Generic error probabilities

This paper presents new forms for an error probability associated, with the phase angle between two vectors perturbed by Gaussian noise. An interesting consequence of the underlying generic form is a new expression for the symbol error rate in MDPSK that is very similar to its counterpart for MPSK. The generic error probability is further shown to contain as special cases MPSK, MDPSK, CPFSK, and digital FM; and to give a new expression for the Marcum Q-function. The generic error probability also simplifies the error probability expressions in other situations such as nonorthogonal signaling, maximum likelihood differential detection of DPSK with block-by-block detection, and Gray coding of MDPSK     

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.     

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.     

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.     

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。     

Relation between bit and symbol error probabilities for FSK withLDI detection

In M-ary, Gray coded digital communication the bit error probability is usually approximated by the symbol error probability divided by the number of bits in a symbol. This approximation is known to be excellent for phase shift keying with coherent detection at high-signal-to-noise ratios and Gaussian channel. Here it is illustrated that this approximation may also be good for M-ary frequency shift keying with limiter-discriminator-integrator detection on Gaussian, Rayleigh, and Rician channels     

Reduced state Viterbi differential phase detection of MDPSK signals

An improved differential phase detection scheme that uses a reduced state Viterbi algorithm (RSVDPD) is proposed for the reception of M-ary differential phase shift keying (MDPSK) signals. The transmitted sequence is estimated from the received signal phases only. The number of trellis states equals that of the signal constellation points M. The branch metric is computed by tracing back the surviving path connected to each state. The bit error rate (BER) performance with RSVDPD is evaluated using computer simulation for 4DPSK transmission in additive white Gaussian noise (AWGN) channels     

CDMA-SFBC Downlink Performance

In this paper a generic code division multiple access (CDMA)-space frequency block coded (SFBC) system for downlink transmission is proposed. Closed form expressions for the bit error rate (BER) performance of the proposed CDMA-SFBC downlink system are derived and numerically evaluated considering different scenarios. The closed form BER expressions are derived for both the M-ary phase shift keying (MPSK) and the M-ary quadrature amplitude modulation (MQAM) techniques considering different CDMA-SFBC configurations. The BER expressions are evaluated for a wide range of system parameters assuming Rayleigh fading. These parameters include M-ary size and channel estimation error variance. Such evaluations are crucial not only for system performance prediction, but also for network management, monitoring and future cross-layer design.     

Some new twists to problems involving the Gaussian probabilityintegral

Using an alternate form of the Gaussian probability integral discovered a number of years ago, it is shown that the solution to a number of previously considered communication problems can be simplified and, in some cases, made more accurate (i.e. exact rather than bounded). These problems include the evaluation of: (1) the bit-error probability of uncoded phase shift keying (PSK) with Costas loop tracking; (2) word-error probability of antipodal modulation in the presence of fading; (3) bit-error probability of coded M-ary PSK (MPSK) over the memoryless fading channel with given channel-state information; (4) conditional symbol-error probability of MPSK in the presence of carrier synchronization error; and (5) the average error probability for the binary additive white Gaussian noise (AWGN) intersymbol interference channel. Also obtained is a generalization of this new alternate form to the case of a two-dimensional Gaussian probability integral with arbitrary correlation which can be used to evaluate the symbol-error probability of MPSK with I-Q unbalance     

Combined frequency and differential phase shift keying withnon-coherent detection in a satellite mobile channel

We analyze the performance of combined binary frequency and M-ary differential phase shift keying (2FSK/MDPSK) in the satellite mobile channel (SMC). We use two detectors in which the frequency symbol is detected by a limiter discriminator detector (LDD) and the phase symbol by a differential phase detector (DPD). It is shown that this system is power and bandwidth efficient when compared with other systems with constant envelope (or nearly constant envelope) and noncoherent detection like L-ary DPSK (LDPSK), Gaussian minimum shift keying (GMSK) and MSK     

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.     

Data detection of MPSK in the presence of rapidly changing carrierphase

We present a novel method for data detection of M-ary phase shift keying (MPSK) in the presence of unknown carrier phase and additive white Gaussian noise. Here, the unknown carrier phase is rapidly changing and random. That is, the unknown phase changes from symbol to symbol in a nondeterministic manner. The rate of phase change is such that phase change over two symbol intervals is negligible, but it is not necessarily negligible over a longer interval. Our proposed system outperforms traditional differential phase shift keying (DPSK) by 1.5 dB at error probabilities of 10^-3 and 10^-4. We also compare the performance of our scheme with that of multiple symbol differential detection (MSDD). Except under very slow phase change conditions, our scheme outperforms MSDD. Our decoder is well suited to mobile communication systems. Here, receivers usually move with different speeds at different times     

Reduced state transition Viterbi differential detection of M-aryDPSK signals

A reduced state transition Viterbi differential detection (RST VDD) consisting of conventional one symbol DD (1DD) and 3^L-1 state VDD is proposed for the reception of M-ary differential phase shift keying (MDPSK) signals, where L+1 is the observation time length in symbols. The proposed RST VDD has a significantly lower degree of computational complexity compared with the M^L-1 state VDD. The bit error rate (BER) performance of 8DPSK in additive white Gaussian noise (AWGN) channels is evaluated by computer simulation     

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。     

译码转发中继系统的广义最大似然非相干分组检测（英文）

This paper considers noncoherent cooperative decode-and-forward(DF) halfduplex multi-branch relay systems.Each relay branch is modeled as a probabilistic transition system at the last hop,and thus it can be considered as a relaying chain comprising multi-hop relays.An approximation to the generalized maximum likelihood(ML) noncoherent block detection is derived for uncoded M-ary modulation in a faded noisy environment.In particular,the derived noncoherent block detection in a noiseless case is equivalent to a multichannel reception with full diversity.Furthermore,the generalized detection is extended specifically to block coded M-ary phase shift keying(MPSK) modulation.For a DF three node relay system using block coded quadrature phase shift keying(QPSK),simulation results are provided to examine the end-to-end error performance of the noncoherent detection with considering the effects of network geometry and power allocation,respectively.It is shown that under a fixed power allocation,a proper relay placement can yield near full diversity for large signal-to-noise ratio.     

Diversity MPSK receivers in cochannel interference

The performance of M-ary phase shift keying (MPSK) in the presence of cochannel interference in microcellular radio environments is analyzed. Average bit error rates (BER) of MPSK using both dual-branch equal gain combining (EGG) and dual-branch selection combining (SC) are derived assuming that the desired signal experiences frequency-nonselective Ricean or Nakagami fading and the multiple interferers experience independent frequency-nonselective Rayleigh fading. Nyquist pulses are used, and perfect coherent detection is assumed at the receiver. The accuracy of the Gaussian interference approximation for diversity receivers is also assessed     

无线光自适应副载波MDPSK调制系统特性分析

无线光通信中的自适应传输技术可有效抑制大气湍流引起的信道衰落.根据接收信噪比和预定目标误比特率要求,本文对通过瞬时湍流特性改变调制阶数的无线光自适应传输的通信系统进行了研究.给出采用Malaga分布湍流模型分别描述Gamma-Gamma、对数正态以及K分布湍流信道的相关参数设置;推导了Malaga湍流信道下无线光自适应多进制差分相移键控（MDPSK,M-ary Differential Phase Shift Keying）调制系统的平均误比特率、频谱效率以及中断概率表达式,以及基于MeijerG函数的渐近表达式.MDPSK自适应和非自适应两种调制系统特性分析结果表明：自适应调制系统不但在相同电信噪比下可获得更低的平均误比特率,还可以大大提高频谱效率,而不需要增加额外传输功率或牺牲误比特率.     

Relation between bit and symbol error probabilities for frequencyshift keying with limiter-discriminator detection

In M-ary, Gray coded frequency shift keying with limiter discriminator detection the bit error probability is usually approximated by the symbol error probability divided by the number of bits in a symbol. This approximation is known to be excellent for phase shift keying with large energy-to-noise ratios and Gaussian channel. In other cases this may be questionable. The authors compute the exact values of bit error probability as a function of energy-to-noise-ratio per bit for Gaussian, Rayleigh and Rician channels. They also compute the relative error involved in this approximation     

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     

Closed-form expressions of approximate error rates for optimum combining with multiple interferers in a Rayleigh fading channel

This paper presents approximate error rates of M-ary phase shift keying (MPSK) for optimum combining (OC) with multiple cochannel interferers in a flat Rayleigh fading channel. For the first-order approximation, we derive the closed-form expression for ordered mean eigenvalues of the interference-plus-noise covariance matrix, which facilitates performance evaluation for the OC with arbitrary numbers of interferers and antenna elements without Monte Carlo simulation and multiple numerical integrals. We also derive the closed-form expressions for approximate error rates of MPSK for the OC in terms of the average error rate of MPSK for maximal ratio combining (MRC). From the simple evaluation of ordered mean eigenvalues, we show that the first-order approximation gives a simple and accurate way to analyze the performance of the OC.