Error rate of asynchronous DS-CDMA in Nakagami fading

An accurate bit-error-rate (BER) calculation method is derived for a binary direct-sequence (DS) spread-spectrum multiple-access (SSMA) system using conventional matched filter receivers and random sequences on flat-fading Nakagami channels. A closed-form expression for the characteristic function of a sum of multiple Nakagami interfering signals is found. The accuracy of the standard Gaussian approximation (SGA) is assessed for DS code-division multiple-access (CDMA) systems operating on Nakagami fading channels.     

Bit error probability of MDPSK in Nakagami fading channels

A general formula for the bit error probability of M-ary DPSK transmission with equal gain combining diversity over frequency non-selective m-distributed Nakagami fading channels is derived. Simulations have shown that the analysis is efficient and accurate     

Error probability performance for W-CDMA systems with multiple transmit and receive antennas in correlated Nakagami fading channels

The bit error rate (BER) performance of a two-dimensional (2-D) RAKE receiver, in combination with transmit diversity on the downlink of a wide-band CDMA (W-CDMA) system, is presented. The analyses assume correlated fading between receive antenna array elements, and an arbitrary number of independent but nonidentical resolvable multipaths combined by the RAKE receiver in the general Nakagami-m (1960) fading channel framework. The impact of the array configuration (e.g., the number of transmit antennas and receive antennas, the antenna element separation) and the operating environment parameters (such as the fading severity, angular spread and path delay profile) on the overall space-path diversity gain can be directly evaluated. In addition, the exact pairwise error probability of a convolutional coded system is obtained, and the coding gain of a space-path diversity receiver is quantified.     

Error probability bounds for M-PSK and M-DPSK and selective fadingdiversity channels

A method is described for obtaining tight closed-form bounds on the probability of error for M-ary phase-shift keying (M-PSK) and M-ary differential phase-shift keying (M-DPSK) on fading diversity channels. The channels exhibit doubly selective fading and have specular components. In addition, the random impulse responses of the diversity channels may be correlated; and the probability distributions for the fading on different diversity channels need not be the same. Error probability expressions are given for binary DPSK, 8-DPSK, and 16-DPSK modulation as examples of the application of the general method described     

Unified error probability analysis for generalized selectioncombining in Nakagami fading channels

We study generalized selection combining (GSC) schemes in independent Nakagami fading channels, where N diversity branches with the largest instantaneous signal-to-noise ratios (SNRs) are selected from the total of L (N⩽L) branches and then coherently or noncoherently combined. We propose two different techniques to derive the moment generating function (MGF) expressions for the GSC output SNR in generalized Nakagami fading channels, where there are distinct and noninteger fading severity parameters, as well as different average SNRs in different diversity branches. For arbitrary fading severity parameter m_k, k=1, ···L, the MGF expression is given in a summation of N-dimensional definite integrals with the limits independent of SNR or channel parameters, and therefore can be evaluated very efficiently with numerical methods. Furthermore, for integer m_k closed-form MGF expressions are derived. Specializations of our results to Rayleigh channels and independent identically distributed (i.i.d.) Nakagami channels are presented, which are either new or equivalent to previously published results. Using the newly derived MGF expression, we provide a unified error probability analysis for many coherent and noncoherent modulation/detection schemes     

Outage probability of multihop transmission over Nakagami fading channels

We present a general analytical framework for the evaluation of the end-to-end outage probability of multihop wireless communication systems with nonregenerative relays over Nakagami fading channels. It is shown that the presented results can either be exact or tight lower bounds on the performance of these systems depending on the choice of the relay gain. More specifically, we obtain a closed-form expression for the moment generating function of the reciprocal of the end-to-end signal-to-noise ratio (SNR) and we then use this expression to calculate the outage probability via numerical inversion of the Laplace transform. Numerical examples show that regeneration is more crucial at low average SNR and for multihop systems with a large number of hops.     

MRC performance for binary signals in Nakagami fading with generalbranch correlation

Exact expressions are derived for the performance of predetection maximal ratio combiner diversity reception with L correlated branches in Nakagami fading. Bit error rates are evaluated for both coherent and noncoherent binary phase-shift-keying and frequency-shift-keying signals, starting from the L-variate moment generating function of the random input power vector. The new formulation presented for the bit error rate, in which the covariance matrix of the fading at the L branches explicitly appears, allows arbitrary branch correlation to be taken into account for any diversity order in the case of identical fading severity on the branches. Results are presented for evaluation of the outage probability, for integer values of fading severity, as well as for the effect of the presence of unbalanced channels with arbitrary correlation     

Information outage probability of distributed STBCs over Nakagami fading channels

Space-time block codes (STBCs) allow utilising the diversity provided by multiple-input-multiple-output (MIMO) communication channels, thereby decreasing the outage probability for a given communication rate. The contribution of this letter is the derivation of a closed-form expression of the outage probability of distributed STBCs deployed over Nakagami flat fading channels with different channel gains and fading parameters.     

Error probability of coherent detection for trellis-coded partialresponse CPM on Rician fading channels

Trellis-coded continuous phase modulation (TC-CPM) schemes are attractive for bandwidth and power limited communication systems such as mobile satellite communications and land mobile radio communications. A coherent receiver for interleaved partial response TC-CPM is derived. A true upper bound on the bit error probability for flat fading channels is derived by showing that TC-CPM is equivalent to a trellis-coded modulation scheme. The upper bound is evaluated by defining an error-state diagram along with a set of characteristic distances and then applying transfer function bounding techniques. Comparison with simulation results shows the upper bound tight to within 1.5-2 dB     

Average error probability for quadriphase modulated DS-SSMA communications through Nakagami fading channel

An asynchronous direct sequence spread spectrum multiple access system using quadrature phase shift keying modulation through Nakagami'sm-distributed fading channel is considered for nondiversity reception. Approximation to the average error probability is evaluated in two steps. Using the Gauss quadrature rule, the moments of the multiple interferences are used to evaluate the conditional probability conditioned on a fixed fading amplitude of the desired signal. The probability density function of the desired signal is Nakagami distributed. The average error probability which is the expected value of the conditional probability is evaluated by the trapezoidal integration method. This method provides a good approximation to the average error probability for a small to a fairly large number of users. Numerical results are presented for a set of Gold code of code length 127.     

Diversity reception of nonorthogonal multipulse signals inmultiuser Nakagami fading channels

We consider the problem of multiantenna reception of nonorthogonal multipulse signals in a multiuser system operating over a flat-flat Nakagami fading channel, wherein each user sends an M-ary information symbol by transmitting one out of M available waveforms. The receiver first-stage is a decorrelative filter, which gets rid of the MAI, and whose output, is then properly processed in order to decode the information symbols from the user of interest. In particular, we derive both the optimum noncoherent and the GLRT detectors, and show that the latter receiver not only is simpler to implement, but also achieves a performance level very similar to that of the former receiver     

Nakagami衰落信道下噪声跟踪干扰检测性能分析

针对慢跳频通信中噪声跟踪干扰的检测问题,提出了一种新的噪声跟踪干扰检测算法.该检测算法应用认知无线电中协作频谱感知方法,分析了接收信号的条件概率密度函数,研究了加性高斯白噪声信道下单跳信号存在干扰的检测性能.在此基础上,推导了Nakagami衰落信道下单跳信号存在干扰的检测概率和虚警概率,通过对检测概率和虚警概率中的多重积分进行化简,得到了检测概率和虚警概率的级数表达式.单跳信号检测后,把检测结果上报到融合中心,应用协作频谱感知中的“k out of n”准则分析了噪声跟踪干扰的检测性能.仿真结果验证了理论分析的正确性.     

Improved-performance noncoherent weighted-coefficients diversity combiner for DPSK and NC-FSK signals in nonidentical Nakagami fading channels

It is well-known that noncoherent equal-gain combining (NC-EGC) is the simplest combining technique for noncoherent and differentially coherent communication systems. However, for nonidentical Nakagami-m channels (channels having nonuniform multipath intensity profile (MIP) and/or arbitrary non-integer fading parameters), the use of NC-EGC has three main disadvantages. First, its performance serves as a lossy upper bound to that of the optimum diversity combiner. Second, it results in complicated expressions for the system average error performance. Third, it incurs noncoherent combining loss (does not aid the use of diversity) at relatively low average signal-to-noise ratio (SNR). In this letter, we propose a modified version of the NC-EGC, which is a noncoherent combiner with weighting coefficients, to overcome the disadvantages of the conventional one. We show that this alternative combiner does provide improvements over the conventional N.C-EGC for all values of average SNRs, it does not incur any noncoherent combining loss, and it leads to a design of the receiver whose average error performance can be evaluated easily.     

A new ML detection algorithm for Orthogonal Multicode system in Nakagami fading channel

Based on the Maximum-Likelihood （ML） criterion, this paper proposes a novel noncoherent detection algorithm for Orthogonal Multicode （OM） system in Nakagami fading channel. Some theoretical analysis and simulation results are presented. It is shown that the proposed ML algorithm is at least 0.7 dB better than the conventional Matched-Filter （MF） algorithm for uncoded systems, in both non-fading and fading channels. For the consideration of practical application, it is further simplified in complexity. Compared with the original ML algorithm, the simplified ML algorithm can provide significant reduction in complexity with small degradation in performance.     

Coded M-DPSK with built-in time diversity for fading channels

Good coded modulation for fading channels requires built-in time diversity. Under a constraint on the interleaving delay, the authors construct and compare three categories of coded M-DPSK (M-ary differential phase-shift keying) schemes with 4⩽M⩽16 for fading channels: two-dimensional trellis-coded, multidimensional trellis-coded, and block-coded. General rules for designing these schemes and their matched bit or symbol interleavers are given. A universal two-state interleaver is shown. These schemes have been extensively evaluated, using computer simulations, for a narrow-band cellular radio channel at different vehicle speeds, with and without twofold antenna diversity     

Cochannel interference computation for arbitrary Nakagami fading

A characteristic function method is used to calculate the probability that the signal-to-interference ratio (SIR) drops below some predefined threshold (probability of outage). The mobile unit receives a desired signal which has undergone Nakagami (1960) fading and multiple, cochannel, and independent Nakagami interferers. The development is based on a technique due to Bealieu (1990). The advantages of the method are twofold. First, it places no integral restriction upon the Nakagami fading parameter. Second, it avoids the evaluation of higher order derivatives (residues)     

Error probability of coded STBC systems in block fading environments

In this letter, a union bound on the error probability of coded multi-antenna systems over block fading channels is derived. The bound is based on uniform interleaving of the coded sequence prior to transmission over the channel. Using this argument the distribution of error bits over the fading blocks is computed and the corresponding pair wise error probability (PEP) is derived. We consider coded systems that concatenate a binary code with a space-time block code (STBC). Coherent detection is assumed with perfect and imperfect channel state information (CSI) at the receiver, where imperfect CSI is obtained using pilot-aided estimation. Under channel estimation environments, the tradeoff between channel diversity and channel estimation is investigated and the optimal channel memory is approximated analytically. Results show that the performance degradation due to channel memory decreases as the number of transmit antennas is increased. Moreover, the optimal channel memory increases with increasing the number of transmit antennas.     

Error probability analysis for 16 STAR-QAM in frequency-selectiveRician fading with diversity reception

The bit-error rate (BER) performance of differential 16 STAR-QAM in frequency-selective Rician fading channels with diversity reception is theoretically analyzed for three different types of delay profiles: double-spike, one-sided exponential, and Gaussian profiles as well as two kinds of pulse-shaping filtering: a raised cosine (RC) Nyquist signaling pulse and the rectangular pulse. The effect of time delay between line-of-sight (LOS) and multipath components is also included in the analysis and shown to degrade the system performance significantly     

Error rates for Nakagami-m fading multichannel reception of binaryand M-ary signals

This paper derives new closed-form formulas for the error probabilities of single and multichannel communications in Rayleigh and Nakagami-m (1960) fading. Closed-form solutions to three generic trigonometric integrals are presented as part of the main result, providing a unified method for the derivation of exact closed-form average symbol-error probability expressions for binary and M-ary signals with L independent channel diversity reception. Both selection-diversity and maximal-ratio combining (MRC) techniques are considered. The results are generally applicable for arbitrary two-dimensional signal constellations that have polygonal decision regions operating in a slow Nakagami-m fading environments with positive integer fading severity index. MRC with generically correlated fading is also considered. The new expressions are applicable in many cases of practical interest. The closed-form expressions derived for a single channel reception case can be extended to provide an approximation for the error rates of binary and M-ary signals that employ an equal-gain combining diversity receiver     

Distributed detection for diversity reception of fading signals innoise

A multiple-antenna diversity scheme is investigated for digital communications. Antenna observations are immediately quantized and sent to a fusion center. At the fusion center, the quantized observations are combined to form a final decision on which symbol was transmitted. The optimum reception scheme is described for the case where frequency-shift keying is employed and where slow Rayleigh fading and Gaussian additive noise are present. Two cases are studied. In the first case, an accurate estimate of the signal-to-noise ratio is available at each receiver. In the second case, estimates are not available. Results indicate that two- or three-bit quantizations may be most appropriate. Further, if binary decisions are made at each antenna, the performance may not improve if an estimate of the signal-to-noise ratio is available at each antenna or if two antennas are used instead of one