An efficient approximation to the correlated Nakagami-m sums and its application in equal gain diversity receivers

There are several cases in wireless communications theory where the statistics of the sum of independent or correlated Nakagami-m random variables (RVs) is necessary to be known. However, a closed-form solution to the distribution of this sum does not exist when the number of constituent RVs exceeds two, even for the special case of Rayleigh fading. In this paper, we present an efficient closed-form approximation for the distribution of the sum of arbitrary correlated Nakagami-m envelopes with identical and integer fading parameters. The distribution becomes exact for maximal correlation, while the tightness of the proposed approximation is validated statistically by using the Chi-square and the Kolmogorov-Smirnov goodness-of-fit tests. As an application, the approximation is used to study the performance of equal-gain combining (EGC) systems operating over arbitrary correlated Nakagami-m fading channels, by utilizing the available analytical results for the error-rate performance of an equivalent maximal-ratio combining (MRC) system

Erasure Insertion in RS-Coded SFH MFSK Subjected to Tone Jamming and Rayleigh Fading

The achievable performance of Reed Solomon (RS) coded slow frequency hopping (SFH) assisted M-ary frequency shift keying (MFSK) using various erasure insertion (EI) schemes is investigated, when communicating over uncorrelated Rayleigh fading channels in the presence of multitone jamming. Three different EI schemes are considered, which are based on the output threshold test (OTT), on the ratio threshold test (RTT) and on the joint maximum output-ratio threshold test (MORTT). The relevant statistics of these EI schemes are investigated mathematically and based on these statistics, their performance is evaluated in the context of error-and-erasure RS decoding. It is demonstrated that the system performance can be significantly improved by using error-and-erasure decoding invoking the EI schemes considered. Index Terms—Tone jamming, OTT, RTT, MO-RTT, SFH, error-and-erasure decoding (EED)

Error Analysis of Fixed-Gain AF Relaying with MRC Over Nakagami-m Fading Channels

This article investigates the error performance of wireless communication systems that employ binary modulations and Amplify-and-Forward (AF) relaying over flat Nakagami-m faded links with maximum ratio combining (MRC) at destination. Specifically, we derive a simple yet accurate closed-form approximation for the average bit error probability (ABEP) and closed-form expressions for its tight upper and lower bounds. The effect of power imbalance between the relayed links is also studied. Numerical investigations show good agreement between proposed theoretical results and simulations whereas our performance bounds are shown to be tighter than previously proposed bounds for the case of unbalanced relayed links

A General Framework for Performance Analysis of Space Shift Keying (SSK) Modulation for MISO Correlated Nakagami-m Fading Channels

International audienceIn this paper, we offer an accurate framework for analyzing the performance of wireless communication systems adopting the recently proposed Space Shift Keying (SSK) modulation scheme. More specifically, we study the performance of a Nt×1 MISO (Multiple–Input–Single–Output) system setup with Maximum–Likelihood (ML) detection and full Channel State Information (CSI) at the receiver. The exact Average Bit Error Probability (ABEP) over generically correlated and non–identically distributed Nakagami–m fading channels is computed in closed–form when Nt=2, while very accurate and asymptotically tight upper bounds are proposed to compute the ABEP when Nt>2. With respect to current literature, our contribution is threefold: i) the ABEP is computed in closed–form without resorting to Monte Carlo numerical simulations, which, besides being computationally intensive, only yield limited insights about the system performance and cannot be exploited for a systematic optimization of it, ii) the framework accounts for arbitrary fading conditions and is not restricted to identically distributed fading channels, thus offering a comprehensive under standing of the performance of SSK modulation over generalized fading channels, and iii) the analytical framework could be readily adapted to study the performance over generalized fading channels with arbitrary fading distributions, since the Nakagami–m distribution is a very flexible fading model, which either includes or can closely approximate several other fading models. Numerical results show that the performance of SSK modulation is significantly affected by the characteristics of fading channels, e.g., channel correlation, fading severity, and power imbalance among the Nt transmit–receive wireless links. Analytical frameworks and theoretical findings are also substantiated via Monte Carlo simulations

Experimental and Analytical Investigations of an Optically Pre-Amplified FSO-MIMO System With Repetition Coding Over Non-Identically Distributed Correlated Channels

This paper presents theoretical and experimental bit error rate (BER) results for a freespace optical (FSO) multiple-input-multiple-output system over an arbitrarily correlated turbulence channel. We employ an erbium-doped fiber amplifier at the receiver (Rx), which results in an improved Rx’s sensitivity at the cost of an additional non-Gaussian amplified spontaneous emission noise. Repetition coding is used to combat turbulence and to improve the BER performance of the FSO links. A mathematical framework is provided for the considered FSO system over a correlated non-identically distributed Gamma-Gamma channel; and analytical BER results are derived with and without the pre-amplifier for a comparative study. Moreover, novel closed-form expressions for the asymptotic BER are derived; a comprehensive discussion about the diversity order and coding gain is presented by performing asymptotic analysis at high signal-tonoise ratio (SNR). To verify the analytical results, an experimental set-up of a 2 × 1 FSO-multiple-inputsingle-output (MISO) system with pre-amplifier at the Rx is developed. It is shown analytically that, both correlation and pre-amplification do not affect the diversity order of the system, however, both factors have contrasting behaviour with respect to coding gain. Further, to achieve the target forward error correction BER limit of 3.8 × 10−3 , a 2 × 1 FSO-MISO system with a pre-amplifier requires 6.5 dB lower SNR compared with the system with no pre-amplifier. Moreover, an SNR penalty of 2.5 dB is incurred at a higher correlation level for the developed 2×1 experimental FSO set-up, which is in agreement with the analytical findings

Performance analysis of wireless relay systems

There has been phenomenal interest in applying space-time coding techniques in wireless communications in the last two decades. In general, the benefit of applying space-time codes in multiple-input, multiple-output (MIMO) wireless channels is an increase in transmission reliability or system throughput (capacity). However, such a benefit cannot be obtained in some wireless systems where size or other constraints preclude the use of multiple antennas. As such, wireless relay communications has recently been proposed as a means to provide spatial diversity in the face of this limitation. In this approach, some users or relay nodes assist the transmission of other users’ information. This dissertation contributes to the advancement of wireless relay communications by investigating the performance of various relaying signal processing methods under different practical fading environments. In particular, it examines two main relaying methods, namely decode-and-forward (DF) and amplify-and-forward (AF). For DF, the focus is on the diversity analysis of relaying systems under various practical protocols when detection error at relays is taken into account. In order to effectively mitigate the phenomenon of error propagation, the smart relaying technique proposed by Wang et al. in [R1] is adopted. First, diversity analysis of a single-relay system under the scenario that only the relay is allowed to transmit in the second time slot (called Protocol II) is carried out. For Nakagami and Hoyt generalized fading channels, analytical and numerical results are provided to demonstrate that the system always obtains the maximal diversity when binary phase shift keying (BPSK) modulation is used. Second, a novel and low-complexity relaying system is proposed when smart relaying and equal gain combing (EGC) techniques are combined. In the proposed system, the destination requires only the phases of the channel state information in order to detect the transmitted signals. For the single-relay system with M-ary PSK modulation, it is shown that the system can achieve the maximal diversity under Nakagami and Hoyt fading channels. For the K-relay system, simulation results suggest that the maximal diversity can also be achieved. Finally, the diversity analysis for a smart relaying system under the scenario when both the source and relay are permitted to transmit in the second time slot (referred to as Protocol I) is presented. It is shown that Protocol I can achieve the same diversity order as Protocol II for the case of 1 relay. In addition, the diversity is very robust to the quality of the feedback channel as well as the accuracy of the quantization of the power scaling implemented at the relay. For AF, the dissertation considers a fixed-gain multiple-relay system with maximal ratio combining (MRC) detection at the destination under Nakagami fading channels. Different from the smart relaying for DF, all the channel state information is assumed to be available at the destination in order to perform MRC for any number of antennas. Upperbound and lowerbound on the system performance are then derived. Based on the bounds, it is shown that the system can achieve the maximal diversity. Furthermore, the tightness of the upperbound is demonstrated via simulation results. With only the statistics of all the channels available at the destination, a novel power allocation (PA) is then proposed. The proposed PA shows significant performance gain over the conventional equal PA