Performance analysis of predetection EGC receiver in Weibull fading channel

The predetection equal gain combining (EGC) receiver is generally known to have a performance that is close to the maximal ratio combining (MRC) receiver while having relatively less implementation complexity. The bit error rate (BER) of an EGC receiver for binary, coherent and noncoherent modulations has been analysed for an independent Weibull fading channel. Numerical results have been compared with the available results for selection combining (SC) and MRC diversity receivers.     

Performance analysis of a predetection EGC receiver in exponentially correlated nakagami-m fading channels for noncoherent binary modulations

Average symbol error rate (ASER) of an equal gain combining (EGC) receiver with an arbitrary number of branches in exponentially correlated, Nakagami-m fading channels has been derived for binary, differential phase-shift keying (DPSK) and noncoherent frequency-shift keying (NCFSK) modulations. A Parseval's theorem based approach has been used. Numerical and simulation results have been found to be in close agreement. Results show that for a given ASER, as expected, exponentially correlated fading requires a higher SNR with respect to independent fading. For a given number of branches L, increase in SNR required (SNR penalty) with respect to independent fading is less for higher values of fading parameter m while for a given m, SNR penalty is more for higher L     

BER performance of dual predetection EGC in correlative Nakagami-m fading

In this letter, an approach to the evaluation of the error performance in dual predetection equal-gain combining (EGC) systems over correlated Nakagami-m fading channels is presented. Deriving an infinite series representation for the characteristic function of the sum of two correlated Nakagami-m variables, a closed-form formula is extracted for binary phase-shift keying and coherent binary frequency-shift keying, while several other modulation schemes are studied, capitalizing on a Parsevals's theorem-based approach, previously published. Numerical results and simulations are also presented to illustrate the proposed mathematical analysis and to point out the effect of the input signal-to-noise ratio unbalancing, the fading severity, and the fading correlation on the system's error performance.     

Closed-form analysis of dual-diversity equal-gain combining over Rayleigh fading channels

Starting with a new expression for the probability density function of the signal-to-noise ratio at the output of dual-diversity equal-gain combining (EGC) over Rayleigh channels, we provide closed-form expressions for the average bit and symbol error rate of M-ary phase-shift keying signals. Numerical examples indicate that EGC maintains a good diversity gain as long as the degree of unbalance is not very low but suffers a sharp and significant degradation when the degree of unbalance approaches zero.     

Analysis of a two-branch maximal ratio and selection diversitysystem with unequal SNRs and correlated inputs for a Rayleigh fadingchannel

An analytical expression for the probability density function of the signal-to-noise ratio (SNR) at the output of a two-branch maximal ratio and selection diversity system is given. The two branches are assumed to be Rayleigh fading, correlated, as well as of unequal average SNRs. Measurements of the cumulative distribution functions after selection and maximal ratio combining were made in Rayleigh fading channels and compared with the analytical results. Also presented are the exact analytical average probabilities of symbol error for coherent binary phase-shift keying and coherent quaternary phase-shift keying before and after two-branch maximal ratio combining for a slow and flat fading correlated Rayleigh channel     

Generation of correlated Rayleigh fading envelopes

A previous technique for generating correlated Rayleigh envelopes is generalized and physically interpreted to model specified propagation delay spread and frequency separation. Two accurate closed-form expressions that give explicitly the squared magnitude of the complex Gaussian cross-correlation coefficient in terms of the real envelope cross-correlation coefficient are derived to improve the efficiency and facility of the technique     

Interference of correlated radio signals with Rayleigh fading

Radio signals from various sources may be correlated due to propagation irregularities. Here, the probability that one signal exceeds another one at least p (protection-ratio) times is determined for the case when both signals are Rayleigh distributed and correlated. The closed-form result is exact and simple. Its applications in radiocommunication are discussed.     

Error rates of DPSK systems with MIMO EGC diversity reception over Rayleigh fading channels

This paper analyzes the average bit error probability (BEP) of the differential binary and quaternary phase-shift keying (DBPSK and DQPSK respectively) with multiple-input multiple-output (MIMO) systems employing postdetection equal gain combining (MIMO EGC) diversity reception over Rayleigh fading channels. Finite closed-form expressions for the average BEP of DBPSK and DQPSK are presented. Two approaches are introduced to analyze the error rate of DQPSK. The proposed structure for the differential phase-shift keying (DPSK) with MIMO EGC provides a reduced-complexity and low-cost receiver for MIMO systems compared to the coherent phase-shift keying system (PSK) with MIMO employing maximal ratio combining (MIMO MRC) diversity reception. Finally, a useful procedure for computing the associated Legendre functions of the second kind with half-odd-integer order and arbitrarily degree is presented.     

Performance analysis of L-branch equal gain combiners in equally correlated Rayleigh fading channels

Theoretical performance results for L-branch (L/spl ges/3) coherent equal-gain combining (EGC) in correlated fading channels are not known. This letter develops a novel approach for performance analysis of L-branch EGC in equally correlated Rayleigh fading channels. Such channel gains can be transformed into a set of conditionally independent channel gains. The cumulative distribution function (cdf) of the EGC output signal-to-noise ratio (SNR) is, therefore, derived. The symbol error rate (SER) of different modulation schemes with EGC in equally correlated Rayleigh fading channels is evaluated. Numerical results that illustrate the effects of equally correlated fading on the SER performance of EGC are also provided.     

Multiple-antenna capacity in correlated Rayleigh fading with channel covariance information

We analyze a mobile multiple input multiple output wireless link with M transmit and N receive antennas operating in a spatially correlated Rayleigh flat fading environment. Only the correlations between the channel coefficients are assumed to be known at the transmitter and the receiver. The channel coefficients are correlated in space and uncorrelated in time from one coherence interval to another. These coefficients remain constant for a coherence interval of T symbol periods after which they change to another independent realization according to the spatial correlation model. For this system we characterize the structure of the input signal that achieves capacity. The capacity achieving transmit signal is expressed as the product of an isotropically distributed unitary matrix, an independent nonnegative diagonal matrix and a unitary matrix whose columns are the eigenvectors of the transmit fade covariance matrix. For the case where the number of transmit antennas M is larger than the channel coherence interval T, we show that the channel capacity is independent of the smallest M-T eigenvalues of the transmit fade covariance matrix. In contrast to the previously reported results for the spatially white fading model where adding more transmit antennas beyond the coherence interval length (M>T) does not increase capacity, we find that additional transmit antennas always increase capacity as long as their channel fading coefficients are spatially correlated with the other antennas. We show that for fast hopping or fast fading systems (T=1) with only channel covariance information available to the transmitter and receiver, transmit fade correlations are beneficial. Mathematically, we prove this by showing that capacity is a Schur-convex function of the vector of eigenvalues of the transmit fade correlation matrix. We also show that the maximum possible capacity gain due to transmitter fade correlations is 10logM dB.     

Transmit diversity for arrays in correlated Rayleigh fading

Transmit diversity is usually presented for the case of independently faded channels. In this paper the structure of a linear transmitter that can be optimized for a Rayleigh-fading environment in which the fading may be correlated is derived. The transmitter achieves the best mix of array gain-obtained by beamforming, and diversity gain-obtained by using multiple transmit beamformers and space-time coding. The authors use a multiinput single output (MISO) transmitter and receiver structure to present a detailed performance analysis, that shows the array gain versus diversity gain tradeoff as the fading correlation changes. This analysis is validated by simulation results.     

Effects of carrier phase error on EGC receivers in correlated Nakagami-m fading

The effects of incoherently combining on dual-branch equal-gain combining (EGC) receivers in the presence of correlated, but not necessarily identical, Nakagami-m fading and additive white Gaussian noise are studied. Novel closed-form expressions for the moments of the output signal-to-noise ratio (SNR) are derived. Based on these expressions, the average output SNR and the amount of fading are obtained in closed-form. Moreover, the outage and the average bit error probability for binary and quadrature phase-shift keying are also studied using the moments-based approach. Numerical and computer simulation results clearly depict the effect of the carrier phase error, correlation coefficient, and fading severity on the EGC performance. An interesting finding is that higher values of the correlation coefficient results to lower irreducible error floors.     

The effect of having unequal branch gains practical predetection diversity systems for mobile radio

A review of practical predetection diversity techniques for mobile radio is presented. Theoretical carrier-to-noise distributions for selection combining, equal-gain combining, and maximal ratio combining in two-branch predection diversity systems are derived as a function of gain unbalance between branches. Experimental results are also presented from an equal-gain system, including predetection level statistics and post detection baseband average noise measurements as a function of gain unbalance. It was found that unbalances as high as 10 dB can be tolerated with equivalent input signal-to-noise degradations less than 3 dB for equal-gain and maximal ratio systems. Selection diversity degrades much faster than equal-gain or maximal ratio, but significant diversity improvement is given for unbalances less than 6 dB.     

Robust space-time codes for correlated Rayleigh fading channels

Space-time (ST) coding has emerged as an effective strategy to enhance performance of wireless communications in fading environments. Many different ST coding schemes have been proposed to achieve reliable communications in independent fading channels. However, a design of robust ST codes for correlated fading channels has not been addressed. We propose a simple robust ST coding scheme that achieves robust performance over a wide range of fading conditions. The key to achieve robust performance is to formulate code design criteria that are not dependent on the channel correlation statistics. A provably robust scheme can be formulated by concatenating a full-rank ST block code with an outer encoder. We derive several robust code examples via the concatenated orthogonal ST block code and TCM construction. The simulation results show that some traditional ST codes perform poorly, whereas the proposed codes achieve robust performance over a broad range of fading conditions.     

A trellis-coded DS-CDMA system in correlated Rayleigh fading channels

We present the trellis-coded code-division multiple-access (TC-CDMA) system based on a multisequence signaling, called orthogonal plane sequence modulation (OPSM), in correlated Rayleigh fading channels and derive its pairwise error probability with different degrees of channel state information. Numerical results show that the OPSM-based TC-CDMA system outperforms conventional convolutionally coded CDMA or TC-CDMA systems.     

Outage probability of MRC with equi-power cochannel interferers in correlated Rayleigh fading

The outage probability of maximal ratio combining (MRC) in the presence of cochannel interference (CCI) in correlated Rayleigh fading is derived. Under the assumption that the branch gains of the desired user signal and interfering signals have the same correlation matrix, this analysis allows an arbitrary number of cochannel interfering users and an arbitrary number of receiver antennas.     

Outage probability of MRC with unequal-power cochannel interferers in correlated Rayleigh fading

Under the assumption that the branch gains of the desired user signal and interfering signals experience Rayleigh fading and have the same correlation matrix, the outage probability of maximal ratio combining (MRC) in the presence of unequal-power cochannel interference (CCI) is derived for the two cases that the correlation matrix is equi-correlated and that the correlation matrix has different eigenvalues.     

The performance of a -steering beamformer in correlated Rayleigh fading

We consider the performance of a -steering adaptive beamformer in a distributed Rayleigh fading environment. To determine the beamformer coefficients, the signal and interference array response vectors must be estimated. An estimator that makes use of the knowledge of the spatial distribution of the signal is proposed and compared with other estimators that do not use this information. As the angular spread of the signal increases, the value of this information is reduced, until, for the case of isotropic scattering, the estimate that uses the spatial distribution is equivalent to the estimate that does not. Performance results are presented that compare the performance of the different estimators. We derive closed-form expressions for the signal-to-interference-plus-noise ratio (SINRO) and probability of error for the case where the training data are orthogonal.     

Generation of two equal power correlated Rayleigh fading envelopes

A procedure for generating two equal power Rayleigh-fading envelopes with any desired cross-correlation coefficient is given. Having this ability will aid researchers in simulating correlated fading envelopes, which can be used to study the impact of correlation on the performance of diversity systems