Bit density based signal and jamming detection in 1-bit quantized MIMO systems

Abstract

This paper studies the problem of deciding on the absence (i.e., null hypothesis, H0) or presence (i.e., alternative hypothesis, H1) 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 H0 and the second to H1. 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.