A Simple Lower Bound on the Noncoherent Capacity of Highly Underspread Fading Channels

Communication channels are said to be underspread if their coherence time is greater than their delay spread. In such cases it can be shown that in the infinite bandwidth limit the information capacity tends to that of a channel with perfect receiver Channel State Information (CSI). This paper presents a lower bound on the capacity of a channel with finite bandwidth, expressed in a form which is mathematically elegant, and computationally simple. The bounding method exploits the fact that most actual channels are highly underspread; and that typically more is known about their impulse response than the channel time variation. The capacity is lower bounded by finding an achievable rate for individual time blocks which are shorter than the channel coherence time, in an orthogonal frequency division multiplexing system model. A highly underspread channel of particular interest is the invehicle channel, and a numerical example is given to verify that the capacity is indeed approximately that of a channel with perfect receiver CSI. The resulting lower bound is shown to be tighter than those previously derived.