Probability of error for noncoherent M-ary orthogonal FSK with postdetection switched combining

The paper extends the notion of postdetection switched combining introduced by the authors to M-ary orthogonal modulation (Alouini and Simon, ibid., p.1591-1602, 2003) and proceeds to analyze and evaluate its average bit-error rate performance for the dual-branch case. The particular variation chosen for the switching strategy uses a different model than that previously used for the binary case and although it results in a slightly poorer performance, it nevertheless outperforms conventional (predetection) switched combining for all values of M. Results are obtained for a variety of popular channel models including Rayleigh, Rician, and Nakagami-m fading. Because of its relative simplicity of implementation, the proposed scheme once again offers a very attractive low-complexity solution for mitigating the deleterious effects of multipath fading.     

Error rates for M-ary noncoherent FSK in impulsive reverberation noise

It is shown that reverberation noise for primary acoustic scattering in the ocean has an integral representation and that a canonical model for its analysis can be found. Exact values of error rates for M-ary noncoherent FSK for correlation receivers in such noise are given. Comparison with the well known Gaussian case is also made.     

Analysis of M-ary FSK square law combiner under Nakagami fadingconditions

M-ary FSK transmission with square law combining over frequency non-selective m-distributed Nakagami fading with arbitrary m is studied. A closed form of the symbol error probability is derived and is verified by simulation to be accurate     

Performance analysis of cooperative network over Nakagami and Rician fading channels

This paper presents an analysis on the performance of single‐relay and multiple fixed‐relay cooperative network. The relay nodes operate in amplify‐and‐forward (AF) mode and transmit the signal through orthogonal channels. We consider maximal‐ratio combining at the destination to get the spatial diversity by adding the received signals coherently. The closed‐form moment‐generating function (MGF) for the total equivalent signal‐to‐noise ratio (SNR) is derived. The exact expressions of symbol‐error rate, outage capacity, and outage probability are obtained using the closed‐form MGF for single‐relay and multiple‐relay cooperative network with M‐ary phase shift keying (M‐PSK) and M‐ary quadrature amplitude modulation (M‐QAM) over independent and non‐identical Nakagami‐m channels and Rician fading channels. The approximated closed‐form expression of ergodic capacity is derived for both Nakagami‐m and Rician fading channels. The performance of the system is analyzed at various relay locations. The theoretical results are then compared with the simulation results obtained for binary PSK, quadrature PSK, and 16‐QAM modulation schemes to verify the analysis. Here, the expressions derived can be easily and more efficiently used to compute the performance parameters than doing Monte Carlo simulations. It is shown that cooperation is significant only for low K values for Rician by plotting cooperation gain versus K. The results show that the cooperative network performs best when the relay is located in the middle of source to destination link, at lower SNR values, and the performance of the system is worst if the relay is located closer to the source than to the destination. Copyright © 2013 John Wiley & Sons, Ltd.     

Performance analysis of wide-band M-ary FSK systems in Rayleighfading channels

Performance analysis schemes for wide-band M-ary frequency-shift keying systems with a limiter-discriminator-integrator receiver are presented along with analysis and simulation results for 4-ary and 8-ary systems. The probability distribution of clicks is required for performance analysis and is determined for Rayleigh fading channels     

Exact performance analysis of M-ary QAM with MRC diversity in Rician fading channels

The exact expression of symbol error rate (SER) is derived for coherent square M-ary quadrature amplitude modulation (M-QAM) using Lth order maximal-ratio combining (MRC) diversity in Rician fading channels with an arbitrary fading parameter. The accuracy of the SER estimates evaluated by this expression is verified through comparison with the results evaluated by numerical integration.     

Exact analysis of postdetection combining for DPSK and NFSK systemsover arbitrarily correlated Nakagami channels

Postdetection combining is a popular means to improve the bit error performance of DPSK and noncoherent FSK (NFSK) systems over fading channels. Nevertheless, the error performance of such systems in an arbitrarily correlated Nakagami environment is not available in the literature. The difficulty arises from inherent nonlinearity in noncoherent detection and from attempts to determine explicitly the probability density function of the total signal-to-noise ratio at the combiner output. We directly determine the error probability from the characteristic function of decision variables, resulting in closed-form solutions involving matrix differentiation. The performance calculation is further simplified by developing a recursive technique. The theory is illustrated by analyzing two feasible antenna arrays used in base stations for diversity reception, ending up with some findings of interest to system design     

Performance analysis of DS/CDMA with noncoherent M-ary orthogonalmodulation in multipath fading channels

The performance of a DS/CDMA system using M-ary orthogonal modulation with noncoherent demodulation is evaluated. The system operates in a multipath fading channel. A RAKE receiver structure with equal gain combining is used for demodulation. An approximation to the bit error probability is given which depends only on the first- and second-order moments of the multipath energies. The analysis results are compared with the results from computer simulations. It is seen that the approximation is accurate for multipath energies with realistic coefficient of variation. The system performance is also evaluated in terms of the capacity, which is defined as the number of users that can be supported at a given bit error probability. The approximation is used to evaluate the capacity reductions due to power variations caused by multipath fading     

Asymptotic analysis of multi‐branch EGC and SC over equally correlated Rician channels

Closed‐form asymptotic expressions for bit error rate and outage probability are derived for multi‐branch equal gain combining and selection combining receiver diversity over equally correlated Rician channels. Numerical results indicate that these analytical solutions can provide accurate estimation of bit error rate and outage probability in large signal‐to‐noise ratio regimes. The analytical results reveal some important insights into the performance characteristics of equal gain combining and selection combining diversity operating over equally correlated Rician fading channels. Copyright © 2013 John Wiley & Sons, Ltd.     

Error probability of M-ary DPSK in fast Rician fading and lognormalshadowing

A new expression for the symbol error probability (SER) of M-ary DPSK in fast Rician fading, lognormal shadowing and Gaussian noise is derived. New SER curves are computed and the effects of K factor, fading bandwidth and shadowing spread on the error probability are analysed and discussed     

Narrowband M-ary DPSK-DPD with L-diversity maximum ratio combining in Rician fading channels

In this paper the bit error probability (BEP) of narrowband M-ary differential phase shift keying with differential phase detection (MDPSK-DPD) and maximum ratio combining (MRC) in Rician fading channels is computed. Two systems shall be investigated. In the first system the transmitted pulse is a Nyquist pulse with bandwidth B = R(1 + β), where R is the symbol rate and 0 ≤ β ≤ 1 is the roll-off and the receiver is matched to the transmitter. In the second system the shaping pulse is a rectangle of duration T = 1/R modified by narrowband Butterworth filters in the transmitter and receiver. The fading channel is both time selective with Doppler frequency shifts of f_DT = 0, 0·01, 0·02 and frequency selective with time delays of t_d/T = 0, 0·1, 0·2. The number of diversity channels is L = 1, 2, 3 and the Rician factor is K = 0, 1, 6 dB, 10, ∞, thus the whole range between Rayleigh and Gaussian channels is covered. © 1997 John Wiley & Sons, Ltd.     

M-ary FSK with limiter discriminator integrator detection and DPSK with differential phase detection in a Rician Fading channel

We derive an expression for the error probability of M-ary differential phase shift keying with differential phase detection and of M-ary frequency shift keying with limiter discriminator integrator detection which is valid for Rician. Rayleigh and Gaussian channels.     

Analysis of the error performance of adaptive array antennas for CDMA with noncoherent M-ary orthogonal modulation in Nakagami fading

This letter presents an analytical model for evaluating the bit error rate (BER) of a direct sequence code division multiple access (DS-CDMA) system, with M-ary orthogonal modulation and noncoherent detection, employing an array antenna operating in a Nakagami fading environment. An expression of the signal to interference plus noise ratio (SINR) at the output of the receiver is derived, which allows the BER to be evaluated using a closed form expression. The analytical model is validated by comparing the obtained results with simulation results.     

Error performance of noncoherent MFSK with L-diversity oncorrelated fading channels

Noncoherent diversity reception of M-ary frequency-shift keying (MFSK) signals becomes increasingly important due to its widespread use in wireless communications. Its error performance analysis, however, is not available in the literature except for the simple case using binary modulation. We address the problem directly based on the decision variables, ending up with closed-form solutions to both conditional and average error probabilities for a general noncoherent MFSK diversity system operating on Rayleigh, Rician, and Nakagami fading channels. The solutions involve some higher order derivatives, and efficient recursive algorithms have been derived for their calculation. The solutions are very general permitting arbitrary diversity order, symbol size, channel parameters, and antenna-array covariance matrix. Numerical examples are also presented for illustration     

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     

Frequency-hopped multiple-access communications with noncoherent M-ary OFDM-ASK

A noncoherent, bandwidth-efficient modulation scheme is proposed for frequency-hopping multiple-access (FH-MA) networks. The proposed scheme is a combination of noncoherent M-ary amplitude-shift keying (NMASK) and orthogonal frequency-division multiplexing (OFDM). Using this scheme minimizes the required data bandwidth. The number of frequency slots available to the users increases significantly for a fixed spread-spectrum bandwidth (BW/sub SS/). The effect of the multiple-access interference is reduced. Simple and accurate bit error rate expressions have been derived for FH-OFDM-MASK in additive white Gaussian noise channels and for FH-OFDM-ASK in Rayleigh fading channels.     

Optimum Reed-Solamon codes for M-ary FSK modulation with harddecision decoding in Rician-fading channels

M-ary frequency shift keying (MFSK) is a power-efficient modulation method that is useful for low power and low data rate applications. The power efficiency of this modulation method increases as the signal alphabet increases at the expense of increased complexity and reduced bandwidth efficiency. We present an analysis of its uncoded and coded performance in Rician-fading channels using noncoherent demodulation with Reed-Solomon (RS) codes and hard decision decoding. Previous numerical difficulties encountered in determining the performance of large alphabet sizes are circumvented by the analysis presented, and the results obtained are used to quantify performance gains that can be realized by expanding the modulation's alphabet size. Optimum RS codes for hard decision decoding are determined using bit error probability as performance measure for a wide range of Rician channel parameters. The results of this paper should be useful as benchmarks of obtainable performance and as a reference for validating the results of simulation studies     

Optimal noncoherent detection of FSK signals transmitted overlinearly time-selective Rayleigh fading channels

Linearly time-varying fading models are used to investigate noncoherent detection of frequency shift keying (FSK) signals transmitted over frequency-flat fading channels. The structure of the optimal noncoherent FSK detector is derived and a novel analytical technique is proposed to compute the error performance of noncoherent FSK detectors in fast fading. Error performance results obtained by computer simulation are in excellent agreement with the analytical predictions     

Performance of multicode DS/CDMA with noncoherent M-ary orthogonal Modulation in multipath fading channels

This paper presents the performance analysis and simulation of a multicode direct-sequence code-division multiple-access system with noncoherent M-ary modulation, in a multipath fading environment. This type of transceiver is specified for the reverse link of the IS-95B and cdma2000 (radio configurations 1 and 2) systems and is intended to serve high-rate applications such as data transfer and video communications. While previous studies considered the analytical error performance of coherent multicode systems, little attention has been devoted in the literature to the noncoherent case. We provide concise and useful expressions for the interference terms as a function of the commonly used aperiodic cross correlation functions. After a statistical characterization of these terms, we make use of the Gaussian approximation (GA) in order to obtain the bit-error rate (BER). However, unlike some other analyses (for coherent detection) relying on the GA, in our derivation, we take into account the fact that all the codes transmitted by a mobile user fade in unison. As demonstrated via computer simulations, this fact is crucial to obtain a reliable estimate of the BER, especially when equal-gain combining (EGC) is used at the receiver. The analysis is also extended to include a simple closed-loop power control algorithm and hard handoff between multiple cells. In particular, we verify-for the multicode case-previous observations that the use of EGC allows improvement only for a certain range of values of the total interference seen at the receiver: When either the number of interfering users is too large, or too many codes are assigned to the high-rate user, the noncoherent combining loss becomes such that the use of many diversity branches can decrease the performance as compared to a system with little or no diversity.     

Exact evaluation of maximal-ratio and equal-gain diversityreceivers for M-ary QAM on Nakagami fading channels

Exact integral expressions are derived for calculating the symbol-error rate (SER) of multilevel quadrature amplitude modulation (MQAM) in conjunction with L-fold antenna diversity on arbitrary Nakagami fading channel. Both maximal-ratio combining (MRC) (in independent and correlated fading) and equal-gain combining (EGC) predetection (in independent fading) diversity techniques have been considered. Exact closed-form SER expressions for two restricted Nakagami fading cases (MRC reception) are also derived. An exact analysis of EGC for MQAM has not been reported previously, despite its practical interest. Remarkably, the exact SER integrals can also be replaced by a finite-series approximation formula. A useful procedure for computing the confluent hypergeometric series is also presented