Autoregressive Time-Varying Flat-Fading Channels: Model Order and Information Rate Bounds

In this paper, we study the effect of channel memory order on the information rate bounds in time-varying flat-fading (FF) channels. We model time variations of the FF channel with autoregressive (AR) processes with varying degrees of model order. We observe that in high SNR conditions (SNR 20 dB), the information rate penalty of not knowing the AR channel is a non-increasing function of the AR model order. This is expected, since the AR channel predictability cannot decrease with increasing its order. However, in low SNR conditions, the information rate penalty in low-order AR channels can be lower than those in high-order AR channels. Likewise, the intuitive and universal monotonic increase of the information rate bounds with the AR model order is only observed in almost noiseless conditions. In the low SNR regime, however, the achievable information rate bounds in low-order AR channels can be higher than those in high-order AR channels