Postdetection phase combining diversity for reception of faded DPSK signals

A new postdetection diversity scheme for the differential phase detection of faded DPSK signals is proposed. It combines the detector outputs in proportion to the squared value of each branch signal envelope. The average BER of pi /4-shift quaternary differential phase shift keying (QDPSK) with two-branch diversity is obtained through computer simulations assuming Rayleigh fading. It is found that the proposed diversity is superior to selection diversity by approximately 1.5 dB.<>     

Frequency offset receiver diversity for differential MSK

A new receiver diversity scheme for differential detection of minimum shift keying (MSK) is proposed. The signal from each receiving branch is translated to a different IF frequency. The IF signals are summed and then detected by a common differential detector. The diversity scheme does not need phase adjusters, signal quality measurement circuits or a switching controller; moreover the error rate performance is equivalent to that of postdetection equal gain combining diversity, which needs plural complete receiving systems. Theoretical analysis and computer simulation results show that the diversity gain of the proposed scheme is about 13 dB at a 10^-3error rate under Rayleigh fading and 5 dB under Rician fading when the signal-to-interference power ratio is 10 dB. The static error rate performance improvement was confirmed by experimental test results. Simulation results with data from mobile propagation studies are also shown. Even in heavily shadowed cases, the probability that fading attenuation is less than 17 dB is improved from 80 to 99 percent, and a 7 to 13 dB improvement in margin requirement for 99 percent of time operation is achieved.     

Noncoherent diversity reception over Nakagami-fading channels

A method for computing the average bit-error probability of binary differential phase-shift keying (DPSK) and frequency shift-keying (FSK) signals transmitted over Nakagami asymptotically slow fading channels with postdetection diversity reception is presented to extend previously published results. The previously published results apply only for maximum ratio combining, i.e., with predetection combining, where phase coherency is necessary. The results for postdetection combining are derived with the explicit expressions for the most practical cases of independent channels and particular cases of correlated channels     

Postdetection optimal diversity combiner for DPSK differentialdetection

Postdetection diversity reception weights and combines all the detector outputs before symbol decision to combat the effects of multipath fading. A theoretical analysis of a postdetection optimal diversity combiner that can minimize the symbol error probability for differential phase shift keying (DPSK) differential detection in the presence of multiplicative Rayleigh fading, and co-channel interference (CCI) is presented. The effect of unequal average powers among diversity branches is taken into account. It is shown that the postdetection maximal-ratio combiner (MRC) described previously by the author is not optimal unless all branches have the same average power. It is also found that the combiner optimized for the effect of CCI (fading induced random FM noise) should weight each branch detector output in inverse proportion to the average CCI power (desired signal power). Assuming two-branch diversity, calculated BER (bit-error-rate) performance of π/4-shift QDPSK due to AWGN, CCI, and random FM is presented. In addition, the BER due to multipath channel delay spread (which is not treated in the theoretical analysis) is also computed to find the optimal combiner     

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.     

Experimental evaluation of postdetection diversity reception ofnarrow-band digital FM signals in Rayleigh fading

Postdetection diversity is attractive for narrowband digital FM signal reception because the cophasing function, which may be difficult to realize in a fast Rayleigh fading environment, is not required. The combining scheme evaluated here is to weight each frequency demodulator (FD) output in proportion to the νth power of the received signal envelope of that branch. Maximum diversity improvement can be obtained with ν=2 (this combiner is referred to as a postdetection maximal ratio chamber (MRC)). Experimental results are presented on postdetection diversity reception in the Gaussian minimum shift keying (GMSK) signal transmission system. Diversity combining and FD-decision algorithms (decision feedback equalizer (DFE) and maximum-likelihood sequence estimator (MLSE)) are performed by software on a computer using the data of the sampled FD output and received signal envelope obtained from a laboratory transmission system. It is shown that the MRC can attain about a 1-dB larger diversity gain than the selection combiner (SC) when two-branch diversity is used. The degradations of two-branch diversity improvement caused by the differences between demodulator sensitivities and between received signal envelope detector gains are evaluated     

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.     

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     

Comparison of diversity with simple block coding on correlatedfrequency-selective fading channels

We investigate the effects of correlation on the performance of diversity systems in wideband wireless radio environments. Specifically, the average bit error rate (BER) performance of M-ary differential phase shift keying (MDPSK) on correlated frequency-selective slow Rayleigh fading channels is analyzed. A two-branch diversity receiver with postdetection equal gain combining is considered. Nyquist pulse shaping is used and differential detection is employed at the receiver. The effects of cochannel interference on the system performance are assessed using a Gaussian interference model. To further enhance the system performance, the effects of combined diversity and forward error correction (FEC) coding on the average BER are investigated. Results using short cyclic block codes with perfect bit interleaving are obtained. The effects of the root mean square (RMS) delay spread, the amount of correlation, and the level of modulation, M, on the average BER are investigated in detail for both coded and uncoded systems. The results show that dual branch diversity combining with a correlation coefficient of 0.5 outperforms (in terms of BER) short block codes with perfect bit interleaving, and that combined diversity and coding strategies are effective in combatting the effects of frequency-selective fading     

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     

Unified analysis of postdetection diversity for binary digital FMmobile radio

An analysis is presented of postdetection diversity using both selection combining and general combining for the reception of a binary digital FM signal in a Rayleigh fading environment. Noncoherent (differential and frequency) demodulation is assumed. In the general combiner, the output of each branch demodulator is weighted by the νth power of the demodulator input signal envelope (weighting factor). The optimum weighting factor is found to be ν=2. It is shown that postdetection general combiners using weighting factors of ν=1 and 2 correspond to predetection equal-gain and maximal-ratio combiners, respectively. A closed-form solution and a fairly simple expression are derived for the average bit error rate. Numerical calculations show that the postdetection two-branch diversity gain is only about 0.9 dB inferior to the predetection system when minimum shift keying (MSK) is used     

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     

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     

SNR estimation in Nakagami-m fading with diversity combining and its application to turbo decoding

We propose an online signal-to-noise ratio (SNR) estimation scheme for Nakagami-m (1960) fading channels with L branch equal gain combining (EGC) diversity. We derive the SNR estimate based on the statistical ratio of certain observables over a block of data, and use the SNR estimates in the iterative decoding of turbo codes on Nakagami-m fading channels with L branch EGC diversity. We evaluate the turbo decoder performance using the SNR estimate under various fading and diversity scenarios (m = 0.5, 1, 5 and L = 1, 2, 3) and compare it with the performance using perfect knowledge of the SNR and the fade amplitudes.     

Noncoherent MT-MFSK signals with diversity reception in arbitrarily correlated and unbalanced Nakagami-m fading channels

This paper studies the performance of diversity applied to an efficient modulation/coding scheme using M-ary frequency-shift keying (MFSK) signals, with postdetection noncoherent diversity reception and combining over slow nonselective arbitrarily correlated and unbalanced Nakagami-m fading channels, in which the diversity branches can have unequal signal-to-noise ratios (SNRs), as well as different severity parameter m. This modulation/coding scheme is referred to as multiple tone MFSK (MT-MFSK) and is implemented based on balanced incomplete block design (BIB-design) from combinatorial theory. In MT-MFSK modulation, the number of tones used to represent the signals set is reduced compared with the conventional MFSK modulation, and each MT-MFSK signal is represented by a number of distinct orthogonal tones selected according to BIB-design. This mechanism drastically increase the bandwidth efficiency of the modulated signal and allows the modulator to create implicit frequency diversity. In this paper, we show that by combining the implicit frequency diversity of MT-MFSK signals with the diversity reception introduced by employing multiple receiving antennas, substantial improvements in performance can be obtained. A noncoherent square-law combining (SLC) soft-decision receiver is introduced and a union bound expression for the average symbol error probability is obtained. The effects of arbitrarily values of fading severity parameter m and the arbitrarily correlation between the unbalanced L diversity channels are considered. The system performance is compared with that of the conventional MFSK system. The results show that this modulation/coding scheme creates a multiplicative diversity and, therefore, performs better than the conventional MFSK system in terms of power and bandwidth efficiency.     

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.     

Optimum selection diversity for BPSK signals in Rayleigh fadingchannels

We propose a new selection diversity scheme, called |ar|-selection diversity, that selects the branch providing the largest magnitude of log-likelihood ratio (LLR). The LLR for BPSK signals in fading channels is found to be proportional to the product of the fading amplitude and the matched filter output after phase compensation. The proposed |ar|-selection diversity scheme is shown to be optimal in the sense of minimizing the bit error rate (BER), and outperform existing selection diversity schemes. We also propose a suboptimal selection diversity scheme, called |aw|-selection diversity, that does not require a phase compensation in the selection process, thereby significantly reducing implementation complexity. We show that the proposed |ar|-selection and |aw|-selection diversity schemes exhibit significant power gains over existing selection diversity schemes in Rayleigh fading channels     

On CDMA with space-time codes over multipath fading channels

We explore code-division multiple-access systems with multiple transmitter and receiver antennas combined with algebraic constellations over a quasi-static multipath fading channel. We first propose a technique to obtain transmit diversity for a single user over quasi-static fading channels by combining algebraic constellations with full spatial diversity and spreading sequences with good cross-correlation properties. The proposed scheme is then generalized to a multiuser system using the same algebraic constellation and different spreading sequences. We also propose a linear multiuser detector based on the combination of linear decorrelation with respect to all users, and the application of the sphere decoder to decode each user separately. Finally, we consider the generalization to multipath fading channels where the additional diversity advantage due to multipath is exploited by the sphere decoder, and a method of blind channel estimation based on subspace decomposition is examined.     

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