Relay Advantage Criterion for Multihop Decode-and-Forward Relaying Systems

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

In this paper, symbol error probability (SEP) for generalized selection combining (GSC) reception of M-ary quadrature amplitude modulation (M-QAM) signals in a block frequency-flat Rayleigh fading channel is considered. The paper presents a closed-form approximate SEP expression for GSC reception of M-QAM signals in the fading channel. The SEP expression is explicit and simulation results validate that it is very accurate

In this work, we derive exact closed-form expressions for the average symbol error probability (SEP) of arbitrary rectangular quadrature amplitude modulation (QAM) when used along with orthogonal space-time block coding (OSTBC) over independent but not necessarily identically distributed multiple-input multiple-output (MIMO) Nakagami-m fading channels. The derived SEP expressions account for diversity branches which may exhibit identical or distinctive power levels while their associated Nakagami indexes can take arbitrary real values not less than 1/2. Our work extends previous results pertaining to the performance analysis of OSTBC using M-ary rectangular QAM over Rayleigh fading channels and M-ary square QAM over Nakagami-m fading channels. For a MIMO diversity system with n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> transmit and n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> receive antennas and a corresponding set of arbitrary real-valued Nakagami indexes, our rectangular QAM SEP results are expressed in terms of Lauricella's multivariate hypergeometric functions F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(L)</sup> and F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(L + 1)</sup> where L = n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> is the total number of diversity branches.

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.

The performance of generalized selection combining (GSC) diversity reception symbol error probability (SEP) of square M-ary quadrature amplitude modulation (M-QAM) signals over frequency-flat Rayleigh fading channels is investigated in this work. The combining techniques considered in this paper are maximum ratio combining and selection combining (SC). We present closed-form approximate expressions for the average combined signal-to-noise ratio (SNR) and SEP in the fading channel for M-QAM signal reception in the GSC using diversity pathways that are independently, identically distributed. The simulation results validate the SEP expressions and demonstrate that, for a given number of accessible diversity paths, combining the strongest paths results in the majority of the diversity gain, and that the SNR declines as the number of combined paths increases. On the other hand, the numerical results demonstrate that, for a certain number of combined paths, increasing the number of available diversity paths can lead to a significant performance improvement.

We consider a decode-and-forward (DF) cooperative relaying system where a source (S) and a single relay (R) use space shift keying (SSK) modulation for information transmission to the destination (D). Using the Euclidean distance between the SSK constellation points in the SD and RD links as the selection metric, selection combining (SC) can be used at D. Instead of SC, in order to take into account the average performance of SRD and SD links in the selection, scaled selection combining (SSC) is performed at D such that the selection metric in RD link is scaled by a factor $\alpha$ . The error performance of SSK DF SSC cooperative relaying is analyzed in this work. We derive the end-to-end symbol error probability (SEP) expression of the system in closed-form for binary SSK modulation and verify the results with simulation. Further we infer that SSK DF SSC system performs better than SSK system without cooperative relaying and SC in SSK DF cooperative relaying.

SEP of rectangular QAM in composite fading channels

This study investigates the performance of two-way decode-and-forward (DF) relaying networks, considering transmissions over independent but not necessarily identically distributed (i.n.i.d.) Rayleigh fading channels, in the presence of multiple co-channel interferers at both the relay and end-source nodes. Both asymmetrical and symmetrical cases, of whether the channels from source terminals to the relay are identically distributed or not, are considered. Specifically, closed-form expressions for the cumulative distribution function of the equivalent signal-to-interference-plus-noise ratio (SINR) in different cases are derived, based on which the exact symbol error probability (SEP) and the systems’ achievable rate are derived and analysed. Based on the analytic results, the authors study the impacts of system parameters, such as interference power and number of interferers on the performance of the system. Furthermore, the system behavior at high signal-to-noise ratio (SNR) values is studied via deriving the asymptotic SEP. The results of this study are attested through Monte Carlo simulations.

This paper analyzes the performance of multicarrier index modulation (MCIM) with greedy detection (GD) in a dual hop, multiple decode and forward (DF) relay network. We propose a novel partial relay selection (PRS) technique combined with index modulation and its energy detection. For performance analysis, we derive novel closed form solutions for both the average pairwise error probability (PEP) and the average symbol error probability (SEP) at the relays and destination over Nakagami-m fading channels. Unlike the information theoretical works, with presence of positive detection error in the relays, the derived expressions provide a useful insight into the error performance of PRS based MCIM in a multiple DF relay network under various fading conditions. Also, we address the impacts of both relays and different rates of sub-carrier index activation.

We analyze the problem of optimum combining with a single spatially correlated interferer in white Gaussian noise and Rayleigh fading by focussing on the conditional characteristic function (c.f.) of the combiner output signal-to-interference-plus-noise ratio, given the interference propagation vector. Unconditioning of this c.f. using the interference statistics, along with a finite-range integration, results in the symbol error probability (SEP) integral, which is a common integral factor to most digital-modulation schemes. We obtain an exact expression, partly in closed form, for the SEP integral. For the case of large values of average signal-to-noise ratio and signal-to-interference ratio per antenna element, we obtain closed-form asymptotic formulas for the SEP integral. Using the SEP integral, we can easily evaluate the symbol error performance of various modulation schemes. The correctness of our analytical results are verified by some numerical examples.

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.

This work presents a closed-form approximation to the symbol error probability (SEP) for cross-quadrature amplitude modulation (cross-QAM) schemes over κ–μ fading channels. The proposed formulation enables accurate performance evaluation while avoiding computationally expensive numerical integration. The analysis covers millimeter-wave (mmWave) frequencies at 55, 60, and 65 GHz, under both line-of-sight (LoS) and non-line-of-sight (nLoS) conditions, and for multiple transmitter–receiver polarization configurations. A key contribution of this work is the experimental validation of the theoretical expression with real channel-measurement data, which confirms the applicability of the κ–μ model in realistic mmWave scenarios. Furthermore, we perform a detailed parametric study to quantify the influence of κ and μ on adaptive modulation performance, providing practical insights for 5G and future 6G systems. The proposed framework bridges theoretical analysis and experimental validation, offering a computationally efficient and robust tool for the design and evaluation of advanced modulation schemes in generalized fading environments.

In this paper, the performance of diversity systems operating in flat double Hoyt fading channels is studied. A novel exact expression, in the form of double finite-range integrals, is derived for the moment generating function (MGF) of the instantaneous signal-to-noise ratio (SNR). Simplified expressions are extracted for various special cases of the underlying propagation model. By using a mixture gamma (MG) distribution in the form of triple finite sums, the probability density function (PDF) of the SNR under double Hoyt fading channels is first approximated. Capitalizing on this, an approximate closed-form expression is then derived for the corresponding MGF and its most important special cases. Furthermore, building on these results, exact and approximate solutions for the ergodic capacity (EC) and symbol error probability (SEP) of M-ary phase shift keying (MPSK) modulation schemes are studied for maximum ratio combining (MRC) diversity receivers. Additionally, a new approximate closed-form expression for the corresponding asymptotic SEP at high SNR is derived. Numerical and complementary simulation results demonstrate the validity of the obtained theoretical results as well as the accuracy of the approximations. The present study is relevant to the performance evaluation of multi-antenna wireless communication systems operating under multipath fading channels that are worse than double Rayleigh fading channels.

Based on the Moment Generating Function (MGF), we derive closed form expressions for the Average Symbol Error Probability (ASEP) and the outage probability of the adaptive Decode and Forward (DF) relaying over independent and identical (i.i.d) Generalized-K channels for BPSK modulated signals. This kind of channel model includes jointly multipath fading and shadowing. It is very versatile and accurately approximates many of the commonly used channel models as Nakagami-m, Log-Normal distributions. Simulation results are discussed and proved to be in good agreement with our theoretical analysis.

This paper is devoted to an investigation of an exact average symbol error probability (SEP) for amplify and forward (AF) relaying in independent Nakagami‐m fading environments with a nonnegative integer plus one‐half m, which covers many actual scenarios, such as one‐side Gaussian distribution (m = 0.5). Using moment generating function approach, the closed‐form SEP is expressed in the form of Lauricella multivariate hypergeometric function. Four modulation modes are considered: rectangular quadrature amplitude modulation (QAM), M‐ary phase shift keying (MPSK), M‐ary differential phase shift keying (MDPSK), and π/4 differential quaternary phase shift keying (DQPSK). The result is very simple and general for a nonnegative integer plus one‐half m, which covers the same range as integer m. The tightness of theoretical analysis is confirmed by computer simulation results.