相关衰落信道上MIMO系统中组合SC/MRC的性能分析

研究相关瑞利衰落信道上MIMO系统中组合发射机选择合并(SC)/接收机最大比合并(MRC)的天线分集系统性能.使用矩生成函数方法,推导相关瑞利衰落信道上采用组合SC/MRC天线分集争相干检测的M进制相移键控(MPSK),M进制正交幅度调制(MQAM),M进制脉冲幅度调制(MPAM)等几种M进制数字调制方式的误符号率精确表达式.数值计算结果阐明相关性和天线阵结构对采用组合SC/MRC天线分集的几种M进制数字调制方式的平均误符号率性能的影响.     

最大比合并接收系统在n-Rayleigh信道下的性能分析

在n-Rayleigh信道下,研究了MRC(Maximal Ratio Combining)合并接收系统的平均码字错误率(ASEP)性能。基于矩生成函数(MGF)的方法,推导了MRC接收系统在n-Rayleigh衰落信道上采用M进制相移键控(MPSK),M进制正交幅度调制(MQAM)和M进制脉冲幅度调制(MPAM)等几种M进制数字调制方式的ASEP的计算式。然后在不同条件下,仿真了系统的ASEP性能,仿真值与理论值相一致,理论分析的正确性得到了证明。分析结果表明:分集支路数和衰弱因子对系统的ASEP性能有重要影响。     

M-ary symbol error outage over Nakagami-m fading channels in shadowing environments

This letter addresses the problem of finding a tractable expression for the symbol error outage (SEO) in flat Nakagami-m fading and shadowing channels. We deal with M-ary phase shift keying (M-PSK) and quadrature amplitude modulation (M-QAM) which extends our previous results on BPSK signaling. We propose a new tight approximation of the symbol error probability (SEP) holding for M-PSK and M-QAM signals which is accurate over all signal to noise ratios (SNRs) of interest. We derive a new generic expression for the inverse SEP which facilitates the derivation of a tight approximation of the SEO in a lognormal shadowing environment.     

Virtual branch analysis of symbol error probability for hybridselection/maximal-ratio combining in Rayleigh fading

We derive analytical expressions for the symbol error probability (SEP) for a hybrid selection/maximal-ratio combining (H-S/MRC) diversity system in multipath-fading wireless environments. With H-S/MRC, L out of N diversity branches are selected and combined using maximal-ratio combining (MRC). We consider coherent detection of M-ary phase-shift keying (MPSK) and quadrature amplitude modulation (MQAM) using H-S/MRC for the case of independent Rayleigh fading with equal signal-to-noise ratio averaged over the fading. The proposed problem is made analytically tractable by transforming the ordered physical diversity branches, which are correlated, into independent and identically distributed (i.i.d.) “virtual branches,” which results in a simple derivation of the SEP for arbitrary L and N. We further obtain a canonical structure for the SEP of H-S/MRC as a weighted sum of the elementary SEPs, which are the SEPs using MRC with i.i.d. diversity branches in Rayleigh fading, or equivalently the SEPs of the nondiversity (single-branch) system in Nakagami fading, whose closed-form expressions are well-known. We present numerical examples illustrating that H-S/MRC, even with L≪N, can achieve a performance close to that of N-branch MRC     

Error Probability of Multicarrier CDMA with Orthogonality Restoring Combining Over Nakagami-m Fading

Orthogonality restoring combining (ORC) is appealing for the downlink of multicarrier code-division multiple- access (MC-CDMA) since it can eliminate multiple access interference (MAI) which would otherwise fundamentally limit the CDMA system performance. The ORC output instantaneous signal-to-noise ratio (SNR), however, takes the form of a harmonic mean of SNRs on different subcarriers, making its error performance difficult to analyze. In this paper, we tackle the problem in the framework of characteristic functions (CF) ending up with useful results for various modulation schemes including M-ary phase-shift keying (MPSK) and M-ary quadrature amplitude modulation (MQAM). The general solution for arbitrary real m can be evaluated numerically, and reduces to closed form for m being an odd multiple of half. Extensive simulations are conducted to verify the theoretical analysis. It is found that in general MQAM outperforms MPSK, and the error performance of MC-CDMA with ORC is insensitive to the number of subcarriers and to the correlation among subcarriers.     

Error probability and channel capacity analysis of wireless system over inverse gamma shadowed fading channel with selection diversity

In this paper, we present an analytical framework to analyse the error probability and the channel capacity of the inverse gamma (I‐Gamma) shadowed fading channel. First, the work discusses the utility of the I‐Gamma over log‐normal (LN) and gamma fading models where the closeness of I‐Gamma with other existing shadowing models is carried out. Utilising the probability density function (PDF) of the I‐Gamma shadowed fading channel, various metrics of the communication system, namely, the average symbol error probability (SEP), the channel capacity under optimal rate adaptation (ORA), channel inversion with fixed rate (CIFR), and truncated CIFR (TIFR) are derived. Further, the work is extended to derive a novel selection combining (SC) PDF, and the analytical results for the SEP and the channel capacity of SC diversity are presented. Furthermore, we also provide simpler asymptotic expressions for the average SEP. In addition, the simplified high and low signal‐to‐noise‐ratio (SNR) solutions to channel capacity are also provided. The derived mathematical formulations have been endorsed by comparing with Monte Carlo simulations.     

Nakagami衰落信道上组合SC/MRC的性能分析

研究Nakagami衰落信道上组合发射机选择合并(SC)/接收机最大比合并(MRC)天线分集系统的性能.使用矩生成函数方法,推导采用组合SC/MRC天线分集和相干检测的MPSK(M进制相移键控)、MQAM(M进制正交幅度调制)、MPAM(M进制脉冲幅度调制)、BFSK(二进制频移键控)、最小相关BFSK(BFSKmin)、差分编码BPSK(DE-BPSK)和预编码MSK(最小频移键控)等几种M进制数字调制方式在Nakagami衰落信道上的误符号率性能,获得了M进制数字调制系统误符号率性能的精确数学表达式.数值计算结果阐明了发射天线和接收天线数目以及衰落参数对数字调制系统误符号率性能的影响.     

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。     

双发射天线选择正交空时码分集系统性能分析

针对任意Nakagami衰落信道,分析了多输入多输出(MIMO)系统中采用双发射天线选择正交空时码的平均误码率(ASER)性能。利用矩生成函数方法,推导出采用相干检测的二进制相移键控/二进制频移键控(BPSK/BFSK)、多进制相移键控(MPSK)和多进制正交幅度调制(MQAM)的精确ASER闭合解析式,对不同条件下的系统性能做了数值仿真,验证了分析结果的正确性。     

A Simple and Accurate Approximation to the SEP of Rectangular QAM in Arbitrary Nakagami-m Fading Channels

Recently, Karagiannidis presented a closed-form solution for an integral which can be used to compute the average symbol error probability of general order rectangular quadrature amplitude modulation (QAM) in Nakagami-m fading channels with integer fading parameters. In this letter, using an accurate exponential bound for the Gaussian Q-function, we derive a simple approximate solution for that integral. In particular, the solution can be used to compute the average SEP of general order rectangular QAM over arbitrary Nakagami-m fading. Numerical results are presented to verify the accuracy of the solution     

Noncentral F-Distribution for an M-ary Phase Shift Keying Wedge-Shaped Region

This letter presents an alternative analytical expression for computing the probability of an M-ary phase shift keying (MPSK) wedge-shaped region in an additive white Gaussian noise channel. The expression is represented by the cumulative distribution function of known noncentral F-distribution. Computer simulation results demonstrate the validity of our analytical expression for the exact computation of the symbol error probability of an MPSK system with phase error.     

Average SEP of Rectangular QAM in Rayleigh Fading with GSC

This letter presents an exact-form expression for the average symbol error probability (SEP) of general rectangular quadrature amplitude modulation (QAM) in Rayleigh fading channels with generalized selection combining (GSC). Expressions for the system average SEP with maximal ratio combining (MRC) and selection combining (SC) are obtained as limiting cases. It is shown that the results herein reduce to some existing ones as special cases.     

Error probability of MPSK OFDM impaired by carrier frequency offset in AWGN channels

In this letter, we evaluate the symbol error probability of orthogonal frequency division multiplexing (OFDM) with M-ary (M>4) phase shift keying (MPSK) impaired by carrier frequency offset (CFO). A signal space decomposition (SSD) approach is proposed for additive white Gaussian noise (AWGN) channels, and then the symbol error rate (SER) performance is expressed as the sum of an infinite series with the Beaulieu series. The derived theoretical expression agrees well with the simulation results     

Performance evaluation of HDAF relaying systems for pilot and data symbol burst transmission over quasi‐static Rayleigh fading channels

This paper analyzes averaged symbol error probabilities of burst transmission consisting of pilot and data symbols for hybrid adaptive decode‐or‐amplify‐forward (HDAF) relaying systems. Under the assumption of quasi‐static Rayleigh fading channels with independent and non‐identically distribution, we consider a channel estimation scheme based on pilot symbols and show how channel estimation error affects received signal‐to‐noise ratio (SNR) and symbol error probability (SEP). Firstly, all the possible detection error‐events are presented for all the relay nodes, and their probabilities are derived as forms related with data symbol burst transmission. For the given error event, we analyze the conditional SEP as an exact form and then, the averaged SEP (ASEP) is approximately derived as a closed‐form. The simulation results verify that our derived ASEP expression is accurate over all the regions of SNR. Utilizing the proposed expressions, we can evaluate ASEP performance of HDAF relay systems easily and fast. Copyright © 2015 John Wiley & Sons, Ltd.     

Adaptive Minimum Symbol Error Rate Beamforming Assisted Detection for Quadrature Amplitude Modulation

We consider beamforming assisted detection for multiple antenna aided multiuser systems that employ the bandwidth efficient quadrature amplitude modulation scheme. A minimum symbol error rate (MSER) design is proposed for the beamforming assisted receiver, and it is shown that this MSER design provides significant performance enhancement, in terms of achievable symbol error rate, over the standard minimum mean square error (MMSE) design. A sample-by-sample adaptive algorithm, referred to as the least symbol error rate, is derived for adaptive implementation of the MSER beamforming solution. The proposed adaptive MSER scheme is evaluated in simulation using Rayleigh fading channels, in comparison with the adaptive MMSE benchmarker.     

有信道估计误差MIMO MRC系统性能研究

利用维希特随机矩阵理论和矩生成函数方法,推导了有信道估计误差的独立瑞利衰落信道上采用多输入多输出（MIMO）最大比合并（MRC）天线分集方案的矩形M进制正交幅度调制（MQAM）的平均误符号率（SER）解析表达式。数值计算结果阐明了信道估计误差和收发天线数对矩形MQAM调制MIMO MRC系统误码性能的影响。     

Energy Savings in OFDM Systems through Cooperative Relaying

Energy savings in orthogonal frequency division multiplexing (OFDM) systems is an active research area. In order to achieve a solution, we propose a new cooperative relaying scheme operated on a per subcarrier basis. This scheme improves the bit error rate (BER) performance of the conventional signal‐to‐noise ratio (SNR)‐based selection relaying scheme by substituting SNR with symbol error probability (SEP) to evaluate the received signal quality at the relay more reliably. Since the cooperative relaying provides spatial diversity gain for each subcarrier, thus statistically enhancing the reliability of subcarriers at the destination, the total number of lost subcarriers due to deep fading is reduced. In other words, cooperative relaying can alleviate error symbols in a codeword so that the error correction capability of forward error correction codes can be fully exploited to improve the BER performance (or save transmission energy at a target BER). Monte‐Carlo simulations validate the proposed approach.     

Error probability of Q-ary symbol consisting of multiple channel symbols under Rayleigh fading

Closed-form expressions for symbol error probabilities are derived for the case when modulation alphabet size M is smaller than symbol size Q. We consider slow Rayleigh fading channel where fading amplitudes and phases remain constant during one Q-ary symbol duration. An exact expression is obtained for noncoherent M-ary frequency-shift keyed (MFSK) modulation and the simple and accurate approximate expressions are obtained for M-ary phase-shift keyed (MPSK) and quadrature-amplitude modulation. Simulation results showed that the derived error probability are well agreed.     

Exact Method for the Error Probability Calculation of Three-Dimensional Signal Constellations

The contribution of this letter is the computation of exact symbol error probability (SEP) of three-dimensional (3-D) signal constellations over an additive white Gaussian noise (AWGN) channel. The originality of the proposed method is that it can be applied to any arbitrary 3-D constellation whose decision regions may not meet at right angles. We express the SEP in a triple integral form which is further simplified. The simplified form requires a single integral evaluation of standard "erf" function. Using the derived exact SEP formula, we plot SEP for a number of selected 3-D constellations. The SEP obtained using the proposed formula is validated by simulation results. It is also compared with the union bound approximation, an upper bound for SEP.     

Exact symbol error probability of general order rectangular QAM with MRC diversity reception over nakagami-m fading channels

Exact average symbol error probability (SEP) of the general order rectangular quadrature amplitude modulation (QAM) with maximal ratio combining (MRC) diversity over L independent and identically distributed Nakagami-m fading channels with arbitrary fading index m is derived in this letter. The average SEP expression is given in terms of the Appell and Gauss hypergeometric functions and is then used to study the impact of diversity reception on the performance of general order rectangular QAM with different values of the quadrature-to-in-phase decision distance ratio. It is shown that the derived expression includes some existing results as special cases.