Benefits of coding in a noncoherent massive SIMO system

We consider one single antenna transmitter communicating with a receiver with a large number of antennas. Motivated by the optimal noncoherent detector in a Rayleigh fading channel, we propose a noncoherent energy-based communication scheme that does not require knowledge of instantaneous CSI (channel state information) at either the transmitter or the receiver; it uses only the statistics of the channel and noise. We explore the impact of coding to reduce the number of antennas needed for this system to achieve a given performance target. In particular, random coding error exponents for this system are used to determine tradeoff curves between the number of antennas and the blocklengths associated with a guaranteed performance target. However, since random codes have exponentially increasing decoding complexity with increasing blocklength, we also consider a simplified codebook design that has significantly lower encoding and decoding complexity. Simulations suggest that for small blocklengths, the performance of this simplified codebook is competitive with random coding constructions.