Experimental Demonstration of Interference Mitigation Using Ultra-Wideband Spreading

Spectrum scarcity for wireless communication and data transfers has prompted interest to analyze interference among wireless links. As more bandwidth is utilized for communication links, there is a growing need to mitigate interference. By exploiting code division multiplexing (CDM) across an ultra-wideband (UWB) spectrum, it is possible to combat dynamic interference scenarios, including spot, sweep, barrage, or base interference. With this in mind, this paper presents a more generalized theoretical analysis of bit error rates (BER) in presence of dynamic interference scenarios. The presented approach is validated using an ultra-wideband secure communication link over a large contiguous 1.3 GHz bandwidth with direct digital conversion. To our knowledge, this is the first-ever validation for such UWB channel. As part of our assessment, this UWB system uses direct RF sampling of the received and transmitted signals. Overall, for the first time, code spreading across a 1.3 GHz band demonstrated up to 1000-fold interference mitigation. This new capability was evaluated experimentally using a custom wireless BER test bench.


I. INTRODUCTION
The growth of wireless applications and the associated overcrowded spectrum lead to inevitable cross-link interference. Concurrently, there is a significant challenge in accessing large contiguous bandwidths. As a result, wireless communication can be vulnerable to dynamic spectrum allocation and inter-modulation issues, including signal fratricide and malicious interference. Therefore, there is a strong interest in addressing the effect of these dynamic interference scenarios analytically and experimentally across large bandwidths. To achieve interference mitigation across ultra wideband (UWB) spectrum, code division multiplexing (CDM) can be employed to spread the signal and turn it into a pseudo-noise (PN) code. Most importantly, this approach provides processing gain to push the actual signal below or close to the noise floor. This assures a low probability of interception and establishes a secure communication link. In this paper, we present a unique hardware demonstration of interference mitigation via signal spreading across 1. 3 GHz. It will be demonstrated that our approach gives about 30 dB of interference immunity.
Indeed, to achieve strong interference mitigation, it is important to consider the presence of dynamic interference scenarios that may be intentional or unintentional. In this paper, we consider these scenarios analytically and experimentally to evaluate system performance.
Although interference mitigation approaches across wide bandwidths have been considered, limited hardware demonstration exists using CDM. Also, no formulation for estimating the analytical bit error rate (BER) exists for comparing dynamic interference scenarios used for our study. Past approaches have employed time-hopping algorithms to bypass the frequency location of the interferer [1]. However, these are limited due to a need for multiple filters and ADCs. Another approach to addressing interference is to use chirp tones and modify the bandwidth of the transmitted pulse [2]. Though this latter approach provides a few dB of BER gain, it requires apriori knowledge of the interferer, not a likely scenario.
Notably, bit error rate expressions for UWB links were reported in [3], but they did not include interference effect.  Also, in [4], BER evaluations included narrow band or partial band interference as a gaussian noise. Of course, in practice, interference can be intentional or unintentional and can be in any form, including spot, sweep, base, or barrage (see Fig. 1). Such dynamic high-power interference is not random and can not be modeled as gaussian noise. A relevant BER study in [5] relates to interference from co-existing wifi signal acting as an interferer. But further, this investigation did not include the effect of unpredictable high-power interference that can be dynamic in nature. Although past BER studies did consider static interference, hardware demonstration comparison of dynamic interference scenarios across UWB links has not been reported.
In terms of interference mitigation, UWB spreading was demonstrated to suppress interference by exploiting hybrid F/CDM in a SDR platform [6]. But this approach focused on a specific scenario of stationary tone interference to demonstrate the interference margin [7] without having any analytical derivation. Notably, several papers have investigated the effects of single-tone and multi-tone interference via simulations [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19]. Statistical models and approaches were also used in these studies. However, as yet, there is no unified process for calculating the BER of an UWB-CDM link in presence of dynamic interference scenarios. Furthermore, to the best of our knowledge, no hardware demonstrations across a large contiguous bandwidth have been published. In this paper, we study dynamic interference scenarios, including dation measurements. The presented interference mitigation associated with an analytical assessment of bit error rates and measurements is unique and can be used for practical communication links as well.

II. DIRECT RF SAMPLING TRANSCEIVER
Direct RF sampling has become a potential candidate for next-generation radio communication due to its simplified topology for reconfiguration [21]. This approach is also known as a direct digital conversion and can be used for accurate measurements and operations across commercial/defense applications. Notably, state-of-the-art wideband high-end digitizers can directly acquire RF signals and down-convert them to post-process this RF wideband signal through a Vector Signal Analyzer (VSA). To evaluate dynamic interference scenarios across UWB links and estimate BER, we will assume this type of receiver in a software radio platform. Fig. 2 depicts direct RF sampling in comparison to a typical heterodyne receiver.
To better understand the features of direct sampling architecture over the heterodyne receiver, following [22], we have analyzed the noise figure of both architectures. We consider two ADCs with the same no of bits, sampling at the rate of 2.6 GSPS and 10.26 GSPS used in heterodyne and direct sampling receivers, respectively. To compare the effective noise figure of the ADCs, ignoring other components gives us 3 dB SNR degradation in a direct sampling receiver for a 1.3 GHz baseband signal (see Fig. 2). However, additional impairments and noise due to other associate components in heterodyne receivers can worsen the receiver noise floor. Noise due to additional components placed before ADCs can be comparable with the following equations (1) and, In the above, NF ht and NF ds refer to the equivalent noise figure (NF ) at the receiver end before ADCs for heterodyne and direct sampling architecture, respectively. NF ht in (1) has been calculated based on the cascaded NF and gain of the components, 1 to 5, used in heterodyne architecture (see Fig. 2). From (1), it can be seen that the overall noise figure of the heterodyne receiver depends on all the components placed before the ADC. Following this, it is clear that the performance of the heterodyne receiver relies on the precise selection of multiple components, which is not favorable in terms of cost, power budget, and complexity. In practice, it is more challenging to select the proper and optimal COTs components in the heterodyne receiver to achieve equivalent SNR compared to direct sampling architecture. On the contrary, the direct sampling receiver has a more simplified topology. Refer to Fig. 2 and (2), only a single component named automatic gain control (AGC) amplifier determines the performance of the direct sampling receiver. Due to this reason, the direct sampling receiver becomes more practical than the typical heterodyne receiver, particularly while we are focusing more on ultrawideband GHz scale communication. Previously direct sampling receivers were treated as power-hungry components. But the theoretical comparison between direct sampling and heterodyne receiver [22] shows that both architectures can exhibit comparable power dissipation, particularly when we need to digitize ultra-wideband signal in the lower band. In addition, maintaining dynamic range is more challenging to prevent converter saturation in a heterodyne receiver due to the dependency on multiple components. Consequently, we have chosen direct sampling architecture for the simplified architecture to demonstrate interference mitigation capabilities across ultrawideband.
Additional challenges associate with typical heterodyne transceivers consist of analog frequency-dependent nonlinear components. These may be prone to spurious signals and image components generated from the local oscillator (LO). Notably, the wider the bandwidth, the greater the severity of this issue. Also, it becomes increasingly challenging to deal with at higher frequencies. On the contrary, direct RF sampling avoids analog LO and reduces the challenges raised by LO synchronization issues. Still, the challenge of code synchronization must be addressed. This requires adaptive equalization to successfully decode the received signal. Direct RF sampling employs RF ADCs with field-programmable gate array (FPGA) processing units. This architecture includes interleaved high-speed multiple ADCs, equalizers, numerically controlled oscillator (NCO) with quadrature mixture, low pass filters, decimators, and I/Q memory (see Fig. 2). The employed wideband digital conversion used ADC 6000 series digitizers from Guzik Technologies with digital signal processing (DSP) on FPGAs. This approach is time and memory efficient. Notably, a digital equalizer and a complex baseband I/Q mixer are used to process the desired signal into the I/Q memory through a decimator and following a low pass filter. A Keysight VSA 89600 was used to characterize the data from the I/Q memory. It is important to note that the digital equalizer plays an important role in compensating for misalignment due to the interleaved ADCs used in high-speed digitizers. This results in increased spurious-free dynamic range (SFDR), required for reducing the need for baseband data processing.
To evaluate receiver performance in presence of interference, it is necessary to distinguish the interference from device-generated spurious signals. Consequently, the original message signal, spread signal, and interference should be bounded by ADC's spur-free dynamic range (see Fig. 3). Concurrently, high sampling rates are important for accurate decoding. As noted earlier, our hardware setup employs a state-of-the-art Guzik digitizer capable of sampling at a rate of 20 GSPS. The existing setup limits our BER up to 10 −6 . As expected after direct sampling, the digitized baseband signal is subjected to de-spreading and matched filtering. ADC saturation also restricts the interference power level in the hardware demonstration. Consequently, we set the interference-tosignal power ratio (I/S) up to only 10 dB for un-coded signals, whereas for coded spread signals, the I/S is around 30 dB. Fig. 3 shows coded and un-coded power spectrum plots with interference.

III. BER ANALYTICAL EXPRESSION
As usual, to compute the BER in an UWB communication link, we will need to evaluate the probability of error (P e ) under different interference scenarios. These scenarios may include a) spot interference, b) sweep interference, c) barrage interference, and d) base interference. The corresponding error probabilities will be denoted as P e_spt , P e_sw p , P e_brg and P e_bs , respectively. Following the signal-space concept in [23], the bit error rate for higher modulation order (MPSK/MQAM) can be calculated over the additive white Gaussian noise channel. In wireless communication, higher-order modulation delivers more data rate but distributes the same energy within more bits. Hence, this higher-order modulation requires more signal-to-noise ratio (SNR) to recover data at the receiver end. On the contrary, BPSK is the most robust modulation scheme as it accepts the highest level of noise before distorting the desired signal at the receiver end. Consequently, we choose BPSK modulated signal as our desired transmitted data to evaluate bit error rate performance, including the effect of different interference scenarios. A well-established error probability expression for BPSK modulation in the presence of Gaussian noise is given by [24] In the above, Q = tail distribution function, E = bit energy and N 0 = noise power density. An issue with the above expression is high-power interference can not be treated as noise. Therefore we will have a different expression for the case of power interference. In our paper, we extend typical bit error rate expression in the presence of high-power different dynamic interference scenarios. Instead of expressing BER in terms of signal-to-noise ratio per bit (E /N 0 ), in addition, we include interference contribution and express BER expression in terms of SINR. Our objective is to quantify the effect of dynamic interference scenarios and evaluate the resilience of wireless communications in terms of bit error rate. This SINR includes a typical signal-to-noise ratio with an additional interference contribution. Furthermore, we model dynamic interference scenarios and compare the effects. For our analysis, we consider the received signal as In this, s(t ) = desirable signal, i(t ) = high power interference and n(t ) = noise. Later we will introduce different suffixes to i(t ) that correspond to the specific interference scenarios. To estimate the error probability, we proceed to calculate the integrator output at the receiver end. This output is the integral of the received signal across a specific bandwidth. A deterministic relationship exists between the bit error rate and the probability density function (PDF) of this integrator output [25]. After calculating the PDF of the integrator output, the expression for error probability will be in the following form Where α refers to interference contribution. This aforementioned error probability equation is analogous to typical error probability expression but has an additional interference contribution term α. Our challenge is to evaluate this interference contribution considering all interference scenarios. However, our derivation gives two generic expressions. One is for a sweep, and another is for spot, barrage, and base. In both expressions, we quantify the effect of interference in terms of BER. It is important to note that, for deriving a bit error rate in the presence of dynamic interference scenarios, we are considering a typical BPSK modulated data as our desired signal for simplicity. We can extend this expression for other higher-order modulation schemes following [23], but this higher-order modulation costs more SNR to achieve a specific BER compared to BPSK.
To begin with, we will first consider spot interference. This refers to a single-tone stationary interference at a particular frequency. Barrage interference will be treated as a summation of multiple stationary tones. On the contrary, base interference occupies multiple tones, which are successive across a set of bandwidth ranges. The signal for the interference can be expressed as where the subscript i refers to the i-th interference. Also, ω i = 2π f i center frequency, θ i = incidence angle, and I i = incident interference power. In addition to the above parameters, k = number of interference tones signals. As an example, k = 1 implies spot interference and i(t ) is denoted as i(t ) = i spt (t ); k > 1 implies barrage interference and i(t ) = i brg (t ). For base interference i(t ) = i bs (t ) with k >> 1. Notably, sweep interference can be expressed as [26] i sw In the above, δω esi refers to the sweeping bandwidth and defines the difference between the start frequency, ω si , and the end frequency, ω ei . Notably, these interferences can occur across a time span of T sw pi . The derivations of the associated error probability for each interference scenario are given in the Appendix.

IV. BER UNDER SPOT, BARRAGE, AND BASE INTERFERENCE
From (6), we can write that spot, barrage, and base interference signals can be expressed as We will also assume a CDM transmit carrier signal operating at frequency ω c , given by In this, P(t ) denotes the PN spread sequence, and b(t ) represents data bits of the BPSK signal. Assumed, the received signal r(t ) passes through the integrator to generate signal g(T ).This integrator output will have a symbol time length, T , and its BER will be a function of the interference characteristics. Specifically, g(T ) is given by In the above, g m (T ) and g i (T ) refer to the message and interference contributions, respectively. They are evaluated in the Appendix. Also, as usual, N (T ) denotes the Gaussian channel noise. To estimate the probability of error, P e in presence of interference, the integrator output g(T ) should be greater than 0 as the bit is +1, implying the following condition [27] P e = P r g m (T ) + g i (T ) + N (T ) > 0 (13) 998 VOLUME 3, NO. 3, JULY 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply. Referring to the Appendix, the resulting probability of error, P e , for k stationary tone interferences is given by In the above, I i and S refer to the i-th tone interference and average signal power, respectively. Also, P G is the processing gain, defined as the ratio of the symbol time duration T to chip duration T c . Further, δω ic denotes the relative frequency difference between the carrier and interference signals.
The aforementioned equation indicates that the error probability depends on the processing gain and the I i /S ratio. Also, from (14), we conclude that interference at the carrier frequency leads to worse P e . Notably, spot interference at the carrier frequency (δω ic = 0) is given by As usual, the average probability of error is given by Fig. 4 plots the average bit error rate for 0 < θ i < 2π . In addition, to understand the effect of dynamic interference scenarios for higher order modulation, in Fig. 5, we simulated and compared BER plots for QPSK and 16-QAM. Refer to [23], and further following equations (5) and (15) give us the BER plot for these higher order modulation schemes in the presence of spot interference at the carrier. Although we restrict our measurement with only BPSK modulated transmission in the presence of high power interferences, our simulation shows that our BER expression with interference can be valid for other higher-order modulations.

V. BER UNDER SWEEP INTERFERENCE
Sweep tone interference can be considered as discrete segments of a series of sinusoidal waves [28], [29]. These sinusoidal waves can be concatenated with varying center frequencies, from ω s to ω e . For our experiment, we chose to sweep between ω s and ω e in a linear manner and across a time of T sw p . As noted earlier, the derivation of BER is given in the Appendix. From the Appendix, for a linear sweep, P e_sw p , is given by where, δω sc = |ω s − ω c | and δω es = |ω e − ω s |. Similarly, BER can be calculated for the case of an exponential tone sweep. Fig. 4 depicts the coding gain and CDM-coded average BER performance. They are given for spot, linear sweep, and barrage interference.

VI. BIT-ERROR-RATE TESTER FOR UWB-RF LINK
To our knowledge, there is no publication of experimental BER evaluation for an UWB-CDM communication channel, except in [30], where the author estimates BER through jitter. In addition, rather than comparing the transmitted and received bits, [30] used an approximate probabilistic model to estimate BER in terms of jitter. In this paper, a Bit-Error-Rate-Tester (BERT) is developed by UWB RF links (past work in [31] focused on based digital circuits only). Notably, measurements were performed using a random bit generator (acting as a transmitter). In our experiments, the transmitter and receiver were realized using Keysight [32] and Guzik Technical Enterprises [33] equipment. To assess wideband interference mitigation, we also used two wideband antenna arrays for reception and transmission. The employed array operated from 1 to 6 GHz [34], [35]. Fig. 6 gives the hardware setup for measuring the bit error rate in presence of a dynamic interference. This multipleinput multiple-output (MIMO) hardware setup consisted of an arbitrary waveform generator (AWG) and a high-speed digitizer for sampling at 20 GSPS. The AWG enabled direct RF conversion over the instantaneous analog bandwidth of 6.5 GHz. Unlike conventional wireless links, by employing analog RF up/down conversion, we realized a fully digital RF transceiver. Interference was directed towards the Rx antenna using a horn antenna. The complete setup (shown in Fig. 6) emulates the scenario of the desired UWB-CDM RF signal with interference. Real-time post-processing was also performed using the integrated software within the digitizer. The subject transceivers employed high-speed ADC and DAC as per Fig. 6(b).
We used digital up/down conversion to realize our transceiver. Two statistical parameters, integral nonlinearity (INL) and differential nonlinearity (DNL), played key roles in the converter's accuracy. Notably, INL represents the maximum allowable deviation between the converter's actual and expected output. Also, DNL controlled the deviation between the measured output and ideal sampling. To minimize the effects of these two parameters, the MIMO ADC and DAC were operated at their maximum 12-bit resolution.
We remark that the experiments included random sequence transmission with repetitive patterns and bit sequences consisting of only zeros or ones. Notably, our custom-built MIMO executed precise multi-module synchronization with the built-in sequencer technology. An FPGA controlled this hardware sequencer. This approach used a feedback loop for synchronization between the AWG and digitizer. Finally, the transmitted and received bits were correlated to estimate the bit error rate.

A. SPOT AND SWEEP INTERFERENCE
We considered single tone and single swept interferers as high power interference injected into the link path. As depicted in Fig. 6(a), interference was injected by a horn placed near the transmitting antenna. This horn injected an interfering signal of 30 dB above the transmitted signal power. The link operated from 3.35 GHz to 4.65 GHz, and the distance between the transmitter and receiver was 1.5 meters. The sweeping interference tone spanned across the entire band, whereas stationary interfering tones were generated at 4 GHz.
We collected multiple sets of measurements to address the effect of spot and sweep interference. Fig. 7(a) shows the spectrum of the desired signal with sweep interference. The interval of the sweep interference from one frequency to the other was 5 ms. BER was plotted in terms of signal-to-noise ratio for linear sweep interference as shown in Fig. 8. Also, Fig. 9 validates the computed theoretical BER performance with measured data for spot interference. We remark that due to error quantization of the analog/digital converters, a 2.5 dB degradation between measurements and simulations is observed. Hence, a performance gap exists between the measured and simulated BER. This deviation occurs due to the mismatch error between multi-channel interleave ADCs architecture. Considering an ideal ADCs, SNR can be defined as SNR ADC = 6.023 N + 1.76 dB (17) Where N is the effective number of bits in ADCs. However, the SNR of the ADC is determined by the ratio of the signal power to the noise floor. This noise floor should include thermal noise, quantization noise, or other impairments within the Nyquist bandwidth. Quantization noise from ADCs depends on the ADCs' resolution as well as the number of bits. It is remarked that the architecture of our high-speed digitizer (Guzik 6000 series) [33] uses interleaved ADCs to achieve a higher sampling rate. Although this interleave  technique enhances the sampling rate but requires addressing concerns for associate distortion called interleave spur. This spur generates due to the gain and phase mismatch between multi-channel ADCs. This interchannel mismatch limits the ideal SNR ADC by affecting the effective number of bits of ADCs [36]. Although modern interleaved ADCs architecture enhances ENOB close to ideal, incorporating different techniques [37], the former hardware (e.g. Guzik 6000 series) we used is prone to have distortion and limit achievable SNR in ADCs. Due to this multi-channel mismatch error between interleaved ADCs, we encountered a few dB deviations between the derived BER and the simulated one.
However, it is important to note that each curve includes the measured BER curve for the uncoded signal and corresponding interference scenario. As seen, the proposed UWB-CDM system exhibits strong immunity to interference. Simulations and measurements also show a close agreement in presence of dynamic interference.

B. MULTITONE OR BARRAGE
Barrage interference can be defined as multiple static tone interference across the frequency band. Fig. 7(b) shows the spectrum of two high-power interferers blocking the desired spread signal. Also, the CDM-BPSK coding performance with barrage interference can be seen in Fig. 10. We used two signal generators to transmit identical signals at different frequencies and therefore emulate barrage interference. After combining, we fed them to the horn antenna that injected this barrage interference in the Rx path.
Notably, all conditions remained the same for each interference scenario. Fig. 11 shows the measured BER comparison for the UWB-CDM coding in the presence of spot, sweep, and barrage interference. It is seen that the sweeping tone is less detrimental, whereas spot interference at carrier frequency has more impact. It is also observed that the addition of interference tones degrades BER by 2 dB per tone for I/S = 30 dB. This demonstration shows 1000-fold interference immunity by using CDM coding for sweep interference.

C. BASE
Base interference falls into the category of barrage interference. It extends the use of continuous blocking tones across a frequency band. To study this interference scenario, a noiselike signal of various bandwidths was generated and used as the blocker. However, due to the equipment's limitations, the transmitted power was limited in terms of bandwidth. Hence, the transmitted power density dropped by 10 dB per decade of added bandwidth (see Fig. 12).
Alternatively, Fig. 13 shows examples of the transmitted noise-like signal and the respective constant power density. Hence, an additional measurement was performed to study the effects of interference with variable bandwidth having constant power density. To address this scenario, we measured the transmitted power of a 100 MHz noise-like signal and kept it constant regardless of bandwidth variation. To do so, a 10 dB attenuation per decade was added at the output of the front end. Fig. 14 provides the resulting BER versus bandwidth for base interferer, considering constant and variable power densities. As expected, the case of constant power density directly impacts BER and degrades performance more than the case of variable power density. Notably, both tests were performed in a high SNR environment to discard AWGN noise effects and focus on base interference.

VIII. CONCLUSION
In this paper, we presented analytical expressions for BER in presence of dynamic interference scenarios in an UWB 1.3 GHz RF link. These expressions were also validated using a custom test bench for multiple interference scenarios. Notably, for the first time, we overcame the challenges of demonstrating a custom wireless test bench to evaluate BER for an UWB-CDM wireless link. It was demonstrated that up to 1000-fold (30 dB) interference mitigation is possible by exploiting UWB-CDM coding. As expected, the practical gain of the SDR transceiver is bounded by the ADC's resolution and other hardware impairments. It was found that interference tones degraded BER by about 2 dB per tone. Further, the effect of sweeping tone interference was found to be less severe than the stationary ones. Overall, the large available bandwidth with code spreading implies a significant interference margin for BER performance in secure communication environments.

APPENDIX
Assuming a transmitted bit of +1, using (12) the desired received signal, g m (T ) at the receiver is given by The above can be simplified by employing the autocorrelation properties of PN code and filtering higher frequency components. Doing so gives Following a similar analysis as above, and referring to (6) and (12), the interference contribution, g i (T ), is given by The above can be simplified by filtering the higher frequency components, giving cos(δω ic t )P(t )dt sin(δω ic t )P(t )dt (19) In (19), Next, using (13), the probability of error can be deduced to the Q function as follows [27] Next, by inserting (21) and (22) into (20), we obtain Notably, the error probability in (23) is under pseudo noise code P(t ). It is remarked that in presence of sweep tone interference, β SI and β CI need to be reevaluated. Indeed, using (7) into (19) gives where, δω sc = |ω s − ω c |, δω es = |ω e − ω s | and again by inserting (24) and (25)