Data Recovery from Sub-Nyquist Sampled Signals: Fundamental Limit and Detection Algorithm

As widely known that Nyquist rate is sufficient to sample a bandlimited signal without information loss, sub-Nyquist rate may also suffice to sample and recover signals under certain circumstances. In this paper, we study the fundamental problem of recovering data sequence from a sub-Nyquist sampled linearly modulated baseband signal, in which the signal dimension is hardly to be reduced and the problem is underdetermined. First, we derive upper bounds of the normalized minimum Euclidean distance for different sub-Nyquist sampling schemes, which shows that, they are proportional to the sampling rate within the fundamental Mazo limit. Then by making use of the finite alphabet of transmitted symbols and the intrinsic interference structure of the sample sequence, we present an efficient time-variant Viterbi algorithm to recover data from the sub-Nyquist sampled sequence. The bit error rates (BER) under different sub-Nyquist sampling scenarios are simulated and compared with both their theoretical limits and its Nyquist sampling counterpart, which validates the excellent performance of the algorithm.