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SEP calculations for coherent M-ary FSK in different fading channels with MRC diversity

机译:具有MRC分集的不同衰落信道中相干Mary FSK的SEP计算

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In this paper, the authors derive symbol error probability (SEP) expressions for coherent Af-ary frequency shift keying (MFSK) modulation schemes in multipath fading channels. The multipath or small-scale fading process is assumed to be slow and frequency non-selective. In addition, the channel is also subjected to the usual degradation caused by the additive white Gaussian noise (AWGN). Different small-scale fading statistics such as Rayleigh, Rician (Nakagami-n), Hoyt (Nakagami-q), and Nakagami-m have been considered to portray diverse wireless environments. Further, to mitigate fading effects through space diversity, the receiver front-end is assumed to be equipped with multiple antennas. Independent and identically distributed (IID) as well as uncorrelated signal replicas received through all these antennas are combined with a linear combiner before successive demodulation. As the detection is coherent in nature and thus involves phase estimation, optimum phase-coherent combining algorithms, such as predetection maximal ratio combining (MRC), may be used without any added complexity to the receiver. In the current text, utilizing the alternate expressions for integer powers (l≤n≤4) of Gaussian Q function, SEP values of coherent MFSK are obtained through moment generating function (MGF) approach for all the fading models (with or without MRC diversity) described above. The derived end expressions are composed of finite range integrals, which can be numerically computed with ease, dispenses with the need of individual expressions for different Af, and gives exact values up to Af = 5. When the constellation size becomes bigger (M≥6), the same SEP expressions provide a quite realistic approximation, much tighter than the bounds found in previous literatures. Error probabilities are graphically displayed for each fading model with different values of constellation size Af, diversity order L, and for corresponding fading parameters (K, q, or m). To validate the proposed approximation method extensive Monte-Carlo simulations were also performed, which show a close match with the analytical results deduced in the paper. Both these theoretical and simulation results offer valuable insight to assess the efficacy of relatively less studied coherent MFSK in the context of the optimum modulation choice in wireless communication.
机译:在本文中,作者推导了多径衰落信道中相干非洲频移键控(MFSK)调制方案的符号错误概率(SEP)表达式。假设多径或小规模衰落过程缓慢且频率非选择性。另外,该信道还遭受由加性高斯白噪声(AWGN)引起的通常的降级。人们已经考虑使用诸如Rayleigh,Rician(Nakagami-n),Hoyt(Nakagami-q)和Nakagami-m等不同的小规模衰落统计数据来描绘各种无线环境。此外,为了减轻空间分集带来的衰落影响,假定接收机前端配备了多个天线。通过所有这些天线接收的独立且均匀分布(IID)以及不相关的信号副本在连续解调之前与线性组合器组合。由于检测本质上是相干的,因此涉及相位估计,因此可以使用最佳的相干合并算法,例如预检测最大比率合并(MRC),而不会给接收机带来任何复杂性。在本文中,利用高斯Q函数的整数幂(l≤n≤4)的替代表达式,通过矩生成函数(MGF)方法获得所有衰落模型(具有或不具有MRC分集)的相干MFSK的SEP值) 如上所述。派生的最终表达式由有限范围的积分组成,可以轻松地对其进行数值计算,无需使用针对不同Af的单个表达式,并给出高达Af = 5的精确值。当星座图变大时(M≥6 ),相同的SEP表达式提供了一个非常逼真的近似值,比以前的文献中所发现的范围更紧密。对于具有不同大小的星座图大小Af,分集阶数L的每个衰落模型,以及对应的衰落参数(K,q或m),以图形方式显示错误概率。为了验证所提出的近似方法,还进行了广泛的蒙特卡洛模拟,这与本文得出的分析结果非常吻合。这些理论和仿真结果都为评估在无线通信中最佳调制选择的情况下评估相对较少研究的相干MFSK的有效性提供了宝贵的见识。

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