Activity detection of a PSK in unknown white gaussian noise: optimal and suboptimal invariant detectors

We propose three solutions for the detection of the activity of phase shift keying (PSK) signals in additive white Gaussian noise environment. The symbol sequence, the complex amplitude of the signal and the noise variance are assumed to be unknown. We show that the uniformly most powerful invariant (UMPI) test does exist only if the signal-to-noise ratio (SNR) is known. We use this UMPI test in order to obtain an upper-bound performance for the evaluation of invariant detectors. We also propose two suboptimal tests namely, the generalized likelihood ratio (GLR) test, and the average likelihood ratio (ALR)-GLR test. It turns out that the computational complexity (CC) of these detectors increases exponentially with the increase of the sequence length. Therefore, we suggest a suboptimal computationally efficient implementation of the GLR. This implementation requires only 0.02 dB higher SNR in order to perform as good as the GLR. Furthermore, we develop a new inexpensive detector for the case of binary PSK (BPSK) signals, namely generalized energy detector (GED). Simulation results illustrate and compare the performance and the efficiency of these methods