Outage probability in the presence of correlated lognormal usefuland interfering components

In many modern wireless communications systems (e.g., in OFDM based digital audio broadcasting/digital video broadcasting (DAB/DVB), CDMA) the received signal can be a superposition of multiple useful and interfering lognormal components, and correlation may exist between the components. We propose a simple method for estimating the correlation coefficient between the total useful and total interfering signals as the function of the correlation between the individual components. We show that, by taking into account this correlation factor in the derivation of the distribution of the signal-to-interference ratio, considerable accuracy improvement can be achieved in the outage probability estimation     

Outage probability for optimum combining of arbitrarily faded signals in the presence of correlated Rayleigh interferers

Exact outage-probability analysis for optimum combining of arbitrarily faded signals in the presence of correlated Rayleigh-faded interferers is not available in the literature. In this paper, we show that the conditional probability density of the reciprocal of the instantaneous signal-to-interference ratio (SIR), given the signal vector, can be represented as the higher order derivative of a simple exponential function in signal power whereby generic formulas for the outage probability and probability density function related to SIR can be determined. The new formulas take simple closed form in terms of the characteristic function of the signal vector. They are, therefore, widely applicable, leading to various results for correlated Rayleigh-, Rician-, and Nakagami-faded signals. Numerical examples are also presented for illustration.     

Outage probabilities of diversity cellular systems with cochannelinterference in Nakagami fading

Analytical, closed-form expressions for cellular outage probabilities in generalized Nakagami fading are derived for three practical diversity combining schemes. The outage is defined as the probability that the signal-to-interference power ratio (SIR) is less than a power protection ratio. The analysis considers L-branch equal gain (EG), selection (SC), and switched (SW) diversity combining schemes. The analyses are not limited to a single interferer, but rather assume the presence of multiple independent cochannel interferers. Previous results have used some approximations to study the performance of the EG combiner. A precise method is used to analyze the performance of an L-branch EG combiner. Selection diversity combining using the total power algorithm, the desired power algorithm, and the signal-to-interference power algorithm is analyzed. The effects of diversity on the reuse factor and on the spectrum efficiency of cellular mobile radio systems are considered in detail. The results for the Rayleigh fading channel are obtained and presented as a special case of the generalized Nakagami fading model     

Outage probabilities of cellular mobile radio systems with multipleNakagami interferers

Closed-form expressions for outage probabilities of mobile radio channels experiencing multiple, cochannel, independent Nakagami interferers are derived. This is done for the case of Nakagami fading alone with an arbitrary number of interferers. Analytical results for the case of Nakagami fading combined with log-normal shadowing are obtained for a single interferer. The case of multiple shadowed interferers is examined by simulation. The fading severity parameter in the Nakagami distribution may be varied to model different fading conditions. Interferers with similar and different Nakagami statistics are analyzed. The probability of cochannel interference is related to the reuse distance, which is one of the key parameters in the design of cellular mobile radio systems. In addition, the effects of specifying a minimum signal power requirement for satisfactory reception are investigated. A number of system examples that illustrate applications of the results are included     

Outage probability of dual-branch coherent equal-gain combining in correlated Nakagami-m fading

The exact outage probability of mobile radio receivers using dual-branch coherent equal-gain combining is analytically derived for correlated Nakagami-m fading. Expressions in the form of infinite series are obtained for the two cases of identical parameters on both diversity branches, and identical m-parameters (multiples of a half-integer) but not-necessarily identical fading powers on each branch.     

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.     

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 SC receiver over exponentially correlated K fading channels

A mathematical expression for the outage probability of a selection combining diversity receiver with an arbitrary number of input branches is presented for exponentially correlated K fading channels. Numerical and simulation results are plotted and the effect of correlation, number of diversity branches and fading parameter on the outage performance of the receiver is studied. Results suggest that a correlation coefficient less than 0.5 may be used in practice.     

Outage probability of dual-branch diversity systems in presence of co-channel interference

Outage probability of two low-complexity dual-branch diversity schemes with the consideration of both minimum carrier-to-interference ratio and the carrier-to-noise ratio constraints is investigated. More specifically, closed-form expressions for this outage probability for selection combining and switch and stay combining in single-interferer Rayleigh fading environment are derived, first under the assumption of perfectly estimated independent diversity paths, then by taking into account the effect of branch correlation and outdated/imperfect channel estimates. When applicable, the results obtained as special cases of the offered generic closed-form expressions are compared with those previously reported in the literature. In addition, some numerical examples are provided and discussed.     

Outage performance for maximal ratio combiner in the presence of unequal-power co-channel interferers

Outage probability for maximal ratio combining (MRC) is usually tackled in the framework of Rayleigh or Nakagami faded co-channel interferers with equal power, which allows for the treatment of the total interference power as a single gamma distributed variable to simplify the analysis. The more general case with unequal-power co-channel interferers is formulated and solved differently in this paper ending up with simple closed-form solutions for Rician/Rayleigh and Nakagami/Rayleigh channel models.     

Evaluation of error probabilities in the presence of timing errors and fading

Using the approximate Fourier series technique we obtain expressions for the probability of error for bandlimited BPSK signalling in the presence of timing errors and fading. The derived results can be used to compute the error probabilities to any desired accuracy for Nakagami-m and Weibull fading channels. The effect of timing error on the performance of the raised cosine pulse has been evaluated for several fading parameters. We also compare the performance of some useful Nyquist pulses known     

Quick simulation of detector error probabilities in the presence ofmemory and nonlinearity

One would like to compare and analyze digital communication systems based upon their overall probability of error. Unfortunately, easily evaluated closed form expressions for these probabilities are almost impossible to derive due to the complexity of the stochastic systems usually encountered. Hence, one must often resort to simulation to obtain the desired quantities. The most obvious technique is Monte Carlo simulation, which directly counts the number of errors in repeated trials. The problem is that error probabilities are usually quite small, requiring numerous simulation runs to sufficiently “hit” the rare event to gain adequate knowledge of its statistics. This places severe demands on the computer's random number generator. Importance sampling strategies simulate under altered input signal distributions (e.g., translation or stretching) so as to “speedup” convergence of the error estimators. The authors discuss a speedup technique termed quick simulation based upon results in large deviation theory. The quick simulation method is shown to compare favorably with three other importance sampling techniques for simulating a simple nonlinear system with memory     

Outage probability of cellular radio systems using maximal ratiocombining in the presence of multiple interferers

In mobile radio systems, antenna diversity is used to combat fading and reduce the impact of cochannel interference. We derived a new expression for probability density functions of the signal-to-interference-plus-noise ratio and apply it to analyze the outage probability (OTP) for a maximal ratio combining diversity system when multiple cochannel interferers are present. Numerical results showing the impact of the number of antenna elements, the number of cochannel interferers, and signal-to-noise ratio on the OTP are presented. Simulation results validating the analytical results are also presented     

Outage probability of mimo optimum combining in presence of unbalanced co-channel interferers and noise

This paper studies the performance of multiple-input-multiple-output (MIMO) systems with optimum combining in the presence of both co-channel interference (CCI) and noise. We assume that both desired and CCI users are subject to Rayleigh fading and allow the number of CCI users to be arbitrary and their short-term average powers to be non-identical. Given these assumptions, we derive exact results on the cumulative distribution function (CDF) of the output signal-to-interference-plus-noise ratio (SINR), or equivalently, the outage probability of this MIMO optimum combining scheme. Finally, we present and discuss some numerical examples to validate our analytical expressions and to show the effect of CCI on the performance of MIMO optimum combining systems     

Effect of macrodiversity on average-error probabilities in a Ricianfading channel with correlated lognormal shadowing

The effect of correlated lognormal shadowing on the average probability of error performance of narrow-band mobile communication systems with micro- and macrodiversity reception in a Rician fading channel is studied by considering a constant correlation model for the shadowed signals at the base stations. The performance degradation due to correlated shadowing is illustrated by considering both coherent and differentially coherent binary phase-shift keying schemes. Numerical results presented show that when the base stations in a cellular system are very closely spaced, the effect of correlated shadowing on system performance cannot be ignored     

Outage and BER analysis of cellular CDMA for integrated services with correlated signal and interference

In this letter, we evaluate the outage and "minimum duration outage" probabilities for integrated services in cellular code-division multiple-acess systems considering correlation among signal and interferers. Correlation is found to lower the outage probability. The effect of correlation and power control error on bit error rate is also studied.     

Suboptimal estimation of the parameters of discrete systems in the presence of correlated noise

Using an unbiased objective function and a fast algorithm which employs an iterative least-squares technique, consistent estimates are obtained for the parameters of a linear difference equation which describes a system having an output corrupted by correlated noise. The method is applied to a simulated process and compared with the generalised least-squares method.     

Space-time spreading and block coding for correlated fading channels in the presence of interference

We consider point-to-point wireless links with multiple antennas in the presence of interference, and exploit channel's spatial correlation and the temporal covariance of the interference to design multiantenna transmitters. We develop a space-time spreading scheme that maximizes average signal-to-interference-and-noise ratio, and an optimally power-loaded space-time beamforming (STBF) scheme which improves error-probability performance. In order to increase transmission rates, we combine orthogonal space-time block coding with STBF, optimize power loading across beams, and develop low-complexity receivers. Optimal training for least-squares error channel estimation, and STBF for minimum mean-square error channel estimation, are also studied. Our analytical and simulated results corroborate that STBF with optimal power loading can considerably reduce error probability and channel-estimation errors.     

MIMO capacity through correlated channels in the presence of correlated interferers and noise: a (not so) large N analysis

The use of multiple-antenna arrays in both transmission and reception promises huge increases in the throughput of wireless communication systems. It is therefore important to analyze the capacities of such systems in realistic situations, which may include spatially correlated channels and correlated noise, as well as correlated interferers with known channel at the receiver. Here, we present an approach that provides analytic expressions for the statistics, i.e., the moments of the distribution, of the mutual information of multiple-antenna systems with arbitrary correlations, interferers, and noise. We assume that the channels of the signal and the interference are Gaussian with arbitrary covariance. Although this method is valid formally for large antenna numbers, it produces extremely accurate results even for arrays with as few as two or three antennas. We also develop a method to analytically optimize over the input signal covariance, which enables us to calculate analytic capacities when the transmitter has knowledge of the statistics of the channel (i.e., the channel covariance). In many cases of interest, this capacity is very close to the full closed-loop capacity, in which the transmitter has instantaneous channel knowledge. We apply this analytic approach to a number of examples and we compare our results with simulations to establish the validity of this approach. This method provides a simple tool to analyze the statistics of throughput for arrays of any size. The emphasis of this paper is on elucidating the novel mathematical methods used.