In continuation of an earlier study, we explore a Neymann-Pearson hypothesis testing scenario where, under the null hypothesis ($\cal{H}_0$), the received signal is a white noise process $N_t$, which is not Gaussian in general, and under the alternative hypothesis ($\cal{H}_1$), the received signal comprises a deterministic transmitted signal $s_t$ corrupted by additive white noise, the sum of $N_t$ and another noise process originating from the transmitter, denoted as $Z_t$, which is not necessarily Gaussian either. Our approach focuses on detectors that are based on the correlation and energy of the received signal, which are motivated by implementation simplicity. We optimize the detector parameters to achieve the best trade-off between missed-detection and false-alarm error exponents. First, we optimize the detectors for a given signal, resulting in a non-linear relation between the signal and correlator weights to be optimized. Subsequently, we optimize the transmitted signal and the detector parameters jointly, revealing that the optimal signal is a balanced ternary signal and the correlator has at most three different coefficients, thus facilitating a computationally feasible solution.

翻译：延续先前研究，我们探讨了奈曼-皮尔逊假设检验场景：在零假设（$\cal{H}_0$）下，接收信号为白噪声过程$N_t$（通常非高斯分布）；在备择假设（$\cal{H}_1$）下，接收信号包含受加性白噪声污染的确定性发射信号$s_t$，其噪声由$N_t$与源于发射器的另一噪声过程$Z_t$叠加而成（同样未必服从高斯分布）。我们的方法聚焦于基于接收信号相关性和能量的检测器，其设计初衷在于实现简便性。我们优化检测器参数以达成漏检与虚警误差指数的最佳权衡。首先，针对给定信号优化检测器，揭示信号与相关器权值间需优化的非线性关系；继而联合优化发射信号与检测器参数，发现最优信号为平衡三进制信号，而相关器最多仅需三种不同系数，从而确保了计算可行解。