The Resilience of MIMO Based Physical Layer Network Coding to Jamming Attack

In this paper, we explore the resilience of Physical Layer Network Coding (PNC) to jamming attacks, focusing on the bit error rate (BER) performance metric. The broadcast nature of the wireless medium has undoubtedly propelled some significant innovations, allowing ubiquitous access to broadband services. In spite of this, it has also created an enormous challenge in mitigating unfriendly interference, where jamming is categorized. A MIMO-PNC based algorithm shows significant improvement in error performance in the lower signal-to-noise ratio (SNR), where the base station (BS) applies linear detection, based on a linear transformed channel matrix, to received symbols, in order to estimate the network coded symbols. We investigate this algorithm in a centralized system of multi-antenna BS with multi-antenna legitimate users, against a barraging attack from a jammer, where the jamming channel is not known to the BS, and the jammer can use any number of transmit antennas. Over Rayleigh fading channels, our simulation results reveal that MIMO-based PNC perform better in lower SNR to jamming attack, as opposed to the non-jammed MIMO system, at twice the spectral efficiency.


I. INTRODUCTION
The broadcast nature of the wireless medium has undoubtedly propelled some significant innovations, allowing users to access network resources from nearly any convenient location, allowing mobile users to access real-time information whilst on the move, allowing increase in coverage and scalable deployment of network resources. However, in open air interface in wireless communication, where signals from multiple sources arrive simultaneously at a receiver, interference has been one of the main challenges to deal with. Although, there is no interference that is friendly, some can be controlled by regulating the transmission strictly. Unfortunately, some are intentional and uncontrollable and fall into the category of denial-of-service (DoS) attack, and are often referred to as radio-frequency (RF) jamming. RF jamming is a malicious attempt to overwhelm a wireless communication system with the objective of circumventing the normal operation of the network.
Physical Layer Network Coding (PNC) is a key physical layer technique that overcomes interference by applying Network Coding (NC) to received radio signals, which constitute This work has been funded by the European Union Horizon 2020, RISE 2018 scheme (H2020-MSCA-RISE-2018) under the Marie Skłodowska-Curie grant agreement No. 823903 (RECENT). a superposition of a multitude of transmitted signals. The concept of PNC has been extensively studied in [1]- [3]. The original idea of applying network coding at the physical layer, leveraging on the additive nature of the wireless medium was detailed in [1], [2]. In these same publications, an information theoretic approach with emphasis on the rate region of the Gaussian two-way relay channel (TWRC) was investigated. Furthermore, a joint channel coding and PNC scheme was also investigated and the performance was improved.
MIMO is increasingly gaining attention in the PNC field, leveraging on its multiplexing gain. In [4], the authors proposed a linear detection based scheme using log-likelihood ratio (LLR) and selective combining. The relay utilizes the summation and difference of the two end packets, and then converts them to a NC symbol. The focus of [4] was only a 2×2 MIMO and BPSK modulation. This work was then extended in [5] to a relay system, with 4 antennas relay node and and two UEs, each equipped with 2 antennas. A multiplexing gain when the number of antennas at both the relay node and the two UEs is observed in [5]. In [6]- [8], analog network coding (ANC) based MIMO TWRC was investigated. However, ANC is known to propagate noise from a node to another, and therefore, the performance, is not as good as the schemes in which each node tries to clean up the noise [9]. A Full-duplex TWRC in Massive MIMO together with a lattice-based PNC was investigated in [10], which showed that their proposed scheme requires just a single timeslot to exchange information across TWRC, whereas four time slots would be needed in a conventional TWRC. PNC has also been considered in 5G MIMO systems for backhauling, as opposed to Cloud Radio Access Network (Cloud-RAN), and also for coordinated multipoint (CoMP) [11]- [13].
Jamming attack in itself is considered under the umbrella of active attack in Physical Layer Security (PLS) [14]. The broadcast nature of the wireless medium makes the physical (PHY) layer the most vulnerable among all the layers. PLS solutions approach security issues from information theoretic perspective, by leveraging on the randomness, interference and other characteristics as observed by the PHY. However, some attacks, particularly, those under active attacks, might require countermeasure approaches that include PHY algorithms and techniques that can withstand the attack with little or no degradation. The countermeasure approaches address the proactive types of jamming attacks [15], where the attacker's main objective is to thwart the normal operation of a wireless system by persistently sending jamming signals. One of the most prevailing jamming technique is deploying noise. Noise jamming techniques reduce the cumulative received SNR at the receiver by increasing the thermal noise level. Barrage jamming, spot jamming and sweep jamming are the three most common types of noise jamming [15]. These noise jamming techniques, respectively, focus on the transmit power on multiple frequencies at the same time, on a fleet of frequencies and a single frequency. A number of jamming attack research in radar have focused on the Barrage jamming, where the entire bandwidthh of the transmission is targeted with noise. The adverse effect of jamming has been extensively studied, as outlined in [16].
In a recently published work [18], was developed a practical approach for deploying PNC in multi-user MIMO systems, utilizing QPSK modulation scheme. In this MIMO-based PNC work, a Maximum a Posteriori (MAP) based PNC mapping scheme, leveraging on the existing MIMO's linear detectors such as Zero-Forcing (ZF) and Minimum Mean Square Error (MMSE) was formulated. The transmissions were over the Rayleigh fading channels with AWGN at the receive antennas and the performance evaluation revealed that in the lower SNR, this PNC scheme outperformed conventional MIMO in those structured noisy channels. The lingering question is if such a robust MIMO-based PNC scheme can withstand uncontrolled jamming signals from a jammer.
In this paper, we study a multi-user MIMO system, where a BS's capacity to perform PNC is challenged by an active jammer that persistently transmits jamming signals. We investigate the error performance of the BS's capability to estimate the PNC symbols amid the active jamming signals. We summarize our contributions as follows: • We investigate the resilience of an existing, but robust MIMO-based PNC scheme over jamming attack over Rayleigh fading channels, focusing on the bit error performance. • We model the jamming signal using Gaussian noise, such that the jamming signal dominates the received AWGN noise at the receive antennas of the BS. • Using Monte-Carlo simulation, we evaluate and analyse, the system model, providing a perspective on the implication of the results.

A. System Model: Uplink Single Cell MIMO
We consider a system model of a single cell MIMO as depicted in Fig. 1, in which an M antennas BS communicates with N legitimate UEs (LUE), each equipped with K antennas, forming an array of L = K × N input antennas. The communication between the BS and the LUEs, is in the presence of an adversary, whose objective is to circumvent the decoding capabilities of the BS. The jamming signal is assumed to originate from outside of the cell that the LUEs belong. The jamming technique deployed by the adversary can be any of the noise jamming techniques mentioned in Section I. In the uplink (UL), all users transmit to the BS simultaneously using a common frequency band. The system model can be represented as where r ∈ C M ×1 denotes received symbols vector, s = s 1 s 2 . . . s L T ∈ C L×1 , is the transmitted symbols vector from all LUEs, H ∈ C M ×L is the channel matrix, J ∈ C M ×J is the jammer to BS channel matrix, z ∈ C J×1 is the jamming signal transmission vector, and n ∈ C M ×1 is independent and identically distributed (i.i.d.) AWGN with zero mean and variance, σ 2 n . We assume that the transmitted symbols are Gray-scale M-ary Quadrature Amplitude Modulation (QAM) and the average transmitted energy per symbol is E[|s i | 2 ] = E s / L, where E s is the M-ary QAM symbol energy at each antenna. Linear detectors such as ZF and MMSE are known to have desirable computational complexity and are proven to perform well in MIMO [17]. At the receiver, the BS is assumed to employ ZF or MMSE to estimate the transmitted symbols from the received symbols vector, by determining the detection matrix, G, respectively, as where σ 2 is the received antennas' noise variance. In the case where there is no jammer, SNR = L×E s /σ 2 n , and when there is a jammer, the signal-to-jamming plus noise ratio, SJNR = L×E s /σ 2 = L×E s /(σ 2 n +σ 2 z ), where σ 2 z is the jamming noise variance. The jamming-to-noise ratio is, JNR = J × E z / σ 2 z . In the system model, we also assume that the BS is capable of carrying out PNC and the consequence of the jamming attack is to adversely impact the correctness of the estimation of the PNC symbols. As already stated previously, in [18], a MIMO-based PNC algorithm was developed, where a multiantenna BS estimates PNC symbols from received interfered symbols, which are composed of superimposed transmitted symbols from multi-user multi-antenna UEs. The concept is based on a linear transformation of the channel between the BS and the UEs, using a sum-difference (SD) matrix, under the assumption that channel is known to the BS. The SD matrix ensures that the transmitted symbols are grouped into clusters of transmit antennas, from the UEs that intend to communicate with each other. The BS then estimates a sum and difference of the transmitted symbols in the cluster, from the received symbols using linear detectors such as ZF and MMSE. The detection matrix is based on the SD transformed channel matrix. We refer the reader to [18] for further details of the PNC scheme.
Applying the MIMO based PNC scheme to the system modem defined in (1), yields where P sd is the SD matrix, H sd = 1 2 HP sd , is the linear transformation of the MIMO channel with a SD matrix, and s sd = P sd s, clusters of SD symbols, whose estimates at the BS, are then mapped to the PNC symbols. Although the term J z in (4) is missing in the corresponding equation in [18], the estimation of the s sd , SD symbols, remains the same using the following equalization matrix and the estimated SD symbols is given as The effect of the term J z in (5), is the prime focus of this investigation. Assuming that z is noise, then the lower bound of the performance of the system model is achieved, if worst case jamming signal is modeled as an AWGN [19]. Therefore, in our system model, the jamming term is modeled as Gaussian. If the jamming signal does not dominate the AWGN, n, then the decoding performance is expected to be similar to the results in [18]. Therefore, the target is to evaluate the error performance of the system model when the jamming term, J z, dominates the AWGN.

III. EVALUATION
In this section, we evaluate the bit error performance of the MIMO-based PNC scheme against jamming attack. The simulation parameters are listed in Table I. In the simulation, we have a BS with multiple number of antennas communicating with LUEs, and for simplicity, we assume that the number of antennas at each LUE is the same. The jammer is also assumed to have multiple number of antennas to transmit, independently of the LUEs. The objective of the BS is to perform PNC employing the proposed algorithm in [18], whereas, that of the jammer is to introduce errors in the PNC algorithm execution. In the simulation setup, the jammer has a couple of possibilities to influence the performance of the BS. We simulated various scenarios that includes conventional MIMO without PNC, MIMO with PNC, with and without jamming attacks. We controlled the transmit power and the number of antennas of the jammer and then countered it by adjusting the dimension of the received antennas of the BS and also the modulation scheme.
In Fig. 2 -Fig. 7, we present the results of the simulation by showing the BER versus the average SNR per receive antenna of the BS for QPSK (4-QAM) and 16-QAM modulation schemes, considering the different usecases of MIMO and PNC and the jammer. Fig. 2 presents the error performance for all usecases when the modulation scheme is QPSK, employing both ZF and MMSE. The BS has 4 antennas, and each of the 2 UEs has two antennas and the jammer has a single antenna with JNR of -10dB. Both jammed MIMO and jammed MIMO with PNC performed comparatively close to the counterpart without jamming until at about 15dB SNR. Beyond this, the jammed BER starts to saturate. This is an indication of the PNC scheme performing well against a jammer at lower SNR, at twice the spectral efficiency.
In Fig. 3, utilizing the same setup as Fig. 2, we increased the number of antennas of the jammer by two. The simulation revealed a degrade in the former compared to the latter. This is an indication that by increasing the number of antennas of the jammer, the jamming signal adversely influences the decoding capabilities of the BS. However, the jammer may not want to expense extra cost in its quest of circumventing the decoding capabilities of the BS, by increasing the number of transmit antennas. Fig. 4 has a similar setup as in Fig. 2, except the JNR of the transmitted jamming signal is decreased by 10dB and the simulation result reveals an expected performance when the jamming power is low. As the jammer reduces the jamming signal power, error performance is better. We increased the number of antennas at the BS to 16 in Fig. 5, with the rest of the simulation parameters remaining the same as in Fig. 2. The simulation result of the former revealed a similar pattern to that of the latter, except the BER starts to saturate after 30dB SNR. This is an indication that the more antennas the BS has, the better the resilience against a jamming attack in the lower SNR.
In Fig. 6 and Fig. 7, we repeated the setup in Fig. 2 and Fig.  3 respectively, except deploying a higher-order modulation scheme of 16-QAM. The results showed a similar pattern to the QPSK counterpart, except the performance is better, as the BER starts to saturate at higher SNR, an indication that PNC performs better in the lower SNR against jamming attack.

IV. CONCLUSION
This paper has explored the resilience of MIMO-based PNC scheme to jamming attacks. The broadcast nature of the wireless medium has undoubtedly propelled some significant innovations, allowing ubiquitous access to broadband services. In spite of this, it has also created an enormous challenge in mitigating unfriendly interference, where jamming is categorized. An existing MIMO-based PNC algorithm was investigated in this paper against jamming attacks, and the focus of the evaluation was determining and analysing the BER against SNR. We simulated different usecases that includes a jamming attack on a system with conventional MIMO without PNC, MIMO with network layer NC and MIMO with PNC. Over Rayleigh channel, our simulation results revealed that MIMObased PNC performs better in lower SNR to jamming attack, as opposed to the non-jammed MIMO system, at twice the spectral efficiency.