Adnan A. Abu-Dayya

Estimating the distribution of a sum of independent lognormal random variables

Four methods that can be used to approximate the distribution function (DF) of a sum of independent lognormal random variables (RVs) are compared. The aim is to determine the best method to compute the DF considering both accuracy and computational effort. The investigation focuses on values of the dB spread, σ, valid for practical problems in wireless transmission, where σ is between 6 dB and 12 dB. Contrary to some previous reports, our results show that the simpler Wilkinsons approach gives a more accurate estimate, in some cases of interest, than Schwartz and Yehs 1982 approach.

Outage probabilities in the presence of correlated lognormal interferers

Several approaches that can be used to compute the distribution of a sum of correlated lognormal random variables (RVs) are investigated. Specifically, Wilkinsons approach (Schwartz and Yeh, 1982), an extension to Schwartz and Yehs (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 Wilkinsons 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. >

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 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

Outage probabilities of cellular mobile radio systems with multiple Nakagami 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 switched diversity systems on generalized-fading channels

The performances of switched diversity systems operating on generalized (Nakagami)-fading channels are analyzed using a discrete-time model. The average bit error rate (BER) of binary noncoherent frequency shift keying (NCFSK) on slow, nonselective Nakagami-fading channels is derived. Closed-form expressions that can be used to determine optimum switching thresholds (in a minimum error rate sense) are also derived. In addition, the use of optimum fixed thresholds is considered. It is found that a considerable amount of diversity gain can be obtained using an optimum fixed (rather than adaptive) switching threshold. Results are obtained for both independent and correlated Nakagami-fading branch signals. The effects of fading severity and the correlation coefficient on both the BER and on the optimum switching threshold are investigated. It is shown that useful diversity gain can be obtained with power correlation coefficients as high as 0.9 when the fading is strong. The results for a Rayleigh channel are obtained and presented as a special case of generalized-fading model. >

Outage probabilities of diversity cellular systems with cochannel interference 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. >

Switched diversity on microcellular Ricean channels

The performances of switched dual diversity systems operating on independent and correlated Ricean fading channels are analyzed using a discrete time model. The average bit error rate (BER) of the discrete time switched diversity system using binary noncoherent frequency shift keying (NCFSK) on slow, nonselective Ricean fading channels is derived. A closed form expression that gives the optimum switching threshold in a minimum error rate sense is derived for the case of independent branch signals. Results for the optimum switching threshold for the case of correlated branch signals, obtained numerically, are also presented. Results using selection diversity combining are obtained for comparison. The effects of fading severity on both the BER and on the optimum switching threshold are investigated. The Ricean fading model may be used to model both the microcellular radio environment and the mobile satellite fading channel. Hence, the results of the paper are useful for both of these areas. >

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.

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. >

Comparison of methods of computing correlated lognormal sum distributions and outages for digital wireless applications

Several approaches that can be used to compute the distribution of a sum of correlated lognormal random variables (RVs) are investigated. 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, we 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. Simulation results are used for verification and comparison. Overall, the results obtained in this paper show that among the three methods considered in this paper Wilkinsons approach may be the best method to compute tire 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.<<ETX>>