Revised analyses of postdetection switch-and-stay diversity in rician fading

The performances of dual-branch postdetection switch-and-stay combining (SSC) for noncoherent orthogonal binary frequency-shift keying and noncoherent orthogonal M-ary frequency-shift keying operating over slow, flat Rician fading channels are a topic of current interest. It is shown that recently published analyses obtain incorrect final results because some incorrect probability distribution parameters are used in the analyses. The previous results are corrected, and it is seen that the final results change significantly. The revised results are used to obtain optimum switching thresholds that minimize the average bit-error rate (BER) performance of these systems. Monte Carlo simulations are presented to verify the results, and it is shown that for a given BER, the signal-to-noise ratio difference of postdetection SSC and predetection SSC is much less than previously reported.     

Selection diversity combining with multiple antennas for MM-waveindoor wireless channels

Presents predetection and postdetection combining schemes for selection diversity reception with multiple antennas for MM-wave indoor radio channels. For those combining schemes, a reduction in complexity is achieved by limiting the number of combined signals to small values and by increasing the number of received signals. Bit error rate (BER) performance of binary phase shift keying (BPSK) with predetection combining of selected signals (CSS) and BER performance of differential BPSK with postdetection CSS are analyzed for slow fading and Rayleigh-distributed envelope statistics. Predetection maximal ratio combining of signals that comes from a single group or several groups of diversity channels as well as postdetection combining of received signals for groups of channels are considered. In comparing predetection combining with groups (PCG) and predetection combining of the best signals (PCB), we observe that the required SNR for achieving a certain BER is approximatively the same (with PCG having a slight advantage of 0.5 dB) for a given number, N, of diversity channels and L combined signals. Furthermore. PCG is equivalent to PCB for L=N since both techniques then correspond to conventional predetection maximal ratio combining (MRC), PCG and PCB are also equivalent when L=1 as both schemes then correspond to conventional selection combining. A small degradation of approximately 2 dB in the required SNR is observed when postdetection diversity reception with groups (PDG) is used instead of PCG. For L=N, PDG reduces to post detection MRC. The PDG technique is considered more suitable than PCB or PCG for MM-indoor wireless systems     

Postdetection phase combining diversity

We propose a postdetection phase combining (PC) scheme for the two branch diversity reception of differential phase shift keying (DPSK) over multipath fading channels. The receiver has a differential phase detector (DPD) in each diversity branch, and the combiner weights each detector output in proportion to the vth power of the signal envelope at the detector's input. For π/4-shift QDPSK over frequency-flat Rayleigh fading channels, we find via computer simulation that the optimum weight factor is v=2, and that our simple, practical combining scheme performs almost as well as postdetection maximal ratio combining (MRC). We demonstrate similar relative performances for frequency-selective fading channels and for channels with co-channel interference (CCI)     

Performance of MFSK signals with postdetection square-law diversity combining in arbitrarily correlated Nakagami-m fading channels

This letter presents an analysis of the error probability for noncoherent orthogonal multiple frequency-shift keying (MFSK) signals with postdetection square-law combining (SLC) when the signals transmitted over additive white Gaussian noise (AWGN) and slow frequency-nonselective arbitrarily correlated Nakagami-m fading channels. New exact expressions in a onefold integral for the probability of error of MFSK signals with postdetection square-law diversity combining operating in AWGN channel as well as in arbitrarily correlated Nakagami-m fading channels are derived. The effects of arbitrarily values of fading severity parameter m and the arbitrarily correlation between the L diversity channels are considered. The derived expressions can be easily computed, and hence, can be usefully exploited in the performance evaluation of digital mobile radio systems.     

Performance of diversity combining techniques for DS/DPSK signalingover a pulsed jammed multipath-fading channel

The effectiveness of antenna and spread-spectrum diversity is evaluated for direct-sequence differential phase-shift-keyed signaling over a worst-case pulse-jammed multipath-fading channel. Two diversity combining techniques are proposed. One uses predetection selective combining followed by postdetection equal-gain combining, and the other uses only postdetection equal-gain combining. The use of coding with hard and soft decision decoding is also considered. It is shown that the proposed diversity techniques can provide a significant improvement in the performance of coded antijam systems operating over jammed multipath-fading channels     

Performance limits of M-FSK with Reed-Solomon coding and diversity combining

This paper examines the asymptotic (M/spl rarr//spl infin/) performance of M-ary frequency-shift keying (M-FSK) in multi-channels, or multiple frequency-nonselective, slowly fading channels, with coding, side information, and diversity reception. In particular, Reed-Solomon (RS) coding is considered in conjunction with the ratio-threshold test (RTT), which generates side information regarding the reliability of received symbols. The asymptotic performance of orthogonal signaling in multichannels with maximal ratio combining (MRC), postdetection equal gain combining (EGC), hybrid selection combining (H-SC), and selection combining (SC) is derived for an arbitrary statistical fading model and diversity order. The derivations reveal that coherent and noncoherent implementations of diversity combining schemes yield the same performance asymptotically. In addition, the asymptotic results are evaluated assuming a Nakagami-m fading model, and the effect of fading severity, diversity order, code rate, and side information upon the performance of the various diversity combiners is investigated. The minimum signal-to-noise ratio (SNR) required to achieve arbitrarily reliable or error-free communication, as well as the associated optimal RS code rate, are determined for various cases.     

Bit error probability for MDPSK and NCFSK over arbitrary Ricianfading channels

In this paper, we analyze the bit error probability (BEP) of binary and quaternary differential phase shift keying (2/4 DPSK) and noncoherent frequency shift keying (NCFSK) with postdetection diversity combining in arbitrary Rician fading channels. The model is quite general in that it accommodates fading correlation and noise correlation between different diversity branches as well as between adjacent symbol intervals. We show that the relevant decision statistic can be expressed in a noncentral Gaussian quadratic form, and its moment generating function (MGF) is derived. Using the MGF and the saddle point technique, we give an efficient numerical quadrature scheme to compute the BEP. The most significant contribution of the paper, however, lies in the derivation of a closed-form cumulative distribution function (cdf) for the decision statistic. As a result, a closed-form BEP expression in the form of an infinite series of elementary functions is developed, which is general and unifies previous published BEP results for 2/4 DPSK and NCFSK for multichannel reception in Rician fading. Specialization to some important cases are discussed and, as a byproduct, a new and general finite-series expression for the BEP in arbitrarily correlated Rayleigh fading is obtained. The theory is applied to study 2/4 DPSK and NCFSK performance for independent and correlated Rician fading channels; and some interesting findings are presented     

Some integrals involving the Q/sub m/(a/spl radic/x,b/spl radic/x) with application to error probability analysis of diversity receivers

This paper derives closed-form formulas for two integrals involving the generalized Marcum Q-function with linear arguments Q/sub m/(a/spl radic/x,b/spl radic/x). These integrals are known to arise in the analysis of multichannel diversity reception of differentially coherent and noncoherent digital communications in Rayleigh and Nakagami-m channels. Applications of the results for efficient performance evaluation of the average bit error rates of dual branch selection diversity combining and postdetection equal gain combining over independent and correlated fading channels are also presented.     

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     

Error rates of M-ary signals with. Multichannel reception in Nakagami-m fading channels

In this letter, we present closed. form expressions for the exact average symbol-error rate (SER) of M-ary modulations with multichannel reception over Nakagami-m fading channels. The derived expressions extend already available results for the nondiversity case, to maximal-ratio combining-(MRC) and postdetection equal-gain combining (EGC) diversity systems. The average SERs are given in terms of Lauricella's multivariate hypergeometric function F/sub D//sup (n)/. This function exhibits a finite integral representation that can be used for fast and accurate numerical computation of the derived expressions.     

Performance of Two Dual-Branch Postdetection Switch-and-Stay Combining Schemes in Correlated Rayleigh and Rician Fading

The performance of binary frequency-shift keying (BFSK) and M-ary frequency shift keying (MFSK) with dual-branch postdetection switch-and-stay combining (SSC) in correlated Rayleigh and Rician fading is studied. Two postdetection SSC receivers are considered and the performances of noncoherent BFSK and MFSK are analyzed. Closed-form expressions are derived for the average bit-error rate (BER) of BFSK and MFSK with postdetection SSC in correlated Rayleigh and Rician fading. Optimum switching thresholds that minimize the average BER are obtained. Extensive Monte Carlo simulations are presented to test the validity of the analytical results. The performance of dual-branch postdetection SSC is compared with the performance of dual-branch predetection SSC. The effects of correlation, fading parameter, average fading power imbalance, and switching threshold on the performances of postdetection SSC receivers are examined     

Soft-limiter RAKE receivers for coded DS/DPSK systems over pulsejammed multipath-fading channels

Two soft-limiter RAKE receivers are evaluated for coded direct-sequence/differential phase shift keying (DS/DPSK) signaling over a pulse jammed multipath-fading channel that use a combination of antenna and multipath diversity. One uses predetection selective (antenna) combining followed by postdetection equal gain (multipath) combining, and the other uses postdetection equal gain combining only. In either case, the postdetection diversity combiner output is soft-limited prior to decoding. It is shown that for increasing levels of diversity the soft-limiter becomes quite effective, resulting in a receiver performance that approaches a maximum likelihood (ML) soft decision receiver with perfect jammer state information     

Sum of gamma variates and performance of wireless communicationsystems over Nakagami-fading channels

Capitalizing on the Moschopoulos (1985) single gamma series representation of the probability density function (PDF) of the sum of gamma variates, we provide a PDF-based approach for the performance analysis of maximal-ratio combining and postdetection equal-gain combining diversity techniques as well as cochannel interference of cellular mobile radio systems over Nakagami (1960)-fading channels with arbitrary parameters. Aside from putting under the same umbrella many of the past results obtained via characteristic function (CF) or moment generating function (MGF)-based approaches, the proposed approach also allows the derivation of additional performance measures, which are harder to analyze via CF or MGF-based approaches     

Asymptotic performance of hybrid-selection/maximal-ratio combining over fading channels

In this letter, we study the asymptotic performance of hybrid-selection/maximal-ratio combining (HS/MRC) and postdetection HS/equal-gain combining (HS/EGC) over generalized fading channels for large average signal-to-noise ratios (ASNRs). By evaluating the asymptotic moment generating function of the HS/MRC output SNR at high ASNR, we derive the diversity and coding gains for HS/MRC for a large class of modulation formats and versatile fading conditions, including different types of fading channels and nonidentical SNR statistics across diversity branches. Our analytical results reveal that the diversity gains of HS/MRC and HS/EGC are equivalent to that of MRC, and the difference in the coding gains for different modulation formats is manifested in terms of a modulation factor defined in this letter. Some new analytical results about effects of the number of combined branches for HS/MRC and noncoherent combining loss of HS/EGC are also provided.     

Outage probability of diversity systems over generalized fading channels

Outage probability is an important performance measure of communication systems operating over fading channels. Relying on a simple and accurate algorithm for the numerical inversion of the Laplace transforms of cumulative distribution functions, we develop a moment generating function-based numerical technique for the outage probability evaluation of maximal-ratio combining (MRC) and postdetection equal-gain combining (EGC) in generalized fading channels for which the fading in each diversity path need not be independent, identically distributed, nor even distributed according to the same family of distributions. The method is then extended to coherent EGC but only for the case of Nakagami-m fading channels. The mathematical formalism is illustrated by applying the method to some selected numerical examples of interest showing the impact of the power delay profile and the fading correlation on the outage probability of MRC and EGC systems.     

Error Performance of DQPSK with EGC Diversity Reception over Fading Channels

This paper derives the average bit error probability (BEP) of differential quaternary phase shift keying (DQPSK) with postdetection equal gain combining (EGC) diversity reception over independent and arbitrarily correlated fading channels. First, using the associated Legendre functions, the average BEP of DQPSK is analyzed over independent Rayleigh, Nakagami-m, and Rician fading channels. Finite-series closed-form expressions for the average BEP of DQPSK over L-branch independent Rayleigh and Nakagami-m fading channels (for integer Lm) are presented. Besides, a finite-series closed-form expression is given for the average BEP of differential binary phase shift keying (DBPSK) with EGC over independent Rician fading channels. Second, an alternative approach is propounded to study the performance of DQPSK over arbitrarily correlated Nakagami-m and Rician fading channels. Relatively simple BEP expressions in terms of a finite sum of a finite-range integral are proposed. Moreover, the penalty in signal to noise ratio (SNR) due to arbitrarily correlated channel fading is also investigated. Finally, the accuracy of the results is verified by computer simulation.     

Analysis of differentially coherent linear receivers over Rician-faded CDMA channels

RicianAccurate performance analysis for linear receivers over frequency- and time-selective asynchronous code-division multiple-access Rician-fading channels is very useful and a general approach to this topic is very desirable. In this paper, by using a decision variable-based moment generating function approach, we provide a unified bit-error probability (BEP) analysis framework for different linear detectors with binary or quaternary differential phase-shift keying and postdetection combining over Rician-fading channels, taking into account the effects of the spreading code correlation, the system and fading-channel parameters, diversity combining, and branch correlation. To reduce the complexity of the exact BEP evaluation, we furthermore provide an approximate multivariate Gaussian assumption (MGA)-based method which entails a low complexity for BEP evaluation. Ideal and approximate linear minimum mean-squared error diversity receivers for correlated Rician-fading channels are proposed. Numerical results show that the phases of the line-of-sight (LOS) components of the desired user significantly affect the receiver performance over correlated multipath Rician channels, and this may be exploited to improve performance. Also, when the LOS components are affected by a significant Doppler shift, automatic frequency control is very useful in improving the receiver performance.     

Error probability of binary NFSK and DPSK with postdetectioncombining over correlated Rician channels

For binary noncoherent orthogonal frequency-shift keying and binary differential phase-shift keying over slow nonselective Rician fading channels having arbitrarily correlated branches and unequal branch powers, a closed-form expression for the symbol-error probability in the case of postdetection equal-gain combining is obtained directly from the characteristic function of the decision variable     

Some new results for integrals involving the generalized Marcum Q function and their application to performance evaluation over fading channels

This letter evaluates some new integrals whose integrand involves the generalized Marcum Q function, both of whose arguments are linear functions of the integration variable. The resulting closed-form expressions obtained for these integrals are then applied to the error probability evaluation of noncoherent and differentially coherent detection with postdetection equal gain combining over Rayleigh and Nakagami fading channels.     

Error rates of DPSK systems with MIMO EGC diversity reception over Rayleigh fading channels

This paper analyzes the average bit error probability (BEP) of the differential binary and quaternary phase-shift keying (DBPSK and DQPSK respectively) with multiple-input multiple-output (MIMO) systems employing postdetection equal gain combining (MIMO EGC) diversity reception over Rayleigh fading channels. Finite closed-form expressions for the average BEP of DBPSK and DQPSK are presented. Two approaches are introduced to analyze the error rate of DQPSK. The proposed structure for the differential phase-shift keying (DPSK) with MIMO EGC provides a reduced-complexity and low-cost receiver for MIMO systems compared to the coherent phase-shift keying system (PSK) with MIMO employing maximal ratio combining (MIMO MRC) diversity reception. Finally, a useful procedure for computing the associated Legendre functions of the second kind with half-odd-integer order and arbitrarily degree is presented.