Error Performance Evaluation of Wireless Communication Systems Using Maximal Ratio Combining with Multiple Interferers

In this paper we evaluate the error performance of wireless communication systems using M-branch maximal ratio combining (MRC) with multiple cochannel interference. Three cochannel interference models are considered: (A) L independent identically distributed (i.i.d.) Nakagami-m cochannel interferers; (B) L independent cochannel interferers consisting of L-N Nakagami-m interferers and N Rayleigh interferers; (C) L independent cochannel interferers in which each interferer follows Nakagami-m distribution for a fraction of time and Rayleigh distribution for the remaining time. In addition, the desired signal assumes Nakagami-m fading. This paper considers that an exponential correlation model is assumed for the desired signals received on each branch, while the interferers are assumed independent. Closed-form expressions are derived for the probability density functions (PDFs) of the instantaneous signal-to-interference power ratio (SIR) at the output of the MRC for the three interference models. Using these SIR PDFs, further closed-form expressions to evaluate the outage probability (OTP) and the average bit error probability (BEP) of differential phase-shift keying (DPSK) are derived. Numerical results showing the impacts of the system parameters on the OTP and the average BEP are then presented.     

Finite-State Markov Chain Models for the Intensity of Nakagami Fading

For the design, analysis, and simulation of communication systems with Nakagami-m fading channels, it is very convenient to model the fading by finite-state Markov chains in which the states represent fade levels or signal-to-noise ratios in decibels. Our approach to the development of such Markov chain models is to work with the intensity of the fading process, which is proportional to the logarithm of squared envelope of the faded signal. We demonstrate that all the parameters of the Markov chains can be determined from the bivariate distribution of the intensity of the Nakagami-m fading process. Several analytical results are derived from the bivariate distribution of the intensity, including expressions for the chain’s transition probabilities for both adjacent and nonadjacent states and the asymptotic distribution of the intensity for deep fades. For several values of m, we verify the accuracy of our Markov chain models as simulation tools by comparisons of the state probabilities and level-crossing rates obtained from simulations of the Markov chain with those obtained from our analytical expressions.     

Capacity of correlative nakagami-m fading channels under adaptive transmission and maximal-ratio combining diversity technique

The study of channel capacity evaluation in conjunction with maximal ratio diversity-combining (MRC) is presented in this paper. Analysis of the capacity in correlative Nakagami-m fading channels is observed. Using the proposed fading model, the power and rate adaptation, constant transmit power, channel inversion with fixed rate and truncated channel inversion adaptation policies are analyzed. Our results show that the power and rate adaptation policy, being only slightly higher than capacity of constant transmit power policy, provides the highest capacity over the other adaptation policies. The results also show that truncated channel inversion adaptation policy is better alternative compared to complete channel inversion policy for all values of fading severity, diversity order and correlation coefficient.     

How significant is the assumption of the uniform channel phase distribution on the performance of spatial multiplexing MIMO system?

Spatial multiplexing (SMX) multiple-input multiple-output (MIMO) systems are promising candidates to enhance the achievable throughput and the overall spectral efficiency in future wireless systems. Performance studies of these systems over different channel conditions assume simplified models for the channel phase distribution. This paper highlights the impact of the channel phase distribution assumption on the performance of SMX MIMO systems. The Nakagami-m and the \(\eta -\mu\) fading channels are considered in this study. In existing literature, performance studies of SMX MIMO systems over Nakagami-m fading channel assume uniform phase distribution. Though, it has been reported recently that the Nakagami-m channel phase distribution is not uniform. In this article, we show that the assumption of the channel phase distribution has a major impact on the performance of SMX MIMO systems. The obtained results demonstrate that the performance of SMX MIMO systems significantly varies with different channel phase distributions. Furthermore, it is shown that uniform assumption of channel phase distribution is incorrect and leads to erroneous conclusions. Detailed performance analysis for more accurate channel models are provided and results are sustained through Monte-Carlo simulations.     

A semi-deterministic propagation model for predicting short-term fading statistics in urban environments based on the Nakagami-m distribution

In this paper, a semi-deterministic propagation model for predicting short-term fading statistics in urban environments is presented. An approach to include surface scattering into deterministic ray-optical propagation models in urban scenarios is derived. This approach considers the coherent and incoherent components of the scattered signal. A statistical characterisation of the received signal at the received position permits to model the short-term fading for a local area around the mobile position using the Nakagami-m distribution. The parameters of the Nakagami-m distribution are obtained taking into account the real environment from a digital map information of the urban area. Computer simulation results and experimental data are compared.     

Capacity of Dual Branch MRC System Over Correlated Nakagami-<Emphasis Type="Italic">m</Emphasis> Fading Channels-A Review

Various papers on the channel capacity using different diversity combining techniques and/or adaptive transmission schemes are available to enhance channel capacity under fading environment without the necessity of increasing bandwidth and transmit powers. This paper provides the review on the channel capacity of MRC (Maximal ratio combining) over uncorrelated and correlated Nakagami-m fading channels with m = 1 (Rayleigh fading channel) under ORA (Optimum rate adaptation with constant transmit power), CIFR (Channel inversion with fixed rate) and OPRA (Optimum power and rate adaptation) schemes. We also highlight the effect of fade correlation on channel capacity and discuss the improvement of the system performance under the different adaptive techniques.     

An Analytical Approach to Outage Analysis and Critical Cooperation Ratio in Coded Cooperation

In this paper, we analyze the performance of a coded cooperation based communication system using independent flat Nakagami-m fading channels. We examine the outage behavior of the cooperative system constrained on instantaneous received power which follows the Gamma distribution. The expression for outage probability of the coded cooperative communication system is derived which is applicable for arbitrary value of parameter m and contains single integral terms only. Finally, we present an analytical approach to evaluate the critical cooperation ratio that minimizes the total outage probability of the cooperative system.     

Performance modeling of finite state Markov chains for Nakagami-q and α–μ distributions over adaptive modulation and coding schemes

In this paper, performance modeling of finite state Markov chain (FSMC) for Nakagami-q and α–μ fading distributions over adaptive modulation and coding (AMC) schemes at the physical layer are discussed in detail, assuming that sufficient data is present to be transmitted continuously during the adaptive transmission period. However, this assumption is not always valid when queuing effects are taken into account at the data link layer. The received SNR obtained from a coded multiuser wireless system in the presence of a heavily shadowed environment is assumed to undergo a Nakagami-q (Hoyt distribution. Performance measures like level crossing rate, steady state probability, state transition probability and state time duration for Nakagami-q distribution and α–μ distribution are derived, plotted and analyzed. The BER for non-coherent FSK is shown to be much better than coherent FSK and PSK in the presence of Nakagami-q fading.     

Performance analysis of dual-hop fixed-gain AF relaying systems with OSTBC over Nakagami-m fading channels

In this paper, we present outage probability and symbol error rate (SER) performance analyses of a dual-hop transmission using fixed-gain amplify-and-forward relaying in flat Nakagami-m fading channels. The system under consideration is equipped with multiple antennas at source and destination adopting orthogonal space-time block coding to provide transmit diversity and maximum ratio combining to provide receive diversity, respectively. For integer and half-integer m values, closed forms of exact outage probability and moment generating function (MGF) expressions are derived through cumulative distribution function (CDF) of the overall system signal-to-noise ratio. Closed-form exact SER expressions based on the overall CDF are obtained for binary phase shift keying, binary frequency shift keying and M-ary pulse amplitude modulation. Exact SER expressions based on the MGF method are also obtained for binary differential phase shift keying, M-ary phase shift keying and M-ary quadrature amplitude modulation. Moreover, the asymptotic diversity order analysis is performed through derivations of asymptotic outage probability and SER. Theoretical analyses are validated by Monte Carlo simulations showing perfect match between each other.     

A comprehensive performance analysis of relay-aided CDMA communications over dissimilar fading channels

In this paper, bit error probability (BEP), outage probability (OP) and channel capacity (CC) of direct-sequence code-division multiple access systems with amplify-and-forward relaying are presented for different fading scenarios. In the first scenario, the source-destination link is assumed to experience Rayleigh fading while it is subject to Nakagami-m fading in the second scenario. The source-relay and relay-destination channels are considered to have Nakagami-m fading conditions in two scenarios. First, analytical expressions for the end-to-end probability density function (PDF) are derived by using the convolution integral. Then, BEP, OP and CC are obtained based on these PDFs in terms of infinite series. Truncation error analyses are presented for different parameter values in order to show that truncation error arising from the infinite series is negligible. Simple and easy-to-compute asymptotic expressions are also introduced for BEP and OP in order to simplify the performance analysis in high signal-to-noise ratio region. Simulation results are provided to show the accuracy of the proposed approximate and asymptotic expressions.     

BER of Differentially Detected π/4-DQPSK with Selection Combining in Nakagami-m Fading

Nakagami’s m distribution is a versatile statistical model to characterize small-scale multipath fading in wireless channels. On the other hand, selection combining (SC) is a widely practiced diversity technique to mitigate the detrimental effects of multipath fading. Thus, when SC is applied over Nakagami fading channel, the error performance improvement for any given modulation format is of considerable interest. Since the last decade, π/4-shifted differential quadrature phase shift keying (π/4-DQPSK) modulation has attracted much attention as it is used for high-capacity code division multiple access (CDMA) based digital cellular systems. One of the major reasons behind this is the provision for differential detection which allows production of low complexity mobile units. In this paper, we present analytical expressions for bit error rate (BER) of π/4-DQPSK modulation with L-branch SC diversity in Nakagami-m fading channels perturbed by additive white Gaussian noise (AWGN). The derived end expressions are in closed form and contain finite series of Gaussian hypergeometric function. This makes evaluation of error rates much more straightforward compared to earlier approaches that required single or even double numerical integration. Some special instances such as the nondiversity case and Rayleigh fading case are also investigated and plotted along with the main findings. For different fading parameter (m) values and for different diversity orders (L), simulated results are shown to be in excellent agreement with the derived analytical results. All the results are, however, limited to integer values of fading severity parameter m.     

Higher Order Capacity Statistics of Diversity Receivers

A statistical analysis for the channel capacity (CC) for several diversity receivers under optimal rate adaptation with constant transmit power is provided. Independent but not necessarily identically distributed Nakagami-m fading channels are considered. Specifically, the moments of the CC at the output of selection combining, maximal-ratio combining, and switched and stay combining are obtained, assuming integer-order fading parameters, while for the Rayleigh model the moments of the CC at the output of equal-gain combining and generalized-selection combining are derived in closed form. Using these formulas, a new performance criterion, namely as fading figure (FF) as well as the variance, skewness, and kurtosis, are studied. Our findings show that the FF improves with an increase of the signal-to-noise ratio (SNR), the fading parameters, and/or the diversity order. Also, unlike to the variance of the error probability, the variance of the CC is a monotonic function of the average input SNR.     

Performance Evaluation of Multiple-Cell DS-CDMA Systems Over Correlated Nakagami-<Emphasis Type="Italic">m</Emphasis> Fading Environments

In this paper, the impact of the branch correlation on the performance of multiple-cell DS-CDMA cellular systems over Nakagami-m fading channels with arbitrary branch correlation is investigated. The received multipath-faded signals are assumed to experience identical but non-independent correlated Nakagami-m channels within the reference cell. A new closed-form formula for the joint probability density function (joint pdf) of the diversity combiner with arbitrary correlation coefficients in terms of the generalized Laguerre polynomial and the new expressions of average bit-error rate (BER) for the DS-CDMA system are given in this paper. The results, which were also compared with the performance of the single cell environments, demonstrate that the BER is significantly dependent on the correlation characteristic of diversity branching for both single-cell and multiple-cell environments.Joy I. Z. Chen was born in Taiwan. He received his B.Sc degree in electronics engineering from the National Taiwan Technical University, Taipei, Taiwan, and M.Sc degree in electrical engineering from the Da Yeh University, Chung Hwa, Taiwan, in 1985 and 1995, respectively, and Ph.D. degree in electrical engineering from National Defense University, Tao-Yuan, Taiwan, in 2001.He is currently an assistant professor of Department of Communication Engineering, Da Yeh University at Chang-Hwa Taiwan. Prior to joining the Da Yeh University, he worked at the Control Data Company (Taiwan) as a technical manager since September 1985–September 1996. His research interests include wireless communications, communication theory, and spread spectrum technical.     

Capacity analysis of distributed antenna systems in MIMO Nakagami fading multicell environment

In this paper, the downlink capacity analysis of distributed antenna systems (DAS) with multiple receive antennas in Nakagami-m fading multicell environment is presented. According to the performance analysis, and using mathematical manipulation, we derive the probability density function (PDF) of the effective signal to interference plus noise ratio of the system. Based on the obtained PDF, an exact closed-form expression of DAS capacity is derived. This expression includes the existing capacity expression as a special case, and avoids the error in the latter. Thus, it can provide good theoretical performance evaluation for downlink DAS. Computer simulation shows that the theoretical analysis is in good agreement with simulation result. Moreover, the increase of receive antenna and/or Nakagami fading parameter m can improve the capacity effectively.     

Reliability of a jammed binary transmission over a Nakagami channel

This study presents a mathematic and numerical analysis of the probability of error in a binary transmission over a fading radio channel described by Nakagami-m distribution and its special cases. The transmission is jammed by a signal occupying the entire (or comparable) band before detection.     

Performance Analysis of Space-Time Block Codes with Transmit Antenna Selection in Nakagami-m Fading Channels

In this paper, multiple-input multiple-output systems employing space-time block codes (STBCs) with transmit antenna selection (TAS) are examined for flat Nakagami-m fading channels. Exact symbol error rate (SER) expressions for M-ary modulation techniques are derived by using the moment generating function based analysis method. In the SER analysis, the receiver is assumed to use maximal ratio combining whereas a subset of transmit antennas that maximizes the instantaneous received signal-to-noise ratio (SNR) is selected for STBC transmission. The analytical SER results are validated by Monte Carlo simulations. By deriving upper and lower bounds for SER expressions, it is shown that TAS/STBC schemes achieve full diversity orders at high SNRs.     

Comparative Performance Analysis of Multi-Antenna Regenerative Cooperative Relay in Nakagami-m Fading Channel

Performance of cooperative relay schemes employing infrastructure based fixed relays having multiple antennas, has been investigated. Closed form expressions of outage probability, bit error rate and throughput for such system have been derived for Nakagami-m fading channels, with integer values of m. Here, relay and destination may perform either maximum ratio combining or selection combining of the signals. Comparative performance analysis of all four possible combinations has been analyzed for various relay locations, different number of antennas on the relay, various transmission rate and different fading conditions.     

Performance Evaluation of Underlay Cognitive Multi-hop Networks Over Nakagami-m Fading Channels

We derive a closed-form bit error rate (BER) formula for underlay cognitive N-hop networks operated over Nakagami-m fading channels where N is the arbitrary integer. This formula is corroborated by Monte Carlo simulations and useful for evaluating the network performance under different parameters such as modulation level, path-loss, maximum transmit power, tolerable interference power level, fading model, and the number of hops. Numerical results illustrate that underlay cognitive multi-hop networks suffer a high error floor and the BER performance not only depends on the number of hops but also the network topology. For the linear network model, the higher the number of hops, the better the network performance.     

Performance analysis of modulation diversity with OSTBC transmission over Nakagami-m fading channels

In this paper performance of modulation diversity with multiple-input multiple-output transmission is studied over flat Nakagami-m fading channels with arbitrary fading parameter m. In the system, orthogonal space-time block coding and maximal ratio combining like combiner are used for transmission and reception, respectively. Exact pairwise error probability expression is derived to observe performance of the system. Moreover, in order to obtain the diversity order of the system, asymptotic pairwise error probability expression is also derived. Optimum rotation angles are analytically obtained for binary and quadrature phase shift keying modulations. Theoretical results are validated by Monte Carlo simulations.     

Performance Analysis of Smart Relaying with Equal Gain Combining

Relaying communications has been proposed as a way to provide spatial diversity. In general, one is interested in a relaying system that can achieve the maximal diversity order with a low system complexity. One enabling technique is equal gain combining (EGC) and its application in relaying systems is the main focus of this paper. In particular, the techniques of EGC and smart relaying are combined in the decode-and-forward (DF) processing method. It is shown that for a system with one relay and M-ary phase-shift-keying (M-PSK) modulation, maximal diversity orders of 2m and 2 are achieved over Nakagami-m and Hoyt fading environments, respectively. With K relays, simulation results suggest that the corresponding diversity orders are m(K?+?1) and (K?+?1).