Channel estimation for stationary fading channels: Orthogonal versus superimposed pilots

Two training schemes namely the orthogonal pilot scheme (OPS) and the superimposed pilot scheme (SPS) are compared in terms of achievable rates in multiple-antenna fading channels with memory. For both schemes, we show that the achievable rate depends on the number of antennas, signal-to-noise ratio (SNR) and fading speed via the channel estimation error variance and the fraction of time for data transmission. To guarantee positive achievable rates, we show that for the OPS the number of transmit antennas that can be accommodated is limited by the fading speed whereas for the SPS the number of antennas can be arbitrary. For most antenna configurations, we observe that while the SPS is superior in the low-SNR and fastfading regimes, the OPS is superior in other regimes. However, for a few number of antennas (e.g., single antenna), the SPS may also be superior in the low-SNR and slow-fading regimes.