Generalized Selection Combining Research Articles

Order Statistics for Correlated Non-Identically Distributed Random Variables

This paper deals with a problem in which the joint statistics of a set of Nrandom variables are known. Based on this knowledge, we derive the joint probability density function (PDF) of the L largest random variables (L≤N). The N random variables will be assumed to be correlated and non-identically distributed. Problems typical to this one are normally encountered in the performance analysis of a certain class of receivers used in multipath fading channels with correlated and unbalanced diversity branches. In this application, the receiver has access to N signal-to-noise ratio (SNR) random variables, and it has to make a symbol decision based on the largest L SNRs. This class of receivers is widely known as generalized selection combining (GSC) receivers.

Exact Error Rate Analysis of Output-Threshold Generalized Selection Combining (OT-GSC)

Generalized selection combining (GSC) is one of the most widely investigated low-complexity diversity techniques. Recently, output-threshold GSC (OT-GSC) was proposed as a power-saving variant of traditional GSC scheme. In this paper, we present an exact performance analysis of OT-GSC over Rayleigh fading channels. In particular, we derive the cumulative distribution function (CDF), probability density function (PDF) and moment generation function (MGF) of the combined SNR with OT-GSC. Then, we apply these results to study the outage probability and average error rate performance of OT-GSC. This analysis allows for a thorough and accurate comparison of OT-GSC with other variants of GSC, such as minimum selection GSC.

Blind Ratio Combining (BRC): An Optimum Diversity Receiver for Coherent Detection With Unknown Fading Amplitudes

We present an optimum diversity receiver called blind ratio combining (BRC), which minimizes the average symbol error probability or maximizes the average output signal-to-noise ratio, where the channels' time delays and the random phases are known while the fading amplitudes are unknown. In contrast to previous works where efforts were made to find a posteriori probabilities at the receiver, the BRC simply calculates the optimum weights, which depend on the channel's statistics, avoiding continuous channel estimation, and thus, it significantly reduces the system's complexity. In nonidentical multipath fading channels with power delay profile (PDP), the BRC receiver performs between maximal ratio combining (MRC) and equal gain combining (EGC), and attains to keep its performance comparable—and in some cases superior—to that of generalized selection combining (GSC), while for large values of the decay factor it approaches MRC. Moreover, in the important practical case of exponential PDP—common in RAKE receivers modeling and adopted for the Universal Mobile Telecommunications System (UMTS) spatial channel modeling by the European Telecommunications Standards Institute-Third Generation Partnership Project (ETSI-3GPP)—the optimum weights can be accurately approximated by simple elementary functions. Furthermore, it is proved that the utilization of these weights ensures an error performance improvement over EGC for arbitrary PDPs. The proposed BRC receiver can be efficiently applied in wireless wideband communication systems, where a large number of diversity branches exists, due to the strong multipath effects.

Average SEP of Rectangular QAM in Rayleigh Fading with GSC

This letter presents an exact-form expression for the average symbol error probability (SEP) of general rectangular quadrature amplitude modulation (QAM) in Rayleigh fading channels with generalized selection combining (GSC). Expressions for the system average SEP with maximal ratio combining (MRC) and selection combining (SC) are obtained as limiting cases. It is shown that the results herein reduce to some existing ones as special cases.

Minimum estimation and combining generalized selection combining (MEC-GSC)

This paper introduces and analyzes a new adaptive minimum-estimation minimum-combining switched-combining based scheme that reduces considerably the average receiver channel estimation complexity and the power drain from the battery while satisfying a certain desired performance requirement. The mathematical formalism is supported by some selected numerical examples that show that the newly proposed combining scheme can essentially achieve the same performance as competing schemes such as generalized selection combining (GSC) while offering 50 % channel estimation and 75 % processing power savings for some system parameters of interest

Performance Analysis of Generalized Sort, Switch, and Examine Combining

Examples of low-complexity diversity combining schemes are, among others, the generalized selection combining (GSC) scheme and the generalized switch-and-examine combining (GSEC). In this paper, we propose a new low-complexity combining scheme, termed generalized sort-switch-and-examine combining (GSSEC), that, in a sense, can be considered as a hybrid GSC/GSEC scheme. A generic expression for the moment-generating function of the GSSEC output SNR in general independent, identically distributed fading channels is derived, and is then applied to the analysis of its error performance

Analysis of Generalized Selection Diversity Systems in Wireless Channels

Motivated by practical considerations in the design of low-complexity receiver structures for wideband cellular code division multiple access, millimeter wave, and ultrawideband communications, the study on the generalized selection combining (GSC) receiver that adaptively combines a subset of M "strongest" paths out of L available paths has intensified over the past few years. This paper derives concise analytical expressions for the moment generating function (MGF) of the GSC(M,L) output signal-to-noise ratio when the fading statistics are independent and identically distributed. The novelty of this mathematical framework in computing the MGF relies on the fact that it allows all common multipath fading channel models (Rayleigh, Rician, Nakagami-m, and Nakagami-q) to be treated in a unified sense. It also leads to a much more computationally efficient formula than those available in the literature and is valid for any combinations of M and L values. Using these newly derived MGFs, a unified error probability analysis for many coherent and noncoherent digital-modulation/detection schemes in a myriad of fading environments was provided

Probability of error analysis of predetection generalized selection combining receivers with correlated unbalanced Nakagami branches

AbstractIn this paper we determine the probability of error of a predetection generalized selection combining (GSC) receiver with correlated and unbalanced diversity branches in a Nakagami‐m multipath fading channel. We start by finding the joint probability density function (PDF) of the decision variables. This involves the derivation of the joint PDF of the L largest random variables (L maxima) of an input population of N > L correlated nonidentically distributed random variables, based on the statistics of the input population. The results obtained are then used in the derivation of the error probabilities of noncoherent FSK (NCFSK) and DPSK receivers. Copyright © 2006 John Wiley & Sons, Ltd.

New results on ordered statistics and analysis of minimum-selection generalized selection combining (GSC)

Diversity combining techniques improve the performance of wireless communication systems at the cost of increased power consumption. Minimum-selection generalized selection combining (MS-GSC) scheme has been proposed as a power saving implementation of conventional generalized selection combining (GSC) scheme. In this paper, noting that previous analytical results on the error rate of MS-GSC are approximate, we carry out a thorough and exact analysis for MS-GSC. In particular, based on a new result on order statistics, we obtain the statistics of the combined SNR with MS-GSC and we then apply these results to analyze the performance of MS-GSC over fading channels. We derive the closed-form expressions of important performance measures, including outage probability and average error rate, for the Rayleigh fading scenario. In addition, we investigate the average number of active MRC branches with MS-GSC, as a quantification of the power saving

Performance of generalized selection combining over Weibull fading channels

The literature is relatively sparse in performance analysis of diversity combining schemes over Weibull fading channels, despite the fact that the Weibull distribution is often found to be suitably fit for empirical fading channel measurements. In this paper, we capitalize on some interesting results due to Lieblein on the order statistics of Weibull random variables to derive exact closed-form expressions for the combined average signal-to-noise ratio (SNR) as well as amount of fading (AF) at a generalized selection combining (GSC) output over Weibull fading channels. We also use some simple AF-based mappings between the fading parameters of the Weibull distribution and those of the Nakagami, Rice, and Hoyt distributions to obtain the approximate but accurate average SNR and AF of GSC over these types of channels. The mathematical equations are validated and illustrated by some numerical examples for scenarios of practical interest. Copyright © 2006 John Wiley & Sons, Ltd.

Infinite Series Representations of the Trivariate and Quadrivariate Rayleigh Distribution and Their Applications

Few theoretical results are known about the joint distribution of three or more arbitrarily correlated Rayleigh random variables (RVs). Consequently, theoretical performance results are unknown for three- and four-branch equal gain combining (EGC), selection combining (SC), and generalized SC (GSC) in correlated Rayleigh fading. This paper redresses this gap by deriving new infinite series representations for the joint probability density function (pdf) and the joint cumulative distribution function (cdf) of three and four correlated Rayleigh RVs. Bounds on the error resulting from truncating the infinite series are derived. A classical approach, due to Miller, is used to derive our results. Unfortunately, Miller's approach cannot be extended to more than four variates and, in fact, the quadrivariate case considered in this paper appears to be the most general result possible. For brevity, we treat only a limited number of applications in this paper. The new pdf and cdf expressions are used to derive the outage probability of three-branch SC, the moments of the EGC output signal-to-noise ratio (SNR), and the moment generating function of the GSC(2,3) output SNR in arbitrarily correlated Rayleigh fading. A novel application of Bonferroni's inequalities allows new outage bounds for multibranch SC in arbitrarily correlated Rayleigh channels.

Performance Analysis of a Class of GSC Receivers Over Nonidentical Weibull Fading Channels

The performance of a class of generalized-selection combining (GSC) receivers operating over independent but nonidentically distributed Weibull fading channels is studied. We consider the case where the two branches with the largest instantaneous signal-to-noise ratio (SNR), from a total of L available, GSC(2, L) are selected. By introducing a novel property for the product of moments of ordered Weibull random variables, convenient closed form expressions for the moments of the GSC(2,L) output SNR are derived. Using these expressions, important performance criteria, such as average output SNR and amount of fading, are obtained in closed form. Furthermore, employing the Pade/spl acute/ approximants theory and the moment-generating function approach, outage and bit-error rate performance are studied. An attempt is also made to identify the equivalency between the Weibull and the Rice fading channel, which is typically used to model the mobile satellite channel. We present various numerical performance evaluation results for different modulation formats and channel conditions. These results are complemented by equivalent computer simulated results which validate the accuracy of the proposed analysis.

Performance analysis of linear diversity-combining schemes on Rayleigh fading channels with binary signaling and Gaussian weighting errors

In this paper, we analyze the error probability performance of maximal-ratio combining (MRC), equal-gain combining (EGC), selection combining (SC), and generalized-selection combining (GSC) diversity schemes with coherent binary phase-shift keying (BPSK) signaling on Rayleigh fading channels with Gaussian channel-estimation errors. We first show that, with weighting errors, averaging the conditional probability of error with the density function of the instantaneous signal-to-noise ratio (SNR) at the output of the combiner yields a lower bound on the exact probability of error. Later, we derive the exact probability of error for MRC, EGC, SC, and GSC diversity schemes and show that, for the case of nonnegative values of the in-phase correlation coefficient between the actual and the estimated channel gains, the exact probability of error with weighting errors is the same as that of the case with perfect channel estimation, but with the average SNR per diversity branch /spl gamma/~, for the case of perfect channel estimation, replaced by the effective SNR /spl gamma/~/sub /spl rho//, due to weighting errors. The effective SNR is a function of both /spl gamma/~ and /spl rho/, the magnitude of the normalized cross correlation between the actual and the estimated channel gains. Finally, we show that, as /spl rho//spl rarr/0, the average probability of error approaches 0.5, irrespective of the order of diversity and the diversity-combining rule.

MRC and GSC Diversity Combining With an Output Threshold

Diversity combining greatly improves the performance of wireless communication systems in fading environment. However, it also increases the power consumption of the receiver. In this paper, we investigate variants of known diversity combining schemes that minimize the processing power at the receiver while still providing considerable performance improvement. In particular, we carry out a thorough performance versus power consumption tradeoff analysis of output-thresholded versions of maximum ratio combining (MRC) and generalized selection combining (GSC) schemes. Numerical examples show that the output thresholded combining schemes lead to considerably less average power consumption than conventional schemes while providing nearly the same performance.

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.

Analysis of coherent MPSK schemes with generalized selection diversity in Rayleigh fading

A simplified performance analysis of coherent M-ary phase shift keying (MPSK) modulation with generalized selection combining (GSC) is presented for Rayleigh fading channels. The symbol error probability (SEP) is derived in a closed-form expression. A previous result used the moment generating function approach to arrive at a rather complex result. In our derivation, we have used the traditional averaging technique to obtain a performance expression that does not require any numerical integration. Copyright © 2004 AEI

Adaptive Selection Combining for Soft Handover in OVSF W-CDMA Systems

In W-CDMA, soft handover is supported at cell boundaries to maintain communication quality. The maximal ratio combining (MRC) and generalized selection combining (GSC) , are two possible approaches. However, soft handover is resource-intensive. In this letter, we propose an adaptive selection combining (ASC) scheme that can switch flexibly between MRC and GSC so as to take care of both channel loading and communication quality. The signal-to-interference-and-noise ratio (SINR) is kept as high as that of MRC while the blocking probability can remain at about the same level as that of GSC.

Performance Analysis of Combined Transmit Selection Diversity and Receive Generalized Selection Combining in Rayleigh Fading Channels

We analyze the average symbol error rate (SER) of M-PSK and M-QAM modulations with transmit antenna selection diversity (SD) and receive generalized selection combining (GSC) in Rayleigh fading channels. SER formulas are derived in closed form, and numerical results show that transmit SD and receive GSC are flexible to tradeoff performance for complexity.

Generalized Selection Combining Based on the Log-Likelihood Ratio

We propose a generalized selection combining (GSC) scheme for binary signaling in which a subset of diversity branches providing the largest magnitude of log-likelihood ratio (LLR) are selected and combined. It is shown that the bit-error probability with maximum ratio combining (MRC) or square-law combining of L branches is identical to that with LLR-based GSC of L/2 branches. We also propose a simple, but suboptimal, GSC based on a noncoherent envelope detection and discuss its potential advantages over the conventional signal-to-noise-ratio-based GSC and MRC.

Performance of Indoor Infrared Wireless CDMA Systems with Angle Diversity

Indoor infrared communication systems is one of the possible ways of offering data rates in excess of 100 Mbit/s without the need for wiring. Multiple users can share an infrared channel by code division-multiple access (CDMA) techniques. However, the CDMA system performance is limited by both background noise and co-channel interference. In this paper we study the use of angle diversity for mitigating the effects of the noise and interference. The system considered uses on-off shift keying modulation with multibeam transmitters and imaging receivers. The overall system performance for different diversity combining techniques is evaluated and compared to a system without diversity. Numerical results for a 2-user CDMA system indicate that signal to noise and interference ratio (SNIR) improvement (over systems with no diversity) of 5 dB is obtained for at least 50% of an ensemble of 10000 sample evaluations. The generalized selection combining (GSC)--a new diversity technique yet to be implemented for infrared systems--offers the best performance even with its reduced complexity.