Finite-SNR Diversity–Multiplexing Tradeoff for Correlated Rayleigh and Rician MIMO Channels

A nonasymptotic framework is presented to analyze the diversity-multiplexing tradeoff of a multiple-input-multiple-output (MIMO) wireless system at finite signal-to-noise ratios (SNRs). The target data rate at each SNR is proportional to the capacity of an additive white Gaussian noise (AWGN) channel with an array gain. The proportionality constant, which can be interpreted as a finite-SNR spatial multiplexing gain, dictates the sensitivity of the rate adaptation policy to SNR. The diversity gain as a function of SNR for a fixed multiplexing gain is defined by the negative slope of the outage probability versus SNR curve on a log-log scale. The finite-SNR diversity gain provides an estimate of the additional power required to decrease the outage probability by a target amount. For general MIMO systems, lower bounds on the outage probabilities in correlated Rayleigh fading and Rician fading are used to estimate the diversity gain as a function of multiplexing gain and SNR. In addition, exact diversity gain expressions are determined for orthogonal space-time block codes (OSTBC). Spatial correlation significantly lowers the achievable diversity gain at finite SNR when compared to high-SNR asymptotic values. The presence of line-of-sight (LOS) components in Rician fading yields diversity gains higher than high-SNR asymptotic values at some SNRs and multiplexing gains while resulting in diversity gains near zero for multiplexing gains larger than unity. Furthermore, as the multiplexing gain approaches zero, the normalized limiting diversity gain, which can be interpreted in terms of the wideband slope and the high-SNR slope of spectral efficiency, exhibits slow convergence with SNR to the high-SNR asymptotic value. This finite-SNR framework for the diversity-multiplexing tradeoff is useful in MIMO system design for realistic SNRs and propagation environments     

Polarization diversity measurements and analysis for antenna configurations at 1800 MHz

In wireless communication systems, multipath interference has a significant impact on system design and performance. Fast fading variations are caused by the coherent summation of multiple echoes from many reflection points reaching the receive antenna. Antenna diversity is one technique that can be used to overcome multipath fading. A test system used to measure the diversity performance of an antenna pair was used to experimentally determine the complex correlation coefficient between the two antenna branches. A local mean estimation algorithm based on the channel mean square error equalization was implemented. Thus, the two parameters that determine the expected diversity gain, i.e., the complex correlation coefficient and the mean level signal difference, were estimated. The test system was used to evaluate the polarization diversity performance of different antenna pairs in Rayleigh and Rician environments, both in the absence and in the presence of a human head phantom.     

Particle swarm optimization–based power allocation for Alamouti amplify and forward relaying protocol

The performance of wireless communication systems is improved over flat fading channel by using Alamouti coding scheme, which provides the quality of diversity gain. In this paper, performance analysis of symbol error rate (SER) and particle swarm optimization (PSO)–based power allocation (PA) for Alamouti amplify and forward (AF) relaying protocol using maximum ratio combining (MRC) technique is presented. Analytical expression of SER upper bound and SER approximation is derived for Alamouti AF relaying protocol with quadrature phase shift keying (QPSK) modulation over Rayleigh fading channel and Rician fading channel. In addition, PSO‐based optimum PA factor is calculated on the basis of the minimum SER of proposed method. PSO‐based optimum PA gives 0.5 dB of improved signal‐to‐noise ratio (SNR) compared with the equal power allocation (EPA). The theoretical approximate SER result is compared with the simulated SER. The proposed protocol provides full diversity gain and reduces SER compared with the existing AF and decode and forward (DF) relaying protocols over Rayleigh fading channel and Rician fading channel.     

Outage probability and error rate analysis of full duplex relay in asymmetric fading channels

Full duplex (FD) technique has evolved as a viable solution to address the spectrum scarce issue. It has gained research interest for its potential to double the wireless link capacity and enhance spectral efficiency (SE). In this paper, the end-to-end performance of an amplify-and-forward full duplex relay(FDR) in asymmetric Rayleigh–Rician fading channels is explored, unlike the other works that assume symmetric fading conditions in both the links. The asymmetric or mixed fading channels properly model the realistic communication scenarios like satellite/terrestrial wireless communication systems. In this work, we consider that the source-relay link experiences Rayleigh fading and the relay-destination link experiences Rician fading. The novel exact and lower bound closed form analytical expressions for outage probability (OP) and bit error rate (BER) for the considered FD system are derived. Moreover, the effect of severity of fading and the amount of residual self-interference (RSI) on the performance of FDR are also studied. In addition, MC simulations are carried out to validate the results. It is observed that the performance metrics, OP and BER, are highly dependent on the severity of fading and the amount of RSI. Furthermore, it is found that typically at the SNR of 10 dB, an improvement of approximately 27.6% in OP is obtained. Also, our work offers appreciable SNR gain, for example, for a BER of 10⁻², an SNR improvement of around 11 dB is achieved. These findings have been compared with the mixed Rayleigh–Rician fading channel conditions considering only half duplex(HD) mode. These parameter metrics are helpful in analyzing the performance of FD in various communication scenarios such as LoS/NLoS conditions and hence pave the way for more realistic FDR.     

BER assessment of FFT-OFDM against WHT-OFDM over different fading channel

Wavelets are brought into the wireless communication field as an orthogonal base of multi-carrier modulation and are now considered as a significant measure. Also, wavelets do contain the capability to improve bandwidth efficiency even more along with lower inter-symbol interference and inter-carrier interference. Appropriately, a BER versus SNR analysis is done for fast Fourier transform (FFT) based OFDM framework and wavelet haar transform (WHT) based OFDM framework in this work. The evaluationis demonstrated over Rayleigh and Rician fading channel utilizing dissimilar M-PSK modulation levels intended for FFT-OFDM and WHT-OFDM. The performance of the simulated test-bed is investigated via BER assessment as a function of SNR. The imitation outcome reports a significant improvement in BER of the simulated system using WHT-OFDM in comparison to FFT-OFDM for both Rayleigh and Rician fading channel. Also, the BER performance of both FFT-OFDM and WHT-OFDM is superior in Rician fading channel in comparison to Rayleigh fading channel.     

A Novel Method for Performance Analysis of OFDM Polarization Diversity System in Ricean Fading Environment

OFDM (Orthogonal Frequency Division Multiplexing) is proven to be a very effective modulation and multiple access technique that enables high data rate transmission. Due to its good performance it is already implemented in several standardized technologies, and it is very promising technique for the next generation wireless communication systems. Still, further system performance improvements under severe frequency selective fading conditions are necessary, and they can be obtained implementing diversity, at either transmit or/and receive end of a wireless link. Since polarization diversity can be realized using only one compact, dual polarized antenna, it can be considered as an attractive, space and cost effective solution. Analysis presented in this paper shows that implementation of dual polarized antenna at the receiver can lead to significant performance improvement, under certain propagation conditions. In order to calculate BER (Bit Error Rate) for the considered OFDM polarization diversity system with a certain level of the received signals correlation, we propose a novel analytical method. The obtained results are compared with the ones attained by simulation.     

Bit-error-probability for noncoherent orthogonal signals in fadingwith optimum combining for correlated branch diversity

Due to the interest in wireless personal communications, there has been a lot of research on the performance of receivers with diversity. Most analyses assume the diversity branches are independent. This paper presents an analysis of the bit-error probability for receivers in which the diversity branches are correlated. Noncoherent orthogonal digital modulation (NCODM) with Rician and Rayleigh slow, nonselective fading models are assumed. Through the use of the diagonalization of quadratic forms, most of the calculations of the bit-error probability can be reduced to a two-dimensional numerical integration. For some cases for dual diversity, a closed-form expression for the error probability is given. A number of diversity combining laws, including square law and maximum likelihood, are considered. We find that Rician fading can be worse than Rayleigh fading in correlated diversity environments, a situation quite different from the independent diversity case. Also, for the Rayleigh fading model with correlated branch diversity, we find that an equal-weight, square-law combiner usually has the same error performance as the more complex maximum-likelihood combiner. However, this is not the case for a Rician fading model with the same correlation environment. Simple diagonalization methods that compensate for the lossy effect of correlation are specified and found to be effective when the dominant noise and interference have almost the same correlation distribution as the fading signals     

Microdiversity on Rician fading channels

The performance of an L-branch equal gain (EG) combiner on slow and nonselective Rician fading channels is analyzed. Two performance criteria are considered; the probability distribution of signal-to-noise power ratio (SNR) at the output of the EG combiner and the average bit error rate (BER). Matched filter receivers are considered for two binary modulation formats, coherent phase shift keying (CPSK) and noncoherent frequency shift keying (NCFSK). Results using both maximal ratio combining (MRC) and selection diversity combining (SC) are presented for comparison. Our results show that from a feasibility and practical tradeoffs point of view, the performance of an EG combiner may be as good as that of a MR combiner. The effects of gain unbalance between branches of the EG combiner on the probability distribution of SNR and on the bit error rates are also investigated. The Rician fading model may be used to model bath the microcellular environment and the mobile satellite fading channel. Hence, the results of this paper may be useful in both of these areas. Furthermore, in the development of the analysis, we present an efficient method for computing the distribution of sums of Rician random variables. This may be useful for other problems involving Rician fading. The suitability of modeling a Rician fading environment by a properly chosen Nakagami model is examined. A formula for determining the corresponding values of Rician parameter K and Nakagami parameter m is also assessed     

Moment analysis of the equal gain combiner output in equally correlated fading channels

Moments of the multibranch equal gain combiner (EGC) output signal-to-noise ratio (SNR) are only known for independent fading channels or exponentially correlated Nakagami-m fading channels. In this paper, we derive the moments of the EGC output SNR in equally correlated Rayleigh, Rician, and Nakagami-m fading channels. Our moment expressions can be used to evaluate the outage and the average error rate as well as purely moments-based measures such as the average output SNR and the amount of fading as functions of the fading correlation. Numerical results that illustrate the effect of fading correlation on the distribution of the EGC output SNR are also provided.     

Spatial, polarization, and pattern diversity for wireless handheldterminals

This paper examines the antenna diversity configurations that improve the performance in handheld radios. Experiments using spatial, polarization, and pattern diversity were conducted for both line-of-sight (LOS) and obstructed outdoor and indoor multipath channels that experienced Ricean fading. Antenna separation, polarization, and pattern were varied independently to the extent possible. Envelope correlation, power imbalance, and diversity gain were calculated from the measurements. Diversity performance is measured by diversity gain, which is the difference in signal-to-noise ratio (SNR) between the output of a diversity combiner and the signal on a single branch, measured at a given probability level. Diversity gain increases with decreasing envelope correlation between the antenna diversity branches. However, diversity gain decreases as the power imbalance between diversity branches increases because a branch that has a weak signal has only a small contribution to the combined signal. Diversity gain values of 7-9 dB at the 99% reliability level were achieved in non-line-of-sight (NLOS) channels for all diversity configurations even with very small antenna spacings. The use of polarization diversity reduced polarization mismatches, improving SNR by up to 12 dB even in LOS channels     

Performance Analysis of the Dual-Hop Asymmetric Fading Channel

In real wireless communication environments, it is highly likely that different channels associated with a relay network could experience different fading phenomena. In this paper, we investigate the end-to-end performance of a dualhop fixed gain relaying system when the source-relay and the relay-destination channels experience Rayleigh/Rician and Rician/Rayleigh fading scenarios respectively. Analytical expressions for the cumulative distribution function of the end-to-end signal-to-noise ratio are derived and used to evaluate the outage probability and the average bit error probability of M-QAM modulations. Numerical and simulation results are presented to illustrate the impact of the Rician factor on the end-toend performance. Furthermore, these results confirm that the system exhibits an improved performance in a Rician/Rayleigh (source-relay link/relay-destination link) environment compared to a Rayleigh/Rician environment.     

Capacity of an FH-SSMA system in different fading environments

The capacity of a previously proposed frequency-hopped spread-spectrum multiple-access system (FHSSMA) is evaluated under three types of fading, namely, Rician, shadowed Rician, and Nakagami fading. The results of experiments have indicated that these fading phenomena occur in various environments, where the FH-SSMA system may be implemented. This paper presents the derivation of the deletion probability for each type of fading and analyzes the system capacity in terms of the maximum number of users versus the average bit-error rate (BER). The effect of a change in the signal-to-noise ratio (SNR) level on the system capacity is also demonstrated. For Rician fading, we find that the capacity of the system with a Rician factor of 2 dB is reduced by 13% as compared to the capacity for the nonfading case. For shadowed Rician fading, three shadowing scenarios are considered: light, average, and heavy. It is shown that the light and average shadowing scenarios provide only a slight decrease in the capacity, while the heavy shadowing scenario renders a capacity identical to that for the Rayleigh fading case. Finally, for Nakagami fading, the capacity is found to decrease by 50% as the fading parameter is reduced to 0.5     

Doppler Spread Estimation for Broadband Wireless OFDM Systems Over Rician Fading Channels

In this paper, we present a new Doppler spread estimation algorithm for broadband wireless orthogonal frequency division multiplexing (OFDM) systems with fast time-varying and frequency-selective Rayleigh or Rician fading channels. The new algorithm is developed by analyzing the statistical properties of the power of the received OFDM signal in the time domain, thus it is not affected by the influence of frequency-domain inter-carrier interference (ICI) introduced by channel variation within one OFDM symbol. The operation of the algorithm doesn’t require the knowledge of fading channel coefficients, transmitted data, or signal-to-noise ratio (SNR) at the receiver. It is robust against additive noise, and can provide accurate Doppler spread estimation with SNR as low as 0 dB. Moreover, unlike existing algorithms, the proposed algorithm takes into account the inter-tap correlation of the discrete-time channel representation, as is the case in practical systems. Simulation results demonstrate that this new algorithm can accurately estimate a wide range of Doppler spread with low estimation latency and high computational efficiency.     

Multiple hops/symbol FFH-SSMA with MFSK modulation and Reed-Solomoncoding for indoor radio

A multiple-hopes-per-symbol fast-frequency-hopped spread-spectrum multiple-access (FFH-SSMA) system for indoor radio communication is treated. The data are Reed-Solomon (RS) encoded and then modulate a carrier by means of M-ary frequency-shift-keying (MFSK) The indoor radio channel is described as a multipath (Rayleigh or Rician) slowly fading channel. The receiver uses predetection diversity by linearly combining the squared enveloped of the different hops of the same MFSK symbol. The bit error rate (BER) performane is evaluated, and how the performance is influenced by various parameters, such as the number of hops per symbol, the size of the symbol alphabet, the ratio of specular power to fading power, and the ratio of nonreference user power to reference user power, is investigated     

带有分集的RS码非相干混合DS-SFH扩频通信系统性能分析

本文针对部分带宽噪声干扰、多址干扰和高斯白噪声等多种干扰以及Ｒｉｃｉａｎ信道衰落存在环境下,编码与非编码的异步非相干ＭＦＳＫ调制混合ＤＳ－ＳＦＨ扩频通信系统性能进行了分析、计算和比较。本文分析的编码为前向纠错编码,包括ＲＳ（Ｎ,Ｋ）码,带有分集的ＲＳ（Ｎ,Ｋ）码。与此同时分析和讨论了分集、Ｒｉｃｉａｎ衰落以及部分带宽噪声干扰、多址干扰等对系统性能的影响,得到一些重要结果。     

Performance of polarization diversity in correlated nakagami-m fading channels

This paper analyzes the performance of systems with dual-polarized antennas in correlated Nakagami-m fading channels as a function of envelope correlation and cross-polarization discrimination by means of the characteristic function of the instantaneous post-maximal ratio combining (MRC) signal-to-noise ratio (SNR). Systems of interest include systems with receive polarization diversity and systems with transmit and receive polarization diversity employing Alamouti space-time code. The expressions for the average symbol error probability as a function of SNR assuming no power control, and the expressions for the average required transmit power to achieve the constant desired post-MRC SNR assuming perfect fast power control, are derived. Finally, a comparison between analytical and simulation results is used to validate the analysis.     

Capacity Performance of Polarized Distributed MIMO System on Rician Channel

The analytical upper bound and lower bound on the ergodic capacity of polarized distributed antenna system and their relation with antenna polarization on Rician channel are deduced by applying properties of complex non-central Wishart matrices and matrix-variate non-central quadratic forms. Compared to the related studies, our analysis is extended to account for the polarized distributed system with Rician fading where a line-of-sight component exists and both ends are affected by spatial correlation. The antenna polarization has some impacts on the capacity bounds according to the expressions of capacity bounds. Both the transmitter and the receiver are equipped with multiple polarization antennas, and the transmitters are of linear layout. A power allocation scheme based on the path loss fading is presented by maximizing the capacity upper bound. The power allocation scheme is feedback efficient compared with those power allocation schemes based on statistical parameters of the channel which need a large amount of feedback. In the simulations, the ergodic capacity of polarized distributed MIMO is analyzed. Comparisons are taken on the effects of angle spread, Rician factor and power on the ergodic capacity. The proposed power allocation scheme is superior to the equal power allocation scheme and has very close performance to the optimal power allocation scheme.     

Spectral efficiency of dual diversity selection combining schemes under correlated Nakagami-0.5 fading with unequal average received SNR

The spectral efficiency results for different adaptive transmission schemes over correlated diversity branches with unequal average signal to noise ratio (SNR) obtained so far in literature are not applicable for Nakagami-0.5 fading channels. In this paper, we investigate the effect of fade correlation and level of imbalance in the branch average received SNR on the spectral efficiency of Nakagami-0.5 fading channels in conjunction with dual-branch selection combining (SC). This paper derived the expressions for the spectral efficiency over correlated Nakagami-0.5 fading channels with unequal average received SNR. This spectral efficiency is evaluated under different adaptive transmission schemes using dual-branch SC diversity scheme. The corresponding expressions for Nakagami-0.5 fading are considered to be the expressions under worst fading conditions. Finally, numerical results are provided to illustrate the spectral efficiency degradation due to channel correlation and unequal average received SNR between the different combined branches under different adaptive transmission schemes. It has been observed that optimal simultaneous power and rate adaptation (OPRA) scheme provides improved spectral efficiency as compared to truncated channel inversion with fixed rate (TIFR) and optimal rate adaptation with constant transmit power (ORA) schemes under worst case fading scenario. It is very interesting to observe that TIFR scheme is always a better choice over ORA scheme under correlated Nakagami-0.5 fading channels with unequal average received SNR.     

Performance analysis of generalized-faded coherent PSK channels with equal-gain combining and carrier phase error

A new method is developed to analyze the performance of partially coherent PSK systems in wireless channels with equal-gain combining diversity receiver. Two performance criteria are considered: the average bit error probability and the probability distribution of the combiner SNR (SNR reliability). Tikhonov-distributed phase error processes are assumed and generalized fading channels including Rayleigh, Rician, and Nakagami-m are investigated. We evaluate the detection loss suffered by the carrier recovery for different SNR reliability levels when BPSK and QPSK systems are used in wireless channels. The analysis is based on a convergent infinite series for the distribution of the sum of random variables. The convergence rate of the proposed series is investigated and the analytical results are presented along with providing results obtained by simulation.     

Exact error performance of square orthogonal space- time block coding with channel estimation

Consider a wireless communication system in flat fading with N transmit and M receive antennas using space-time block coding, where N/spl times/1 code vectors are transmitted over L symbol intervals, resulting in an N/spl times/L code matrix. A least-squares estimate (LSE) as well as a minimum mean-square estimate (MMSE) of the M/spl times/N channel matrix is obtained from a sequence of pilot code vectors. For the case of linear square (i.e., with N=L) orthogonal codes over constant envelope constellations, we obtain an expression for the exact decoding error probability (DEP) for coherent maximum-likelihood decoding. We also find the coding gain for high average signal-to-noise ratio (SNR) per diversity branch in the case of Rayleigh fading. A comparison between both channel-estimation techniques is done in terms of the average pilot-power-to-signal-power ratio (APPSPR). It is found that MMSE requires lower pilot power than LSE for the same DEP and the same average SNR per diversity branch. In addition, the error performance with LSE approaches that with MMSE, with an increase of average SNR per branch or an increase of APPSPR.