Bit Density Based Signal and Jamming Detection in 1-Bit Quantized MIMO Systems

This paper studies the problem of deciding on the absence (i.e., null hypothesis, $\mathcal{H}_0$) or presence (i.e., alternative hypothesis, $\mathcal{H}_1$) of an unknown signal embedded in the received signal in a multiple-input, multiple-output (MIMO) receiver, employing 1-bit quantization. The originality of our solution lies in quantizing the received signal by an adapted 1-bit window comparator, rather than a traditional 1-bit quantizer. This enables us to divide the space of observed binary sequences into two typical sets (w.r.t. the distribution of the no. of 1's in a sequence) asymptotically, where the first set corresponds to $\mathcal{H}_0$ and the second to $\mathcal{H}_1$. As a result, we reduce the detection problem to determining the highly probable set for an observed sequence. Thus, a very low-complexity binary hypothesis detector is proposed and its probability of detection is given. To show the high efficacy of the proposed 1-bit receiver structure, we consider two wireless applications; jamming detection in a massive MIMO system, and probing a non-stationary low-power transmitter in a wireless sensor network (WSN), assuming unknown Rayleigh-fading channels. Compared with an unquantized system employing a chi-square test, it is shown that the performance loss can be roughly as large as $10\%$ in massive MIMO and this gap diminishes as sequence length or/and jamming power increases. For WSN, we show that compared with an unquantized system, the performance gap becomes smaller when the observation interval is extended over a few symbols.