Capacity scaling in noncoherent wideband massive SIMO systems

This paper studies noncoherent wideband systems with a single antenna transmitter and a multiple antenna receiver with many elements, under signaling with peak-to-average power ratio constraints. The analysis considers the scaling behavior of capacity and achievable rates by letting both the number of antennas and the bandwidth go to infinity jointly. In contrast to prior work on wideband single input single output (SISO) channels without a-priori channel state information, it is shown that a sufficiently large number of receive antennas can make up for the vanishingly small SNR at each antenna. In particular, it is shown that when bandwidth grows sufficiently slowly with the number of antennas, the capacity scaling with an increasing number of receive antennas is the same as the optimal coherent capacity scaling. If the bandwidth grows faster than a certain threshold, however, the additional bandwidth does not help because a finite transmit power is spread over an excessively large bandwidth.