Devendra Singh Gurjar

Beamforming in asymmetric two-way relay systems with imperfect channel estimation

In this paper, we consider a two-way relay system that employs transmit/receive beamforming for bidirectional communication using analog network coding (ANC) protocol in the presence of channel estimation error (CEE). For this set-up, we first obtain the instantaneous end-to-end signal-to-noise ratios (SNRs) with partial self-interference cancellation pertaining to imperfect channel estimation. Then, by considering asymmetric traffic requirements, we derive an accurate expression of overall outage probability (OOP) of the considered system under Nakagami-m fading. We further derive a tight lower bound on OOP that has a simple and compact closed-form representation. Moreover, we present an asymptotic OOP expression at high SNR to examine the achievable diversity order with CEE. Numerical and simulation results validate our theoretical analysis and highlight the impact of CEE and different traffic patterns on the system performance with various antenna configurations and fading severity parameters.

Impact of channel estimation error on zero-forcing-based multiple-input–multiple-output two-way relaying

In this study, the authors investigate the impact of channel estimation error (CEE) on the performance of a multiple-input–multiple-output (MIMO) two-way relay system under Rayleigh fading. Herein, transmit/receive zero-forcing (ZF) is employed at the two source nodes, whereas analogue network coding is used at the relay node. Fundamentally, for making use of transmit/receive ZF, all nodes must be aware of channel state information (CSI). As perfect CSI may not always be available in practical scenarios, the CEE does exist in the considered system. By taking the imperfect CSI into account, they enucleate that the residual self-interference and additional noise pertaining to the CEE have effect of reducing end-to-end signal-to-noise ratios (SNRs) at the two source nodes. Based on the statistical characterisations of these post-processing SNRs, they carry out the overall system outage probability analysis. Further, they investigate the asymptotic outage behaviour to deduce the achievable diversity order. They substantiate that the diversity order may reduce to zero under severe impact of CEE. In addition, they derive a closed-form expression of ergodic sum-rate of the considered system with CEE. Numerical and simulation investigations are conducted to support all the theoretical findings using various values of CEE and antenna configurations.

Performance analysis of zero-forcing-based multiple-input multiple-output two-way relaying in overlay device-to-device communications

In this study, the authors conduct the performance evaluation and resource allocation for two-way multiple-input multiple-output-based device-to-device (D2D) communications overlaying a cellular network. The considered system model comprises of a base station, a mobile user, and a pair of D2D users, where each of them is equipped with multiple antennas and employs transmit/receive zero forcing. Based on overlaying approach, both D2D and cellular communications take place bidirectionally by employing analogue network coding with a best selected D2D user as two-way relay for the cellular links. The authors analyse the outage performance of cellular and D2D systems in a Rayleigh fading environment. They also deduce asymptotic outage behaviour of cellular system and highlight the achievable diversity order. In addition, they derive the expressions of ergodic sum rate for both the systems. Above all, they provide a selection algorithm for the best relaying D2D user and describe feasible range of power splitting factor to maximise the data rate of cellular system for a given data rate of D2D system. Numerical and simulation results validate the authors’ theoretical findings and illustrate the performance gains of the considered scheme under various antenna configurations.

Outage performance of zero-forcing based MIMO two-way relaying with channel estimation error

In this paper, we investigate the effect of imperfect channel state information (CSI) on the performance of a multiple-input multiple-output (MIMO) two-way relay system that employs transmit/receive zero-forcing (ZF) at the sources and analog network coding (ANC) at the relay. In fact, for the transmit/receive ZF, the source nodes require estimation of the CSI that may not be perfect in practice, and hence the channel estimation error (CEE) does exist in the system. By taking this CEE into account, we deduce that the post-processing end-to-end signal-to-noise ratios (SNRs) at the two sources are reduced by an additional noise pertaining to the CEE and the residual self-interference. Based on these SNRs, we analyze the overall system outage probability and the asymptotic outage behavior under a Rayleigh fading scenario. We demonstrate that the CEE has a severe impact on the overall outage performance and it may reduce the system diversity order to zero. Numerical and simulation investigations are conducted with various values of estimation errors and antenna configurations to support the theoretical analysis.

Overlay Device-to-Device Communications in Asymmetric Two-Way Cellular Systems With Hybrid Relaying

Device-to-device (D2D) communications in cellular systems have been envisioned as a promising technique to compensate for spectrum scarcity. In this paper, we analyze the performance of overlay D2D communications in two-way cellular systems by employing a three-phase hybrid decode-amplify-forward (3P-HDAF) relaying scheme. Herein, two D2D users provide relay cooperation to the bidirectional cellular transmissions to support certain target rates with the opportunity of sharing same cellular spectrum for their own information exchange. With the proposed 3P-HDAF scheme, one complete round of end-to-end information exchange for both cellular and D2D systems can be accomplished in three time phases, wherein the D2D users can adaptively select either decode-forward or amplify-forward relaying strategy to facilitate the cellular transmissions. For performance analysis of considered setup, we derive the expressions for outage probability (OP) of both cellular and D2D systems by posing asymmetric traffic requirements under Nakagami- m fading. Further, to gain better insights, we obtain the asymptotic OP expressions in a high signal-to-noise ratio (SNR) regime. Hereafter, we deduce some key design parameters such as the critical value of power splitting factor and spectrum sharing region. Moreover, we also obtain an expression of average system throughput to conduct a fair performance comparison with similar existing schemes.

Overlay spectrum sharing for device‐to‐device communications in two‐way cellular networks with nodes mobility

In this paper, we propose and investigate a three-phase overlay spectrum-sharing scheme for device-to-device (D2D) communications in a bidirectional cellular network with nodes mobility. In this scheme, a pair of D2D users facilitates relaying to the cellular nodes (base station and mobile user), and in return, they get the opportunity to exchange their own information by exploiting the same cellular spectrum. With this, the two end-to-end bidirectional communications (D2D and cellular) can be realized in three time phases by using selection-combining technique at both cellular nodes and decode-and-forward (DF) relaying scheme at both participating D2D users. For DF operation, we consider two strategies, namely, exclusive-OR (XOR)-based DF, and superposition-based DF. All the channels are assumed to be time varying, and Markovian model is used to characterize the impact of nodes mobility. For this set-up, we first derive the outage probability for both cellular and D2D links under Rayleigh fading. Then, we obtain the asymptotic expressions of outage probability for both systems and used them further to reveal the critical value of power-splitting factor for spectrum sharing. Above all, we acquire the expression of average system throughput to perform a fair performance comparison with the other existing schemes.

Joint impact of nodes-mobility and channel estimation error on the performance of two-way relay systems

Abstract This paper presents the performance analysis of a two-way relay system with nodes-mobility (NM) and channel estimation errors (CEE) under time-varying Rayleigh fading. Herein, analog network coding protocol is employed at the relay node. All the participating nodes are half-duplex and equipped with single-antenna devices. Specifically, we utilize first-order Markovian model to characterize the impact of NM in the channel. Along with the NM, we also consider that the CEE may exist in practical scenarios, where nodes require to estimate the channel state information. By incorporating these factors, we first derive the instantaneous end-to-end (e2e) signal-to-noise ratios (SNRs) at two source nodes. Then, we obtain the exact closed-form expressions for distribution and density functions of the two e2e SNRs. After that, we derive the accurate expressions of various performance metrics, viz., sum-bit error rate, overall outage probability, and ergodic sum-rate. Further, to attain more insights into the considered system, we deduce the asymptotic behavior of these performance metrics. Finally, numerical and Monte-Carlo simulation results are provided to validate our theoretical analysis and to illustrate the impact of NM and CEE on the performance measures of the considered system.

Beamforming in Traffic-Aware Two-Way Relay Systems With Channel Estimation Error and Feedback Delay

This paper presents a comprehensive performance analysis of a multi-antenna-based traffic-aware two-way relay system with unavoidable imperfections in channel state information (CSI) under Nakagami-m fading. Herein, we employ transmit/receive beamforming at source nodes and analog network coding (ANC) at the relay node in the presence of CSI imperfections due to channel estimation errors (CEE) and feedback delay. With such a practical setup, we first deduce the pertinent instantaneous end-to-end signal-to-noise ratios (SNRs) after performing partial self-interference cancellation. Then, by imposing asymmetric traffic requirements in two opposite directions, we conduct an accurate analysis of overall outage probability (OOP) of the considered system. We further derive a tight lower bound on OOP that has a simple and compact closed-form representation. Moreover, based on the asymptotic OOP expression at high SNR, we examine the achievable diversity order of the system. In addition, we acquire an upper bound expression of ergodic sum-rate (ESR) and simplify it further in useful compact form for high SNR regime. Besides, we investigate the optimization problems of relay position to minimize the OOP and to maximize the ESR. Numerical and simulation results validate our theoretical analysis and highlight the impact of CEE and feedback delay under various traffic patterns on the overall system performance.

Three-phase overlay D2D communications in traffic-aware two-way cellular systems

In this paper, we propose a new reliable scheme for device-to-device (D2D) communications overlaying a traffic-aware two-way cellular system. The considered system comprises a pair of D2D users, a base station (BS), and a mobile user (MU). In the proposed scheme, both participating D2D users provide relay assistance to the cellular nodes (BS, MU), and in return, they are allowed to exchange their own information by utilizing the same licensed cellular spectrum. Hereby, two end-to-end bi-directional transmissions (cellular and D2D) can be realized in three-time phases. Moreover, we employ decode-and-forward (DF) relaying strategy at both relaying D2D users and selection combining (SC) scheme at both cellular nodes. For this set-up, we investigate the performance of both cellular and D2D links in terms of outage probability (OP) under Nakagami-m fading. Further, we obtain an expression of average system throughput (AST) to conduct fair comparison with the other existing schemes. Numerical and simulation analyses are performed to validate our analytical findings and to present useful insights into performance of cellular and D2D systems.