Performance analysis of a multi-relay cooperative diversity network with decode and forward relaying

Cooperative diversity is a technique that mitigates fading without additional cost, hardware and complexity. A cooperative diversity system having a source, multiple relays and a destination is considered. The end-to-end symbol error probability (SEP) of a full channel state information (CSI) selection combining scheme for cooperative communication, with selective decode and forward (S-DF) relaying for binary phase-shift keying (BPSK) symbol in a flat Rayleigh fading environment, is derived. Here, the effect of source-to-relay channel is included in the error analysis of cooperative diversity systems with selection combining. The threshold for S-DF is set with ratio factor α. On the basis of the optimised α value, the partner selection is performed. This scheme offers better SEP when compared with conventional selection combining scheme.

This paper proposes a novel optimal receiver for an $N$ -branch receive diversity power line communication (PLC) system subject to Rayleigh fading and perturbed by Nakagami-m background noise. A Gauss-optimal receiver is obtained from the optimal receiver which is further utilized to derive a closed form expression for the symbol error probability (SEP) for binary phase-shift keying (BPSK) modulation using a characteristic function approach under the condition that mN is an integer. An asymptotic expression for the SEP at high signal-to-noise ratio (SNR) shows the diversity order of the PLC system to be independent of the noise shape parameter $m$ . Numerical studies demonstrate that the diversity order of the optimal receiver is preserved with the suboptimal receiver as well. Furthermore, the advantage of using multiple receive branches in terms of achieving better error performance and the effect of the shape parameter $m$ on the SEP of the suboptimal receiver are also presented.

In this paper, we study the design of network codes for multi-source, multi-relay networks over frequency non-selective slow fading channels. Specifically, we consider a system with M sources each having independent information to be transmitted to a common destination with the help of N relays (called an M - N - 1 system). A finite field (nonbinary) based method is suggested to design binary network codes. For construction of the codes, we investigate full system diversity achieving criteria and constraints imposed by it in terms of linear independence of columns (or sets of columns) of generator matrix for codes over finite fields (including binary). First, we design such full diversity achieving codes over polynomial fields of the form GF(2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</sup> ) and then using a novel uplifting technique (matrix representation of finite fields), convert these back into frame based binary codes to reduce encoding complexity at relays (as only binary operations are used). Simulation results confirm the diversity claims of the proposed codes under perfect as well as realistic source-to-relay (S-R) channel links. We also apply belief propagation (BP) decoding on these codes. The codes are compared with that from existing algorithm and similar performance is observed with smaller frame size for the case considered.

Performance Analysis of Wireless Adhoc Networks in Flat Fading and Frequency Selective Fading channels

This paper studies optimal power allocation to minimize symbol error rate (SER) of amplify-and-forward cooperative diversity networks. First, we analytically solve optimal power allocation problem to minimize SER for three different scenarios, namely, multi-branch single-relay, single-branch multi-relay and multi-branch multi-relay cooperative diversity networks, all subject to a given total relay power consumption. In addition to the total relay power constraint, for the multi-branch single-relay scenario. Next, we assume that every single relay is subject to a maximum power constraint. To this end, we present an iterative algorithm to find the optimal power rates. Finally, we study an off-line scenario in which the relays are energy harvester and equipped with infinite-sized batteries. For this scenario, the maximum SER is minimized over the whole harvesting time slots. We propose a water filling algorithm for the classical relay channel and an iterative algorithm for the multi-branch single-relay cooperative scheme. Through the numerical results, it is shown that optimal power allocation policies enhance the system performance.

An intelligent reflecting surface (IRS) assisted wireless communication system, with statistically correlated channels between the transmitter and the IRS pair and between the IRS and the receiver pair, is studied in the absence of channel state information (CSI). Assuming the phases added by IRS elements to be deterministic, the closed-form analytical expression for the symbol error probability (SEP) and the upper bound on the channel capacity are derived, with the transmitter employing binary phase-shift keying (BPSK) modulation for data transmission. The asymptotic SEP expression is derived and the achievable diversity order of the system is shown to be independent of the number of IRS elements. A search based algorithm is proposed to obtain the optimal phase at IRS minimizing the average SEP, as a equal phase configuration. The optimal equal phase is also found to maximize the average channel capacity. Numerical results are presented for the case of channels following a practical IRS correlation model.

A cooperative diversity system improves the communication reliability and throughput in a multipath fading environment with the help of relay nodes. We consider a cooperative diversity system with a source (S), a decode-and-forward relay (R), and a selection-combining-enabled destination (D). In this paper, we derive the exact end-to-end symbol error probability (SEP) for $M$ -ary phase-shift keying (MPSK) signaling using a paired error approach and differential binary phase-shift keying (DBPSK) signaling over correlated, nonidentical, slow, and flat Nakagami- $m$ fading channels by assuming the correlation between SD–RD, SR–SD, and SR–RD fading channels. In addition, we perform the exact outage probability analysis for the same scenario. Furthermore, we provide the asymptotic expressions for SEP and outage probability by removing the infinite-series terms to investigate the diversity order. In a nutshell, the numerical results reveal that the SR–RD correlated channel scenario outperforms the uncorrelated channel scenario in terms of SEP. In addition, SEP performance degradation is observed in the case of other correlated channel scenarios compared with the uncorrelated channel scenario. Moreover, marginal performance improvement in outage probability is observed in the low-signal-to-noise-ratio (SNR) regime of the SR–RD correlated channel scenario compared with the uncorrelated channel scenario. Finally, Monte Carlo simulations are performed to validate the theoretical results.

Aiming at efficient utilizing the licensed spectrum, in this paper, we develop an interference cancellation based transmission strategy (ICTS) for the cooperative cognitive radio networks (CRN) which will take advantage of the opportunities that arise during the primary automatic repeat requests (ARQ) and cancel the primary interference in both the primary initial transmission and retransmission slots. Simultaneously, the secondary system will cooperate with the primary system by supporting its outage quality-of-service (QoS) requirement to speedup the primary transmission and acquire more interference-free spectrum opportunities. Specifically, in the primary initial transmission slot, the secondary users (SU) will transmit in the underlay mode. In addition, SUs try to decode the primary signal to cancel the primary interference and overhear the primary ARQ signal. In the retransmission slot, SUs can cancel the primary interference directly when the primary signal is successfully decoded in the initial slot or utilize the primary information redundancy to cancel the interference. With statistical channel state information (CSI), SUs can calculate their interference cancellation probabilities in both slots and derive their average transmission rate. To maximize SUs' average transmission rate while meeting PUs outage QoS requirement, we formulate the optimization problem and efficiently allocate SUs transmit power. The closed-form expressions of the average transmission rates for both PUs and SUs are derived. Furthermore, SUs' upper bound symbol error probability (SEP) and PUs' SEP are derived. Simulation results demonstrate the performance superiority of our developed ICTS over conventional ARQ-based transmission strategies in terms of SUs' average throughput and PUs' outage probability and SEP.

In this paper the performance of a cooperative communication system operating over a composite fading environment and is also subject to interference is investigated. More specifically, assuming a decode-and-forward (multi-relay) cooperative network with relay selection, exact and approximated expressions are derived for the cumulative distribution function of the output signal to interference plus noise ratio. Based on these expressions, the outage and the average bit error probabilities of the system under consideration are studied and used to obtain various numerical performance evaluation results, depicting in all cases the usefulness of the proposed approach.

Outage performance of cognitive DF relay networks with nonidentical Rayleigh fading channels and maximal ratio combining

In this paper, we analyze the performance of cooperative wireless networks with multiple-relays with single-relay selection using limited feed back, exploiting the concepts of Alamouti space-time coding. A two-stage protocol is used with the relay terminals operating in the amplify-and-forward mode (AF). The analysis uses the Rayleigh fading model to reduce the complexity in handling versatile Nakagami fading channels. Taking these effects into account, symbol error probability (SEP) for single relay selection in a multiple-relay environment is derived . The selection is based on the gain of the source-relay (SR) channel and we claim that this is the best achievable SEP for transmission of the Alamouti code using the described protocol, under the given selection criteria. Numerical results are provided to verify the accuracy of the formulation.

Due to the increase in massive device connectivity and increasing demands of future technologies, the Fifth-Generation (5G) networks are expected to support high spectral efficiency and low latency. In this regard, Non-Orthogonal Multiple Access (NOMA) technique has grabbed drastic attention from researchers and industry. Furthermore, to improve the performance of the NOMA system, we have incorporated the idea of cooperative communication. This paper considers a downlink NOMA system consisting of a Base Station (BS), two relays named R1 and R2, employed with Decode and Forward (DF) protocol, one far user, and one near user. In this work, an algorithm to investigate the Symbol Error Probability (SEP) performance of cooperative downlink NOMA system with Quadrature Phase Shift Keying (QPSK) modulation in the presence of the Rayleigh channel fading environment is developed. From the simulation results, it is observed that the SEP performance of the proposed NOMA system is significantly enhanced compared to that of the existing downlink NOMA system due to cooperation from the relay nodes. In addition to that, the SEP performance analysis has been made by varying the distance between the relays and BS resulting in increased SNR and reduced SEP.

Two three‐dimensional (3D) 16‐ary signal constellations having extended lattice structures are presented in this paper. The theoretical symbol error probabilities (SEPs) of the new constellations in additive white Gaussian noise (AWGN) and Rayleigh fading channel are derived. Computer simulation confirms that the closed‐form expressions for average SEPs of the constellations in the AWGN channel are very accurate. The theoretical SEP upper bounds in the Rayleigh fading channel are very tight. Since the presented constellations have larger minimum Euclidean distance (MED) than the conventional one, error performance can be improved up to 0.9 dB in an AWGN environment. Hence, the proposed constellations and their theoretical analysis can be used as a reference for the development of a wireless communication system with 3D signal constellations.

Digital phase modulation is a class of power‐ and bandwidth‐efficient modulations widely used in telecommunications. In this article, the reader will first be introduced to the general concept of digital phase modulation, and the notions of bandwidth and power efficiency. The commonly used class of digital phase modulation schemes, that is, M ‐ary phase shift keying (MPSK), are described in detail. Their signal waveform expressions, signal constellations, and power spectral densities (PSDs) are presented. The block diagrams of the modulator and the optimal coherent demodulator are presented and explained. The symbol and bit error rate (BER) of the demodulator is derived and symbol error probability graphs are given. Widely used binary PSK (BPSK) and quaternary PSK (QPSK) are treated as special cases of MPSK. Next, differential PSK schemes are introduced, which are particularly useful in wireless fading channels. Their symbol error probability expressions and graphs are presented. At the end, two important phase modulation variations, namely, offset QPSK (OQPSK) and π/4‐DQPSK, and the advanced continuous‐phase modulation (CPM), including multi‐ h CPM, are briefly introduced.

This letter presents a study on statistical and symbol error performance analysis of the two-hop orthogonal frequency division multiplexing (OFDM) relay link with amplify-and-forward (AF) protocol and subcarrier mapping (SCM) scheme. Closed-form expressions for probability density function (PDF) and symbol error probability (SEP) of the signal-to-noise ratio (SNR) for the kth mapped subcarrier pair link (k-MSPL) are provided. Our asymptotic SEP analysis reveals that the traditional SCM which can maximize the capacity can not improve the average SEP for uncoded OFDM system, however the average SEP can be decreased significantly by dropping several worst links.