Exact error probability of Orthogonal Space-Time Block Codes over flat fading channels

Space time block coding is a modulation scheme recently discovered for the transmit an- tenna diversity to combat the effects of wireless fading channels. Using the equivalent Single-Input Single-Output (SISO) model, this paper presents closed-form expressions for the exact Symbol Error Rate (SER) and Bit Error Rate (BER) of Orthogonal Space-Time Block Codes (OSTBCs) with M-ary Phase-Shift Keying (MPSK) and M-ary Quadrature Amplitude Modulation (MQAM) over flat un- correlated Nakagami-m and Ricean fading channels.     

A unified approach for calculating error rates of linearlymodulated signals over generalized fading channels

We present a unified analytical framework to determine the exact average symbol-error rate (SER) of linearly modulated signals over generalized fading channels. The results are applicable to systems employing coherent demodulation with maximal-ratio combining multichannel reception. The analyses assume independent fading paths, which are not necessarily identically distributed. In all cases, the proposed approach leads to an expression of the average SER involving a single finite-range integral, which can be easily computed numerically. In addition, as special cases, SER expressions for single-channel reception are obtained. These expressions reduce to well-known solutions, give alternative (often simpler) expressions for previous results, or provide new formulas that are either closed-form expressions or simple to compute numerically     

相干DS-SS/MPSK系统中频差影响的简化评估

该文针对单径慢衰落信道模型下的相干DS-SS/MPSK系统,分析了频差对系统性能的影响,得到了误比特率的封闭表达式。首先推导了匹配滤波解扩符号的信噪比特性和相干相位估计误差的分布;然后给出了衰落信道中误比特率的精确积分式,并利用MPSK条件误符号率的麦克劳林级数形式,推导了AWGN,Nakagami-m衰落和瑞利衰落信道中BPSK,QPSK误比特率的简化逼近式。最后的数值结果表明:逼近式的精度非常高,基本没有损失,可应用于实际系统设计和性能评估。     

On the error probability of binary and M-ary signals in Nakagami-m fading channels

In this letter, we present new closed-form formulas for the exact average symbol-error rate (SER) of binary and M-ary signals over Nakagami-m fading channels with arbitrary fading index m. Using the well-known moment generating function-based analysis approach, we express the average SER in terms of the higher transcendental functions such as the Gauss hypergeometric function, Appell hypergeometric function, or Lauricella function. The results are generally applicable to arbitrary real-valued m. Furthermore, with the aid of reduction formulas of hypergeometric functions, we show previously published results for Rayleigh fading (m=1) as special cases of our expressions.     

发射天线选择空时分组码的误符号率分析

研究瑞利衰落信道上使用发射天线选择和空时分组编码的多输入多输出系统的误码性能。使用矩生成函数法和Apell超几何函数、Lauricella多变量超几何函数,推导采用相干检测的M进制相移键控(MPSK)和广义矩形M进制正交幅度调制(GR-MQAM)的平均符号错误概率(SEP)的精确闭合表达式。数值计算结果表明:增加发射天线或/和接收天线数可以改善MIMO瑞利衰落上MPSK和GR-MQAM的平均SEP性能。     

Relay Selection in Two-Way Cooperative Systems

In this paper, we present a design of two-way communication system with relay selection in two-way cooperative system over cascaded Nakagami- \(m\) fading channels. In the proposed scheme, in which all terminals are in motion as mobiles or vehicles, two users first broadcast their information to relays. Then, a single relay with a minimum sum symbol error rate (SER) will be selected to broadcast the received signals back to the sources. In other words, in the selection process, we investigate a simple suboptimal min-max criterion for relay selection, where a single relay that minimizes the maximum SER of two source nodes will be selected. Specifically, we have derived expressions of cumulative distribution function and moment generating function of end-to-end signal-to-noise ratio. By using these expressions, we have analyzed the performance of considered system in terms of outage probability and SER expression. Numerical and simulation results show the validity of the proposed mathematical analysis and point out the confirmation of the analytical results.     

增强合作中继系统在多径阴影联合衰落信道下的性能分析

针对数字通信系统在多径阴影联合衰落信道下不易获得性能闭式解的问题,运用MG（mixture Gamma）模型近似了NL（Nakagami-lognormal）衰落信道模型,在各跳具有独立不同衰落分布下研究和推导了增强合作中继系统的误码率和中断性能,数值和仿真分析验证了理论分析的正确性。结果表明运用MG近似NL模型有助于合作中继系统在多径阴影联合衰落信道下的性能研究。     

New exponential bounds and approximations for the computation of error probability in fading channels

We present new exponential bounds for the Gaussian Q function (one- and two-dimensional) and its inverse, and for M-ary phase-shift-keying (MPSK), M-ary differential phase-shift-keying (MDPSK) error probabilities over additive white Gaussian noise channels. More precisely, the new bounds are in the form of the sum of exponential functions that, in the limit, approach the exact value. Then, a quite accurate and simple approximate expression given by the sum of two exponential functions is reported. The results are applied to the general problem of evaluating the average error probability in fading channels. Some examples of applications are also presented for the computation of the pairwise error probability of space-time codes and the average error probability of MPSK and MDPSK in fading channels.     

相关Nakagami衰落信道上DE-QPSK性能分析

推导m为整数的任意相关Nakagami-m衰落信道上采用最大比合并(MRC)分集接收和相干检测的差分编码四相相移键控(DE-QPSK)调制的平均误符号率(SER)精确表达式,并利用高斯Q函数指数形式的近似表达式推导相关Nakagami-m衰落信道上采用MRC分集接收的DE-QPSK调制的平均SER近似表达式。计算机仿真结果验证了精确理论分析的正确性和近似分析的准确性。     

Adaptive trellis-coded multiple-phase-shift keying for Rayleighfading channels

An adaptive scheme for trellis-coded modulation of MPSK signals, called adaptive trellis-coded multiple-phase-shift keying (ATCMPSK), is proposed for slowly Rayleigh fading channels. The adaptive scheme employs a slightly modified rate 1/2 convolutional encoder and the corresponding Viterbi decoder to realize a family of codes of different rates which are employed according to channel conditions. During poor channel conditions, trellis-coded QPSK (TCQPSK) together with repetition schemes are employed. As channel conditions improve, higher rate schemes such as trellis-coded 16 PSK are used. An interleaving/deinterleaving method suitable for the adaptive scheme is proposed. Theoretical bounds for the error performance and an exact expression for the throughput of the proposed adaptive scheme are derived, and are compared against simulation results. Simulations have been performed to measure the performance of the scheme for different parameters and some nonideal conditions. It is shown that ATCMPSK results in considerable improvement in bit-error-rate (BER) performance of MPSK signals. Under ideal conditions, gains in the range of 3-20 dB are achieved over conventional fixed rate pragmatic trellis-coded schemes     

Generalized receiver selection combining schemes for alamouti MIMO systems with MPSK

Analytical results for the symbol error rate (SER) of M-ary phase shift keying (MPSK) in a slow, flat Rayleigh fading channel for a multiple-input multiple-output (MIMO) system using an Alamouti transmission scheme and generalized selection combining (GSC) scheme are given. Two new receiver selection schemes, generalized space-time sum-of-squares (GSTSoS) selection diversity and generalized space-time sum-of-magnitudes (GSTSoM) selection diversity are proposed. The first provides the same performance as conventional GSC, and the second provides slightly poorer performance, but neither requires channel state information and both have much simpler implementations. The SER of MPSK in Rayleigh fading using these two selection schemes is studied and compared to that of conventional GSC. The effects of channel estimation errors on each selection scheme are examined.     

Moment Generating Function Based Performance Analysis of Maximal-Ratio Combining Diversity Receivers in the Generalized-K Fading Channels

In this paper, we have analyzed the performance of maximal ratio combing (MRC) diversity receiver of the wireless communication systems over the composite fading environment, which is modelled by using the generalized-K distribution. However, this distribution has been considered as a versatile distribution for the precise modelling of a great variety of the short-term fading in conjunction with the long-term fading (shadow fading) channel conditions. In this proposed analysis, we have derived the mathematical expression for the moment generating function (MGF) of the generalized-K fading channel model that is used to evaluate a novel closed-form expression of the average bit error rate for (BER) the binary phase-shift keying /binary frequency-shift keying and average symbol error rate (SER) for the rectangular quadrature amplitude modulation scheme. We have also derived the mathematical expressions for the outage probability as well as the channel capacity for the generalized-K fading channel model.     

Performance analysis of coherent equal gain combining overNakagami-m fading channels

We study the exact average output signal-to-noise ratio (SNR) and symbol error rate (SER) of M-ary phaseshift-keying (PSK) signals with coherent equal gain combining reception. The analysis assumes independent Nakagami-m (1960) fading paths, which are not necessarily identically distributed. On one hand, we use geometric summations to obtain closed-form expressions for the average output SNR over diversity paths with an exponentially decaying power delay profile. On the other hand, capitalizing on an alternative integral representation of the conditional SER along with Gauss-Hermite quadrature integration, we derive an average SER expression in the form of a single finite-range integral and an integrand composed of tabulated functions. We also present a simpler but approximate approach for the closed-form evaluation of the SER of these signals over independent identically distributed Nakagami-m fading paths     

OFDM-MQAM在相关Nakagami-m衰落信道上的性能分析

本文研究频率选择性相关Nakagami衰落信道上采用最大比合并(MRC)分集接收的正交频分多路复用M进制正交幅度调制(OFDM-MQAM)系统.使用矩生成函数(MGF)方法和高斯超几何函数、Appell超几何函数或Lauricella函数,推导任意衰落参数频率选择性相关Nakagami衰落信道上MRC分集接收的OFDM-MQAM系统的误符号率(SER)性能,获得了OFDM-MQAM误符号率的一个新的解析表达式.数值计算结果阐明了多径路径数、Nakagami衰落参数和信道脉冲响应抽头间的相关系数对OFDM-MQAM误符号率性能的影响.     

An Exact Error Probability Analysis of OFDM Systems with Frequency Offset

In this paper, we derive exact closed form bit error rate (BER) or symbol error rate (SER) expressions for orthogonal frequency division multiplexing (OFDM) systems with carrier frequency offset (CFO). We consider the performance of an OFDM system subject to CFO error in additive white Gaussian noise (AWGN), frequency flat and frequency selective Rayleigh fading channels. The BER/ SER performances of BPSK and QPSK modulation schemes are analyzed for AWGN and frequency-flat Rayleigh fading channels while BPSK is considered for frequency-selective Rayleigh fading channels. Our results can easily be reduced to the respective analytical error rate expressions for the OFDM systems without CFO error. Furthermore, the simulation results are provided to verify the accuracy of the new error rate expressions.     

Performance Analysis of OSTBC Transmission in Amplify-and-Forward Cooperative Relay Networks

A performance analysis is presented for amplify-and-forward (AF) cooperative relay networks employing transmit antenna diversity with orthogonal space-time block codes (OSTBCs), where multiple antennas are equipped at the transmitter. We develop a symbol-error-rate (SER) and outage performance analysis for OSTBC transmissions with and without cooperative diversity over flat Rayleigh fading channels. We first derive exact probability density functions (pdf's) and cumulative distribution functions (cdf's) for the system SNR without direct transmission with an arbitrary number of transmit antennas and then present the exact closed-form SER and outage probability expressions. Next, we derive the moment-generating function (MGF) for the overall system SNR with direct transmission and present the exact SER and outage probability with joint transmit antenna diversity and cooperative diversity. The theoretical analysis is validated by simulations, which indicate an exact match between them. The results also show how the transmit antenna diversity and the cooperative diversity affect the overall system performance.      

Signaling constellations for fading channels

The performance of various coherent 8-ary and 16-ary modulations in additive white Gaussian noise (AWGN) and slowly fading channels are analyzed. New expressions for the exact symbol error rates (SER) in fading with diversity combining are derived for any two-dimensional signaling format having polygonal decision boundaries. Maximal ratio combining, equal gain combining, and selection combining are considered. The SER formulas obtained make it possible for the first time to optimize parameters of various constellations precisely and to determine,which constellation has the lowest probability of error. For example, a star constellation such as that specified in the CCITT V.29 standard can be improved by adjusting the amplitude ratios of the points in the constellation to save about 0.63 dB power in AWGN without sacrificing the phase error tolerance, while maintaining the same error rate. The sensitivity of each constellation to phase error is presented and comparisons are made. Six 8-ary signal sets and 11 16-ary signal sets are examined using the new symbol error probability formulas to determine best signal sets for fading channels     

Performance analysis of space-time block codes over keyhole Nakagami-m fading channels

In multiple-input-multiple-output (MIMO) fading environments, degenerate channel phenomena, called keyholes or pinholes, may exist under the realistic assumption that the spatial fading is uncorrelated at the transmitter and the receiver, but the channel has a rank-deficient transfer matrix. In this paper, we analyze the exact average symbol error rate (SER) of orthogonal space-time block codes (STBCs) with M-PSK and M-QAM constellations over Nakagami-m fading channels in the presence of the keyhole. We derive the moment generating function (MGF) of instantaneous signal-to-noise ratio (SNR) after space-time block decoding (signal combining) in such channels. Using a well-known MGF-based analysis approach, we express the average SER of the STBC in the form of single finite-range integrals whose integrand contains only the derived MGF. Numerical results show that the keyhole significantly degrades the SER performance of the STBC from idealistic behaviors in independent identically distributed MIMO channels.     

Optimal diversity combining based on linear estimation of rician fading channels

Optimal receiver diversity combining employing linear channel estimation is examined. Based on the statistical properties of least-squares (LS) and minimum mean square error (MMSE) channel estimation, an optimal diversity receiver for wireless systems employing practical linear channel estimation on Rician fading channels is proposed. The new receiver structure includes the conventional maximal ratio combining receiver as a special case. Exact analytical expressions for the symbol error rates (SERs) of LS and MMSE channel estimation aided optimal diversity combining are derived. It is shown that, if an optimal detector is used, an MPSK wireless system with MMSE channel estimation has the same SER when the MMSE channel estimation is replaced by LS estimation. This is an interesting counterexample to the common perception that channel estimation with smaller mean square error leads to smaller SER. Extensive simulation results validate the theoretical results.     

Nakagami-m衰落信道下空时分组码的性能估计

基于等效单输入单输出SISO (Single-input Single-output) 模型,利用矩量母函数 (MGF) 分析法,空时分组码STBC (Space-Time Block Coding) 的误符号率是可以得到其准确闭式表达式的.对于独立同分布Nakagami-m衰落信道下的空时分组码的性能进行了研究,给出了采用M-PSK 和M-QAM调制方案的不同空时分组编码矩阵误符号率的闭式解以及基于闭式解的解析性能结果,通过蒙特卡洛仿真验证了闭式解的准确性.还从调制方案的角度对于几种新的空时分组码的性能进行了一些新的讨论.