Performance comparison of cooperative relay links with different relay processing strategies: Nakagami/Gamma approximation approaches

Abstract

In this article, we investigate and compare the error performance of two-hop communication links (THCLs) with multiple relays, when distributed and cooperative relay processing schemes are respectively employed. Our main objectives include finding some general and relatively simple ways for estimating error performance and demonstrating the trade-off of using cooperative relay processing. One distributed relay processing and two cooperative relay processing schemes are compared. In the two cooperative relay processing schemes, one assumes the ideal relay cooperation, in which relays exchange information without consuming energy, while the other one assumes energy consumption for relay cooperation. In this paper, the error performance of the THCLs employing the considered relay processing schemes is investigated, when the channels from source to relays, the channels for information exchange and that from relays to destination experience various types of fading modeled by the Nakagami-m distributions. In order to derive the formulas for the bit error rate (BER) of the THCLs employing binary phase-shift keying (BPSK) modulation and various relay processing schemes, we introduce the Nakagami and Gamma approximation for finding the distribution functions of various variables encountered. Our studies show that the proposed approximation approaches are highly effective, which are capable of accurately predicting the BER of the THCLs supported by the different relay processing schemes.

Transmitter-Precoding-Aided Spatial Modulation Achieving Both Transmit and Receive Diversity

“…The situation becomes even worse when the TMMSE precoder is employed, as in this case v is more complicated than that in the TZF case. Therefore, in the case of finite N , we approximate η = v + w as a Gamma distributed random variable, i.e., Gammaapproximation (Gamma-Ap) 3 [48]. As shown in Section V of this paper, the Gamma-Ap is highly effective for performance evaluation.…”

“…However, their values can be readily obtained via numerical simulations. As shown in [48], about 10 4 channel realizations are usually sufficient for obtaining reliable estimations of m η and Ω η . Therefore, in our following studies, we use 10 4 Monte-Carlo simulations to estimate the parameters of the Gamma PDF of (39).…”

The Maximum-SNR Optimal Weighting Matrix for a Class of Amplify-and-Forward MIMO Relaying Assisted Orthogonal Space Time Block Coded Transmission

“…In order to circumvent this problem, we adopt a Gamma distribution to approximate the probability density function (PDF) of the received SNR r [20], [21]. Specifically, the PDF of SNR r is approximated as…”

“…In this case, we adopt a simulation based method to estimate these parameters [21]. It can be shown later in simulation results that the simulation based PDF Gamma approximation could be very accurate.…”

Performance Analysis of AF Relaying With Selection Combining in Nakagami-$m$ Fading

“…A Turbo code was applied in [5] for asymptotic outage probability in relay selection networks. The distributed relay processing, ideal centralized maximal ratio combining and centralized maximal ratio combining relay processing were employed in [6], which introduced Nakagami and Gamma distribution for approximate bit error rate of binary phase shift keying. Incremental DF and AF relaying were considered in [7] for analyzing the diversity multiplexing tradeoff.…”