Tradeoff Analysis of Performance and Complexity on GSECps Diversity Combining Scheme

Generalized switch and examine combining (GSEC) was recently proposed as a low-complexity diversity combining scheme for diversity-rich environment. In this paper, we present and analyze a modified version of GSEC scheme, termed as GSEC with post-examine selection (GSECps). The GSECps scheme operates in the same way as GSEC when channel conditions are favorable and becomes equivalent to the generalized selection combining (GSC) scheme otherwise. We show, through a thorough and accurate tradeoff analysis of performance versus complexity, that GSECps can deliver a better performance-complexity tradeoff than both GSEC and GSC schemes.     

Generalized switch-and-examine combining (GSEC) over fading paths with unequal average SNR

A generalized switch-and-examine combining (GSEC) scheme was previously proposed by the authors as a low-complexity diversity technique for diversity-rich environments. In this letter, we extend the study of GSEC to independent and nonidentically distributed (i.n.d.) fading environments. In particular, after presenting the mode of operation of the GSEC scheme over i.n.d. fading paths, we analyze its error performance based on the moment generating function of combined signal-to-noise ratios. We then study its complexity in terms of the average number of path estimations. We finally investigate the effect of path examination order on the performance and complexity of GSEC over i.n.d. paths.     

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.     

Theoretical diversity improvement in GSC(N,L) receiver with nonidentical fading statistics

The study on generalized selection combining (GSC(N,L)) diversity systems that adaptively combines a subset of N paths with the highest instantaneous signal-to-noise ratios (SNRs) out of L available diversity paths has both theoretical and practical importance in the design of low-complexity receiver structures for cellular wideband CDMA, indoor millimeter-wave and ultra-wideband communications. This paper presents a novel mathematical framework to tackle the problem at hand by deriving a single integral expression for the moment generating function (mgf) of the GSC(N,L) output SNR when the L resolvable multipaths are independent with nonidentical fading statistics. The mgf is then used to unify the performance evaluation of a broad range of digital modulation/detection schemes in practical wireless channels.     

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.     

An iterative maximum SINR receiver for multicarrier CDMA systems over a multipath fading channel with frequency offset

A robust iterative multicarrier code-division multiple-access (MC-CDMA) receiver with adaptive multiple-access interference (MAI) suppression is proposed for a pilot symbols assisted system over a multipath fading channel with frequency offset. The design of the receiver involves a two-stage procedure. First, an adaptive filter based on the generalized sidelobe canceller (GSC) technique is constructed at each finger to perform despreading and suppression of MAI. Second, pilot symbols assisted frequency offset estimation, channel estimation and a RAKE combining give the estimate of signal symbols. In order to enhance the convergence behavior of the GSC adaptive filters, a decisions-aided scheme is proposed, in which the signal waveform is first reconstructed and then subtracted from the input data of the adaptive filters. With signal subtraction, the proposed MC-CDMA receiver can achieve nearly the performance of the ideal maximum signal-to-interference-plus noise ratio receiver assuming perfect channel and frequency offset information. Finally, a low-complexity partially adaptive (PA) realization of the GSC adaptive filters is presented as an alternative to the conventional multiuser detectors. The new PA receiver is shown to be robust to multiuser channel estimation errors and offer nearly the same performance of the fully adaptive receiver.     

Generalized receiver selection combining schemes for alamouti MIMO systems with MPSK

Analytical results for the symbol error rate (SER) of M-ary phase shift keying (MPSK) in a slow, flat Rayleigh fading channel for a multiple-input multiple-output (MIMO) system using an Alamouti transmission scheme and generalized selection combining (GSC) scheme are given. Two new receiver selection schemes, generalized space-time sum-of-squares (GSTSoS) selection diversity and generalized space-time sum-of-magnitudes (GSTSoM) selection diversity are proposed. The first provides the same performance as conventional GSC, and the second provides slightly poorer performance, but neither requires channel state information and both have much simpler implementations. The SER of MPSK in Rayleigh fading using these two selection schemes is studied and compared to that of conventional GSC. The effects of channel estimation errors on each selection scheme are examined.     

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.     

A Decision Aided CDMA Receiver with Partially Adaptive Decorrelating Multi-User Interference Cancellation

A CDMA receiver with enhanced multiple access interference (MAI) suppressionis proposed for a pilot symbols assisted system over multipath channels. Thedesign of the receiver involves the following procedure. First, blind adaptivecorrelators are constructed at different fingers based on the scheme ofgeneralized sidelobe canceller (GSC) to collect the multipath signals andsuppress MAI. A low-complexity partially adaptive (PA) realization of the GSCcorrelators is proposed which incorporates multi-user information for reducedrank processing. By a judiciously designed decorrelating procedure, a new GSCstructure is obtained in which the MAI are decorrelated and suppressedindividually. The next step is then a simple coherent combining of thecorrelator outputs with pilot aided channel estimation. Finally, furtherperformance enhancement is achieved by an iterative scheme in which the signalis reconstructed and subtracted from the GSC correlators input data, leadingto faster convergence of the receiver. The proposed low-complexity PA CDMAmulti-user receiver is shown to be robust to multipath fading and channelerrors, and achieve nearly the same performance of the ideal maximum SINR andMMSE receivers by using a small number of pilot symbols.     

Generalized selection combining with double threshold and performance analysis

In this paper, we propose a new diversity combining scheme to save power, which is called as the generalized selection combining with double threshold (DT‐GSC). It selects the branch whose SNR is above an input threshold to combine, and this process will keep running until the combined output SNR is larger than an output threshold or until all paths are examined. The values of both thresholds are required to be predetermined on the basis of the practical communication conditions. For comparing the complexity of various combining schemes, we will show the mathematical formulas of the average number of path estimation and the average number of combined branches. Moreover, we will also compare the average bit‐error‐ratio performance of the proposed DT‐GSC with absolute threshold GSC (AT‐GSC) and output threshold MRC (OT‐MRC). Numerical examples and simulation results show that the proposed DT‐GSC leads to a lower complexity than the conventional AT‐GSC and OT‐MRC while it has a satisfactory performance.Copyright © 2012 John Wiley & Sons, Ltd.     

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     

An MGF-based performance analysis of generalized selectioncombining over Rayleigh fading channels

Using the notion of the “spacing” between ordered exponential random variables, a performance analysis of the generalized selection combining (GSC) diversity scheme over Rayleigh fading channels is presented and compared with that of the conventional maximal-ratio combining and selection combining schemes. Starting with the moment generating function (MGF) of the GSC output signal-to-noise ratio (SNR), we derive closed-form expressions for the average combined SNR, outage probability, and average error probability of a wide variety of modulation schemes operating over independently, identically distributed (i.i.d.) diversity paths. Because of their simple form, these expressions readily allow numerical evaluation for cases of practical interest. The results are also extended to the case of non-i.i.d. diversity paths     

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 coded modulation with generalized selection combining in Rayleigh fading

We consider coded modulation with generalized selection combining (GSC) for bandwidth-efficient-coded modulation over Rayleigh fading channels. Our results show that reception diversity with generalized selection combining can conveniently trade off system complexity versus performance. We provide a number of new results by calculating the cutoff rate, and by deriving analytical upper bounds on symbol-interleaved trellis-coded modulation (TCM) and bit-interleaved-coded modulation (BICM) with GSC. All are verified by simulation. We show that our new bounds on TCM with GSC, which includes maximum ratio combining and selection combining as special cases, are tighter than the previously derived bounds. A new asymptotic analysis on the pairwise error probability, which can be used as a guideline for designing coded modulation over GSC channels, is also given. Finally, we show that BICM with iterative decoding (BICM-ID) can achieve significant coding gain over conventional coded modulation in a multiple-receiving-antenna channel.     

Efficient performance evaluation for generalized selection combining on generalized fading channels

The authors propose an efficient moment generating function (MGF)-based method to evaluate the performance of generalized selection combining (GSC) over different fading channels. Employing a recently proposed method which is, however, only applicable to GSC diversity with independent and identically distributed branches, they derive a general MGF expression for the GSC output signal-to-noise ratio (SNR) for generalized fading channels, where the channel statistics in different diversity branches may be nonidentical or even distributed according to different distribution families. The resulting MGF expression is applicable to the analysis of the error probability, the outage probability, and the SNR statistics for GSC in a number of wireless communications scenarios with generalized fading. Numerical examples are presented to illustrate the application of the new analysis.     

Soft handover overhead reduction by RAKE reception with finger reassignment

We propose and analyze in this paper a new finger assignment technique that is applicable for RAKE receivers when they operate in the soft handover (SHO) region. This scheme employs a new version of generalized selection combining (GSC). More specifically, in the SHO region, the receiver uses by default only the strongest paths from the serving base station (BS) and only when the combined signal-to-noise ratio (SNR) falls below a certain pre-determined threshold, the receiver uses more resolvable paths from the target BS to improve the performance. Hence, relying on some recent results on order statistics we attack the statistics of two correlated GSC stages and provide the approximate but accurate closed-form expressions for the statistics of the output SNR. By investigating the tradeoff among the error performance, the path estimation load, and the SHO overhead, we show through numerical examples that the new scheme offers commensurate performance in comparison with more complicated GSC-based diversity systems while requiring a smaller estimation load and SHO overhead.     

Error analysis of generalized selection combining over relay channel

Cooperative communication is a recently popular concept which allows single-antenna devices to benefit from spatial diversity. The performance analysis of cooperative communication using generalized selection combining (GSC) over independent not necessarily identically distributed Nakagami-m fading channels is presented and compared with that of the conventional maximal ratio combining (MRC) and selection combining (SC) schemes. With the aid of Padé approximants theory, new closed-form expression is derived for the moment-generating function (MGF) of the GSC output signal-to-noise ratio (SNR). MGF is an important tool for researching the system performance. In this paper, the average bit-error probability is accurately approximated using the well-known MGF approach. Numerical results show that the proposed mathematical analysis is accurate and that for the more severe fading cases, the GSC receivers are closer to the optimum MRC receivers.     

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.     

Performance of generalized selection combining receivers in K fading channels

In this letter, we present a moment generating function (MGF) based performance analysis of generalized selection combining (GSC) receivers operating over independent and identically distributed (i.i.d.) K fading channels. Analytical expressions for the marginal MGF of the signal-to-noise ratio of a single diversity branch for integer plus one-half values of the fading parameter are obtained and used to efficiently evaluate the average error probability of GSC receivers.