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     

Multiple-symbol differential detection for MPSK space-time block codes: decision metric and performance analysis

Approximately 3 dB signal-to-noise ratio (SNR) loss is always paid with conventional differential space-time block codes (STBCs), compared with coherent STBCs. In this paper, a multiple-symbol differential detection (MSDD) technique is proposed for M-ary phase-shift keying (PSK) STBCs. The new scheme can greatly narrow the 3-dB performance gap by extending the observation interval for differential decoding. The technique uses maximum-likelihood sequence detection instead of traditional symbol-by-symbol detection, and is carried out on the slow, flat Rayleigh fading channel. A generalized decision metric is derived for an observation interval of arbitrary length. It is shown that for a moderate number of symbols, MSDD provides approximately 1.5 dB performance improvement over conventional differential detection. In addition, a closed-form pairwise error probability and approximate bit-error probability (BEP) are derived for multiple-symbol differential binary PSK STBC. Results show that the theoretical BEP matches simulation results well. The BEP is shown to converge asymptotically with the number of symbols in the observation interval to that of the differential scheme with coherent detection.     

Exact closed-form performance analysis of optimum combining with multiple cochannel interferers and Rayleigh fading

A new closed-form expression is derived for the exact bit-error probability (BEP) for optimum combining with binary phase-shift keying. The exact BEP expression is for multiple, equal power, cochannel interferers and multiple reception branches. It is assumed that the aggregate interference and noise is Gaussian and that both the desired signal and interference are subject to Rayleigh fading. The derivation starts by expressing the optimum combining decision statistic as a sum of quadratic forms of Gaussian random variables and it proceeds to average over the fading interference. The new BEP expression has low complexity as it contains only finite sums and products.     

Performance of generalized selection combining for mobile radiocommunications with mixed cochannel interferers

The performance of generalized selection combining (GSC) space diversity for mobile radio systems in the presence of multiple cochannel interferers is studied. Two cochannel interference models are considered: (1) L cochannel interferers consisting of L-N Nakagami-m (1960) interferers and N Rayleigh interferers and (2) L cochannel interferers in which each interferer follows Nakagami-m distribution for a fraction of time and Rayleigh distribution for the remaining of time. The fading parameters of the Nakagami-m interferers are limited to integer values only. The desired signal is assumed to be Rayleigh faded. Also, all the desired signals and the cochannel interferers received on each branch are independent of each other. Closed-form expressions are derived for the probability density functions (PDFs) of the instantaneous signal-to-interference power ratio (SIR) at the output of the GSC for the two cochannel interference models. Using these SIR PDFs, closed-form expression for evaluating the outage probability and the average bit error probability (BEP) are subsequently derived. A differential phase-shift keying scheme is considered in the derivation. Numerical results showing the influences of various system parameters on the outage probability and the average BEP are then presented     

Analysis of UWB transmitted-reference communication systems in dense multipath channels

Transmitted-reference (TR) signaling, in conjunction with an autocorrelation receiver (AcR), offers a low-complexity alternative to Rake reception. Due to its simplicity, there is renewed interest in TR signaling for ultrawide bandwidth (UWB) systems. To assess the performance of these systems, we develop an analytical framework based on the sampling expansion approach. In particular, we derive closed-form expression for the bit-error probability (BEP) of TR signaling with AcR that can be used to exploit multipath diversity inherent in wideband channels. We further extend our analysis to the BEP derivation of modified AcR with noise averaging. Our methodology does not require the Gaussian approximation and is applicable for any fading scenario, provided that the correlator output signal-to-noise ratio (SNR) can be characterized in terms of a characteristic function. We show that the validity of the conventional Gaussian approximation depends on the time-bandwidth product and the number of transmitted pulses per symbol. Our results enable the derivation of a computationally simple lower bound on the BEP of TR signaling with AcR. This lower bound allows us to obtain the SNR penalty associated with an AcR, as compared with All-Rake and Partial-Rake receivers.     

Differential phase shift keying in two-path Rayleigh channel withadjacent channel interference

A formula is derived for the error probability of M-ary differential phase-shift keying with differential phase detection in a two-path Rayleigh fading channel taking into account adjacent channel interference (ACI), cochannel interference (CCI), intersymbol interference (ISI), and Doppler frequency shift. Square-root Nyquist filters are used with roll-off, β, the transmitter and receiver as in the proposed US digital mobile radio system. The presence of the second path has a profound effect on increasing the bit error probability (BEP) because it causes ISI. In the absence of ISI, ACI has a smaller effect on BEP than CCI. In the presence of ISI their effect is essentially the same. For a given bit energy-to-noise ratio, the binary system has the lowest BEP; however, the bit rate is also the lowest for a given bandwidth. When the main interference is ACI or CCI, a quaternary system has a lower BEP than the octal system. When the main interference is ISI, this is reversed     

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.     

阴影移动卫星信道中采用DPD和MRC的PRCPM的检测性能

本文给出了阴影移动卫星信道中采用差分相位检测(DPD)和最大比组合(MRC)的部分响应连续相位调制(PRCPM)信号的检测性能,并给出了实际阴影移动卫星信道中该方案的检测性能数值计算结果.     

Multiple symbol differential detection with diversity reception

In this letter we first consider the maximum-likelihood sequence estimator for multiple symbol differential detection (MSDD) over the slow fading diversity channel. Since this optimum decision metric results in a complex receiver implementation whose average bit-error probability (BEP) performance is difficult (if not impossible) to obtain analytically, we then focus our attention on evaluating the average BEP for MSDD with diversity reception in the form of postdetection equal-gain combining (EGC) giving emphasis to its ability to bridge the gap between EGC of conventional differentially detected M-PSK and maximal-ratio combining of coherently detected M-PSK with differential encoding     

Performance analysis of equalized OFDM systems in Rayleigh fading

Channel estimation is usually needed to compensate for the amplitude and phase distortions associated with a received orthogonal frequency-division multiplexing (OFDM) waveform. This paper presents a systematic approach for analyzing the bit-error probability (BEP) of equalized OFDM signals in Rayleigh fading. Closed-form expressions for BEP performance of various signal constellations [phase-shift keying (PSK), differential phase-shift keying (DPSK), quaternary phase-shift keying (QPSK)] are provided for receivers that use a linear pilot-assisted channel estimate. We also derive the optimal linear channel estimates that yield the minimum BEP and show that some previous known results are special cases of our general formulae. The results obtained here can be applied to evaluate the performance of equalized single-carrier narrowband systems as well.     

BPSK Bit Error Outage over Nakagami-m Fading Channels in Lognormal Shadowing Environments

In this letter, we address the problem of finding a tractable expression for the bit-error outage (BEO) defined as the probability to observe a given average bit error rate (BER) over a fading channel in a shadowing environment. Our contribution is two-fold: (1) a simple yet tight approximation of the bit error probability (BEP) for binary phase shift keying (BPSK) over a frequency-flat Nakagami-m fading channel is derived, which (2) facilitates the derivation of a tight lower bound of the BEO in presence of lognormal shadowing in closed form. Theoretical results are corroborated by means of simulation results, confirming the tightness of the bounds.     

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.     

M-ary CPFSK-DPD with L-diversity maximum ratio combining in Ricianfast-fading channels

We derive a formula for the bit error probability (BEP) of M-ary continuous phase frequency shift keying with differential phase detection and maximum ratio combining diversity in Rician fast-fading channels. We assume that transmitter and receiver filters distort the signal and limit the noise. We compute the BEP as a function of energy-to-noise ratio per bit (E_b/N₀) and other system and channel parameters: Rician factor K=0, 6 dB, 10, ∞; number of diversity channels L=1, 2, 3; Doppler frequency shift f_D T=0, 0.01, 0.02; Butterworth filters in transmitter and receiver of order N_T=3 and N_R=4; optimal sampling time and filter bandwidth. In all cases the BEP is significantly reduced by diversity     

Unified Analysis of UWB Transmitted-Reference Schemes in the Presence of Narrowband Interference

Transmitted-Reference (TR) signaling, in conjunction with an autocorrelation receiver (AcR), offers a low- complexity alternative to Rake reception in ultrawide bandwidth systems. This paper provides a unified performance analysis of various TR schemes by developing an analytical framework based on the sampling expansion approach. Specifically, we derive the uncoded bit error probability (BEP) of different TR signaling schemes, including TR and differential TR (DTR) signaling valid for a broad class of fading channels. We consider both AcRs and modified AcRs with noise averaging. We further develop a quasi-analytical method as well as an approximate analytical method to extend the BEP analysis to include the effect of narrowband interference (NBI). We show that the approximate analytical method is particularly useful in obtaining BEP expressions that provide insight into the effect of NBI. We quantify the effects of NBI and channel power dispersion profile on the optimum integration interval of an AcR. Finally, we compare TR and DTR signaling in terms of their sensitivity to NBI.     

Performance of Optimum and Suboptimum Combining Diversity Reception for Binary and Quadrature DPSK Over Independent, Nonidentical Rayleigh Fading Channels

dThis paper is concerned with the error-performance analysis of binary and quadrature differential phase-shift keying with differential detection over the nonselective, Rayleigh fading channel with combining diversity reception. The diversity channels are independent, but have nonidentical statistics. The fading process in each channel is assumed to have an arbitrary Doppler spectrum with arbitrary Doppler bandwidth. Both optimum diversity reception and suboptimum diversity reception are considered. Results available previously apply only to the case of second-order diversity and require numerical integration for their actual evaluation. Our results are more general in that the order of diversity is arbitrary. Moreover, the bit-error probability (BEP) result is obtained in an exact, closed-form expression which shows the behavior of the BEP as an explicit function of the one-symbol-interval fading correlation coefficient at the matched-filter output, the mean received signal-to-noise ratio per symbol per channel, and the order of diveristy.      

Error probability for coherent and differential PSK over arbitraryRician fading channels with multiple cochannel interferers

This paper discusses the performance of communication systems using binary coherent and differential phase-shift keyed (PSK) modulation, in correlated Rician fading channels with diversity reception. The presence of multiple Rician-faded cochannel users, which may have arbitrary and nonidentical parameters, is modeled exactly. Exact bit error probability (BEP) expressions are derived via the moment generating functions (MGFs) of the relevant decision statistics, which are obtained through coherent detection with maximum ratio combining for coherent PSK modulation, and differential detection with equal gain combining (EGC) for differential modulation. Evaluating the exact expressions requires a complexity that is exponential in the number of interferers. To avoid this potentially time-consuming operation, we derive two low-complexity approximate methods each for coherent and differential modulation formats, which are more accurate than the traditional Gaussian approximation approach. Two new and interesting results of this analysis are: (1) unlike in the case of Rayleigh fading channels, increasing correlation between diversity branches may lead to better performance in Rician fading channels and (2) the phase distribution of the line-of-sight or static fading components of the desired user has a significant influence on the BEP performance in correlated diversity channels     

Analytical Methods for CDMA Systems with Parallel Interference Cancellation: The Large Deviation Approach

For a simple CDMA system, we compute the bit-error probability (BEP)with soft-decisionparallel-interference-cancellation (SD-PIC). Instead of approximatingthe signal-to-noise ratio, we use a different measure to calculateperformance. This measure is the exponential rate of the BEP, i.e., thelimit of n^–1 log(BEP) = –I, for the processinggain n , where I depends only on the number of users. Weshow, using the rate as a measure, that SD-PIC improves the performance.The values of I follow as the solution of an optimization problem whichcan be calculated numerically. We use these results to derive theasymptotic behaviour of the rate for large k. We also derive results forthe second order asymptotics of the BEP. Inclusion of second orderasymptotics leads to excellent approximations.     

Binary PRCPM with differential phase detection and maximal ratiocombining diversity in fading channels

We derive a formula for the bit-error probability (BEP) of binary partial-response continuous-phase modulation (PRCPM) with N-bit differential phase detection (DPD) in a Rician fading channel subject to L-branch maximum ratio combining (MRC) diversity. We compute the BEP for minimum-shift keying (MSK), Gaussian MSK (GMSK), and 2 RC (2-b-duration raised cosine) frequency signals as a function of the energy-to-noise ratio per bit E_b/N₀ and other system and channel parameters [N=1 and 2 and L=1, 2, and 3, Rician factor K=-∞, 0, 6, 10, and ∝ dB, Doppler frequency shift f_DT=0, 0.01, and 0.02, Gaussian premodulation filter bandwidth B_gT=∞, 0.5, 0.25, and the presence or absence of a Doppler frequency tracking loop (DFTL) in the receiver]. In all cases, the BEP is significantly reduced by diversity     

Performance of Differentially Detected DPSK Over Nonselective Rayleigh Fading Channels With Maximal Ratio Combining and Multiple Cochannel Interferers

In this paper, we investigate the performance of differentially detected differential phase-shift keying (DPSK) modulation with postdetection maximal ratio combining, in nonselective Rayleigh fading channels with multiple asynchronous cochannel interferers. The approach is based on an analytical technique we have presented earlier in the literature. Exact bit-error probability (BEP) results for binary DPSK and quaternary DPSK are derived. More specifically, we look into the effects of symbol-timing offsets between the interfering signals and the desired signal on the error performance. Our results show that when all the interfering signals are synchronous with the desired signal, the impairment caused by the cochannel interference to the desired user is maximum. On the other hand, when all the interfering signals are half-symbol-duration-delayed with respect to the desired user, they introduce the minimum impairment. Based on these findings, upper and lower bounds on the BEP are derived in simple closed form. Our explicit BEP results also show that the error probabilities of different transmitted symbols of the desired user are affected differently by the interfering signal     

Performance of asynchronous DS-CDMA using a maximal ratio combiningdiversity over a Rician fading channel

The final closed-form expression for bit error probability (BEP) is presented for a DS-CDMA system using a maximal ratio combining (MRC) diversity over a Rician fading channel. The accuracy of the BEP estimate evaluated by this expression is verified by comparison with a semi-analytic simulation result. The effect that diversity order has on the BEP is also considered for typical multipath delay profiles with different Rician ratios