In this paper, an upper bound on the symbol error probability (SEP) of the M-ary \(\theta \)-quadrature amplitude modulation scheme, in a channel subject to additive white Gaussian noise (AWGN) and \(\eta -\mu \) fading, is calculated by means of the union bound. In addition, an exact and closed-form expression for the pairwise error probability (PEP) of the system is derived. The PEP expression obtained is written in terms of the Beta function and the Lauricella hypergeometric function. Another expression for the PEP, written in terms of the Beta function and the Appell hypergeometric function, and two bounds for the PEP, one lower and one upper, are also presented. An exact expression for the optimum rotation angle for quadrature phase shift keying constellation, considering this channel model, is also determined. In addition, an analysis, in terms of PEP, of the modulation diversity system combined with a maximum ratio combining receiver in channels subject to \(\eta -\mu \) fading and AWGN noise, is performed. PEP and SEP curves, as a function of signal-to-noise ratio, are plotted and corroborated by simulations performed with the Monte Carlo method under different parameters that characterize the channel mathematically. All the expressions determined in this article are closed and new.

在本文中，一个上界的符号差错概率（SEP）中号进制\（\ THETA \）正交幅度调制方案，在一个信道受加性高斯白噪声（AWGN）和\（\ ETA - \ mu \）衰落是通过联合边界计算的。另外，导出了系统的成对错误概率（PEP）的精确且封闭形式的表达式。获得的PEP表达式是根据Beta函数和Lauricella超几何函数编写的。还介绍了用β函数和Appell超几何函数表示的PEP的另一种表达式，以及PEP的两个边界，一个较低和一个较高。考虑该信道模型，还确定了正交相移键控星座图的最佳旋转角的精确表达式。另外，就受PE （\ eta-\ mu \）影响的信道，以PEP方式分析了调制分集系统并结合了最大比例合并接收机执行衰落和AWGN噪声。PEP和SEP曲线作为信噪比的函数，通过蒙特卡罗方法在数学上表征信道的不同参数下进行的模拟绘制并得到了证实。本文确定的所有表达式都是封闭的和新的。