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     

Comparison of diversity with simple block coding on correlatedfrequency-selective fading channels

We investigate the effects of correlation on the performance of diversity systems in wideband wireless radio environments. Specifically, the average bit error rate (BER) performance of M-ary differential phase shift keying (MDPSK) on correlated frequency-selective slow Rayleigh fading channels is analyzed. A two-branch diversity receiver with postdetection equal gain combining is considered. Nyquist pulse shaping is used and differential detection is employed at the receiver. The effects of cochannel interference on the system performance are assessed using a Gaussian interference model. To further enhance the system performance, the effects of combined diversity and forward error correction (FEC) coding on the average BER are investigated. Results using short cyclic block codes with perfect bit interleaving are obtained. The effects of the root mean square (RMS) delay spread, the amount of correlation, and the level of modulation, M, on the average BER are investigated in detail for both coded and uncoded systems. The results show that dual branch diversity combining with a correlation coefficient of 0.5 outperforms (in terms of BER) short block codes with perfect bit interleaving, and that combined diversity and coding strategies are effective in combatting the effects of frequency-selective fading     

Micro- and macrodiversity MDPSK on shadowed frequency-selectivechannels

The performance of M-ary differential phase shift keying (MDPSK) on frequency-selective slow Rayleigh fading, lognormal shadowed channels with diversity combining is analyzed for mobile and portable applications. The use of L-branch equal gain postdetection microdiversity combining to mitigate the effects of fading and P-port macrodiversity to alleviate the effects of shadowing are investigated. Four performance criteria are considered for a frequency-selective multipath fading, intersymbol interference channel. These are, the short term bit error rate (BER), the irreducible BER, the complementary distribution over the lognormal shadowing of the average BER, and the probability that the instantaneous BER exceeds a threshold value, averaged over a spatial environment. Closed-form expressions for the four performance criteria are obtained. The BER and outage performance results show that diversity combining is an effective method for improving the system performance (and hence system reliability), when the normalized delay spread is not large. It is also seen that, in most cases, 4DPSK gives the best performance followed by 8DPSK and 2DPSK, respectively, for a given information throughput     

Bandwidth efficient QPSK in cochannel interference and fading

The performances of QPSK in the presence of cochannel interference in both nonfading and fading environments are analyzed. Three approaches for representing the cochannel interference are investigated. These are a precise error probability method, a sum of sinusoids (sinusoidal) model, and a Gaussian interference model. In addition to determining precise results for the performance of QPSK in cochannel interference, we examine the validity of these two interference models in both additive white Gaussian noise (AWGN) environments and in different flat fading environments; Rayleigh, Ricean, and Nakagami. Nyquist pulse shaping is considered and the effects of cross channel ISI produced by the cochannel interference are accounted for in the precise interference model. Also accounted for are the random symbol and carrier timing offsets of the interfering signals. Two performance criteria are considered. These are the average bit error rate and the interference penalty. The latter is defined as the increase in signal-to-noise power ratio (SNR) required by a system with cochannel interference in order to maintain the same BER as a system without interference. Attention is given, in particular, to the outdoor microcellular fading environment. In this environment, the fading experienced by the interfering signals may be represented by a Rayleigh-fading model while the fading experienced by the desired signal may be represented by a Ricean or a Nakagami-fading model     

Outage probabilities in the presence of correlated lognormalinterferers

Several approaches that can be used to compute the distribution of a sum of correlated lognormal random variables (RVs) are investigated. Specifically, Wilkinson's approach (Schwartz and Yeh, 1982), an extension to Schwartz and Yeh's (1982) approach, and a cumulants matching approach (Schleher, 1977) are studied. The aim is to determine which method is best for computing the complementary distribution function (CDF) of a sum of correlated lognormal RVs considering both accuracy and computational effort. Then, using these techniques, the authors compute the outage probability of a desired lognormal shadowed signal in the presence of multiple correlated lognormal cochannel interferers. The outage results are presented as a function of the reuse factor. The reuse factor is defined as the distance between the centers of the two nearest cells using the same frequencies divided by the cell radius. It is a key parameter in the design of any frequency reuse system. Simulation results are used for verification and comparison. Overall, the results obtained show that among the three methods considered Wilkinson's approach may be the best method to compute the CDF of sums of correlated lognormal RVs (and hence the outage probability in correlated lognormal shadowed mobile radio environments). This is due to both its accuracy and computational simplicity over the range of parameters valid for practical applications     

Diversity π/4-DQPSK on microcellular interference channels

The average bit-error rate (BER) performance of π/4-shifted differential quadrature phase shift keying (π/4-DQPSK) in the presence of multiple independent cochannel interferers in frequency-nonselective fading environments is analyzed. Nyquist shaped pulses are used and post detection diversity combining is employed at the receiver. The use of both L-branch post detection equal gain combining (EGC) and L-branch post detection selection combining (SC) are considered. Two approaches for representing the cochannel interference are investigated. These are a Gaussian interference model and a synchronous interference model. The accuracies of both of these models are assessed by comparing their BER performances with precise BER results. The precise BER results are obtained by using a combination of analysis and simulation. Attention is given, in particular, to the outdoor microcellular environment. The results of this paper indicate that the synchronous interference model may overestimate the effects of interference while the Gaussian interference model may underestimate the effects of interference     

General forms for maximal ratio diversity with weighting errors

This paper introduces two general relationships concerning the output signal-to-noise ratio distribution and the bit error performance of the nonideal maximal ratio combiner. The imperfections are modeled as Gaussian distributed weighting errors in the channel gain estimates used for coherent combination. The general form for the bit error rate is applicable to any modulation format     

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     

Analysis of equal gain diversity on Nakagami fading channels

An infinite series for the complementary probability distribution function (CDF) of the signal-to-noise ratio (SNR) at the output of L -branch equal-gain (EG) diversity combiners in Nakagami (1960) fading channels is derived. The bit error rate for a matched filter receiver is analyzed for the L-branch EG combiner and different fading parameters. Both coherent phase shift keying (CPSK) and differential coherent phase shift keying (DCPSK) are considered. The effects of gain unbalance between branches on the probability distribution of the SNR and on the bit error rates are investigated. Bit error rate results are also obtained for coherent and noncoherent reception of frequency shift keying (FSK). The effects of gain unbalances on FSK modulations are also investigated. Bit error rates for EG combining on Rayleigh fading channels are obtained for L>2. These results are presented as a special case of the more generalized Nakagami fading model