Error performance analysis of decode‐and‐forward and amplify‐and‐forward multi‐way relay networks with binary phase shift keying modulation

Abstract

In this study, we analyse the error performance of decode and forward (DF) and amplify and forward (AF) multi-way relay networks (MWRNs). The authors consider a MWRN with pair-wise data exchange protocol using binary phase shift keying (BPSK) modulation in both additive white Gaussian noise (AWGN) and Rayleigh fading channels. The authors quantify the possible error events in an L-user DF or AF MWRN and derive accurate asymptotic bounds on the probability for the general case that a user incorrectly decodes the messages of exactly k (k ∈ [1, L − 1]) users. They show that at high signal-to-noise ratio (SNR), the higher order error events (k ≥ 3) are less probable in AF MWRN, but all error events are equally probable in a DF MWRN. They derive the average BER of a user in a DF or AF MWRN in both AWGN and Rayleigh fading channels under high SNR conditions. Simulation results validate the correctness of the derived expressions. The authors results show that at medium to high SNR, DF MWRN provides better error performance than AF MWRN in AWGN channels even with a large number of users (e.g. L = 100). Whereas, AF MWRN outperforms DF MWRN in Rayleigh fading channels even for much smaller number of users (e.g. L > 10).

Optimal User Pairing to Improve the Sum Rate of a Pairwise AF Multi-Way Relay Network

“…For δ small enough and with the optimum α and β m , the achievable rate approaches the upper bound in (8). Now, we investigate the sum rate of an AF MWRN with the proposed pairing scheme.…”

“…The prior works on AF MWRNs consider error performance [8] and outage probability [1], as well as, sum rate and diversity multiplexing tradeoff [9]. The message transmission in a MWRN could be either in a pairwise [1], [3], [8] or a non-pairwise [2], [7], [9] manner.…”

“…The message transmission in a MWRN could be either in a pairwise [1], [3], [8] or a non-pairwise [2], [7], [9] manner. In this letter, we consider pairwise transmission only to avoid the high signal processing complexity at the relay from non-pairwise transmission .…”

“…In a pairwise AF MWRN, when a user wrongly extracts another user's signal, it leads to incorrect detection of the following users' messages and significant degradation in the received signal to noise ratios (SNRs) [8]. This problem results from the choice of user pairs and thus, user pair formation is a critical issue for pairwise MWRNs.…”

Performance analysis of end-to-end SNR estimators for AF relaying

“…For instance, rate adaptation needs SNR information. Also, SNR knowledge is required in power control for code-division multiple-access systems, link adaptation for adaptive modulation and coding systems, and iterative decoding for "turbo" and low-density parity-check (LDPC) codes [1], in conventional system as well as in [2][3][4][5] for relaying systems where authors analysed the decode-and-forward (DF) and AF performances in two-way relaying or multi-way relay networks. Nonetheless, these works assumed perfect SNR knowledge and did not consider SNR estimation or SNR error.…”