taps to mimic the effective SI channel, whose RMS delay spread is enlarged due to RF beamforming. For digital cancellation, its performance is affected by the number of transmitter RF chains, the number of subarrays at receiver, transceiver distortions, and RF cancellation. More RF chains at transmitter, more subarrays at receiver, and deeper RF cancellation are always wanted to reduce the overall noise induced by the SI. However, it hardly has more benefits from more than 30 dB of RF cancellation when transceiver distortion is not too large. On the other hand, the CCI is efficiently mitigated through the user allocation policy and highly direction beams formed by RF beamformers, providing highly reliable URLLC services. Such efficient IBFD radios provide the private 5G network with 1.92 times throughput and almost doubled device density compared to HD radios and reduces VOLUME 4, 2016 latency of UL eMBB devices by half. Utilising 4× scaled numerology (60 kHz of subcarrier spacing), mini-slot (7 symbols in a slot), and self-contained sub-frames in 5G NR standard, we theoretically analyse that the latency of DL URLLC devices can be reduced to be within 0.5 ms and simulation results demonstrate its reliability to be ≥ 99.99999%.
Numerical results also show that multi-Gbps peak data rates can be achieved by eMBB devices. However, these results are derived with theoretical models and hypothetical values of some parameters while lacking the practical hardware impairments effects. The future direction of this work should be implementing the SIC scheme in practice and evaluating the performance with practical hardware impairments and adapting 3GPP channel models under specific scenarios (e.g., urban-micro (UMi) or indoor hotspot (InH)). To sum up, our proposed SIC and user allocation techniques can enable IBFD private 5G NR standard Networks in FR2 band for heterogeneous IIoT environment, which supports massive connectivity, enhanced ultra-reliable low latency communications, and multi-Gbps data rates for eMBB and its practical performance is supposed to be evaluated in future. .

APPENDIX A NOTATION
This appendix gives a tabular form for the most essential notations in this paper as Table 5.

APPENDIX B RF BEAMFORMER PROPERTIES
The RF beamformers are implemented via phase shifters in practice, which only adjust the phase of the input signal, so each non-zero element of the RF beamformers can be described as e jθ , where θ ∼ U (0, 2π). Assume f m and f n are two non-zero elements of the RF precoder matrix F RF , then we have E {f m f * n } = f m f * n = 1 if m = n. For the case that m = n, we have E {f m f * n } = E e jθm e −jθn = E e j(θm−θn) , where the probability density function of x = θ m − θ n is given as  Symbol Description a i complex coefficient induced by the RF beamformer at the i th antenna α ij,l attenuation of the l th path between the i th receive antenna and the j th transmit antenna b number of effective bits of ADCs drs distance between the s th transmit antenna and r th receive antenna D RF ij,g,k RF SIC depth at the k th subcarrier of the SI channel between the j th transmit antenna to the i th receive antenna at the g th BS D dig g,k digital SIC depth at the k th subcarrier of the SI channel at the g th BS K Rician factor