Equal Gain Combining Receiver Research Articles

On the Distribution of the Sum of Nakagami-$ m$ Random Variables

In this paper, we investigate the classical problem of finding the probability density function (pdf) of the sum of Nakagami-m random variables. Exact infinite series representations are derived for the sum of three and four identically and independently distributed (i.i.d.) Nakagami-m random variables, and subsequently, it is extended to the sum of general number of random variables. A useful pattern emerged as a result of these extensions, and a new Fourier transform pair that involves parabolic cylinder function and Gauss hypergeometric function is obtained. Bounds on the error resulting from truncation of the infinite series of pdfs are also presented. These pdfs are used to analyze the performance of dual, triple, and quadruple branch predetection equal gain combining (EGC) receivers over Nakagami-m fading environment. Furthermore, a hypergeometric relation is derived as a result of those derivations. Subsequently, the analysis is extended to the case of L branch EGC receiver performance as well. Selected simulation plots are provided to compare the results with the approximate results available in the literature and to illustrate the validity of the formulation.

Approximation Error Analysis for Partially Coherent EGC Receiver under Nakagami-m Fading Channels

We present the approximated bit error rate (BER) performance of a binary phase shift keying (BPSK) modulated equal-gain combining (EGC) diversity receiver with phase noise over independent and non-identical Nakagami fading branches. The approximated BER becomes accurate with phase-locked loop (PLL) gain, K = 20. Also, for special values of fading parameter, m, and branch number, L, we derived the closed form expression of the BER.

Closed-Form Analysis of Equal-Gain Diversity in Wireless Radio Networks

This paper deals with the performance of predetection equal-gain combining (EGC) receivers operating over multipath fading plus cochannel interference (CCI) and additive white Gaussian noise channels. The desired components of the received signals are considered to experience independent but not-necessarily identically distributed Nakagami-m fading, while the interferers are subject to independent Rayleigh fading. The analysis is not only limited to equal average fading power interferers, but the case of interferers with distinct average powers is also examined. By following the coherent interference power calculation, novel closed-form expressions for the moments of the EGC output signal-to-interference-plus-noise ratio (SINR) are derived, which are being used to study the performance of the average output SINR. Furthermore, by assuming an interference-limited fading scenario, novel closed-form union performance bounds are derived. More specifically, tight upper bounds for the outage and average symbol error probability for several constant envelope modulation schemes, and lower bounds for the Shannon average spectral efficiency, are provided. Numerical results demonstrate the effect of the number of interferers, the number of the receiver branches, and the severity of fading on the EGC receiver performance. Computer simulations have been also performed to verify the tightness of the proposed bounds and the correctness of the mathematical analysis. It is shown that the performance of cellular radio systems in the uplink is degraded mainly from the first-tier CCI of the adjacent cells

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

Ultra-reliable communication over vulnerable all-optical networks via lightpath diversity

In this paper, we propose using spatial diversity via multiple node-disjointed lightpaths at the optical layer to achieve ultra-reliable communication with low delay between any source-destination pair in all-optical networks. Using a doubly stochastic point process model and a "genie-aided" receiver, we obtain an exponentially tight error probability bound for the lightpath diversity scheme under an independent lightpath failure model. Error probability of the proposed scheme can be designed to be significantly lower than that of a system without lightpath diversity, and system parameters (e.g., the number of lightpaths) can be optimized to achieve efficient utilization of a limited amount of transmitted optical energy. In particular, at the optimum operating point, each lightpath is allocated an optimum average number of signal photons per bit and is biased to have an effective error probability 2f if the decision is based on that path alone, where f is the lightpath failure probability. We also investigate the tradeoff between the error probability and the implementation complexity within the class of all "structured" receivers. We derive receiver architectures for both the optimal receiver, which has the best error performance but complicated receiver architecture, and the equal-gain-combining (EGC) receiver, which has suboptimum error performance but simpler receiver architecture. Closed-form error bounds for both receivers are obtained and compared with the "genie-aided" limit of the lightpath diversity scheme. Performance comparison shows that the simpler equal-gain-combing receiver provides similar performance as the optimal receiver in the regime of high signal-to-noise photon rate ratio (/spl Omega/=/spl lambda//sub s//M/spl lambda//sub n/, where /spl lambda//sub s//M is the signal photon rate per path, /spl lambda//sub n/ is the noise photon rate per path), and performs slightly worse than the optimal receiver in the low and medium signal-to-noise photon rate ratio regimes. It indicates that the simpler EGC receiver is preferred over the complicated optimum receiver in practical receiver design.

Diversity reception of DAPSK over generalized fading channels

The accurate performance evaluation of differential amplitude and phase-shift keying (DAPSK) with postdetection equal gain combining (EGC) over generalized fading channels is of great theoretical interest and practical importance. In this paper, by using a decision variable-based moment generating function approach, exact error probability results for DAPSK over generalized Rician and Nakagami fading channels are derived, taking into account the effects of all the system and fading channel parameters. Several maximum likelihood (ML)-based detectors that do not require channel state information (CSI) are proposed for generalized Rician fading channels, and an exact bit error probability (BEP) union bound for the ML detection is derived. Assuming CSI, a performance upper bound for DAPSK with EGC is also presented. Simulation and numerical results show when both detectors have no CSI, the conventional DAPSK detector may perform closely to (though worse than) the ML detector. However, the EGC receiver with CSI performs substantially better than the ML detector without CSI, and very closely to the coherent APSK detector.

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.

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.

Equal-gain and maximal-ratio combining over nonidentical Weibull fading channels

We study the performance of L-branch equal-gain combining (EGC) and maximal-ratio combining (MRC) receivers operating over nonidentical Weibull-fading channels. Closed-form expressions are derived for the moments of the signal-to-noise ratio (SNR) at the output of the combiner and significant performance criteria, for both independent and correlative fading, such as average output SNR, amount of fading and spectral efficiency at the low power regime, are studied. We also evaluate the outage and the average symbol error probability (ASEP) for several coherent and noncoherent modulation schemes, using a closed-form expression for the moment-generating function (mgf) of the output SNR for MRC receivers and the Pade/spl acute/ approximation to the mgf for EGC receivers. The ASEP of dual-branch EGC and MRC receivers is also obtained in correlative fading. The proposed mathematical analysis is complimented by various numerical results, which point out the effects of fading severity and correlation on the overall system performance. Computer simulations are also performed to verify the validity and the accuracy of the proposed theoretical approach.

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 of<tex>$M$</tex>-PSK With GSC and EGC With Gaussian Weighting Errors

Using a moment-generating function (MGF)-based approach, we study the performance of M-ary phase-shift keying (M-PSK) with generalized selection combining (GSC) and equal gain combining (EGC) in fading channels (including Rayleigh, Rician, Nakagami-m, and Nakagami-q fading) with independent and identically distributed (i.i.d) branches. Analytical expressions for the error and outage probabilities, the signal-to-noise-ratio (SNR) statistics, and the channel capacity of M-PSK diversity receivers are derived, taking into account the effects of Gaussian weighting errors and all relevant system and channel parameters. Unlike the case of perfect channel-state information (CSI), the outage probability for the case of imperfect channel estimation (ICE) is not only a function of the normalized SNR with respect to the SNR threshold, but also a function of the operating SNR itself. The SNR loss of the M-PSK GSC and EGC receivers due to ICE and the relation between the receiver input and output SNRs for ICE are derived. Our results show that, even with ICE, GSC and EGC are effective in improving the output SNR and significantly reduce the error floor and the channel-capacity loss caused by ICE.

On frequency domain equalization for MC-CDMA in Nakagami fading channels

In this letter, we evaluate the performance of multicarrier code division multiple access (MC-CDMA) in terms of average bit error probability (BEP) in Nakagami fading channels. The results are applicable to MC-CDMA systems employing coherent demodulation with maximal-ratio combining (MRC) or equal gain combining (EGC) reception. The effects of fading parameters and number of users are presented. The accuracy of the proposed analysis is demonstrated by computer simulations. The BEP performance of the EGC receiver in the uplink is highly influenced by the fading parameter compared with that of the MRC receiver. The EGC receiver outperforms the MRC receiver in the downlink, but the MRC receiver gives almost the same performance as the EGC in the uplink. Copyright © 2004 AEI

Postdetection diversity receiver for DAPSK signals on the Rayleigh- and Rician-fading channel

In this paper, the optimum decision boundaries for (N, M) differential amplitude phase-shift keying on the Rayleigh-fading channel are analyzed. A postdetection maximal ratio combining (MRC) and weighted maximal ratio combining (WMRC) diversity receivers are proposed. In the Rayleigh-fading channel, assuming a high signal-to-noise ratio and a small normalized Doppler frequency, the analytical optimum decision boundaries are obtained. In addition, it is shown that an outer optimum decision boundary is the inverse of the inner optimum decision boundary. In the proposed MRC receiver, the decision at each branch is made based on the minimum distance criterion. The performance of the MRC receiver is analyzed, in terms of the union bound for bit error probability. The proposed WMRC receiver assigns weighting factors to the decision variable at each branch, based on the optimum decision boundaries. The performance of the WMRC is investigated through computer simulation and compared with those of MRC and equal gain combining (EGC). From the results, the performances of MRC and WMRC are found to be better than those of the EGC receiver on both the Rayleigh- and Rician-fading channels. It is also found that the performance improvement of WMRC over MRC is more pronounced as the number of diversity branches increases.