Capacity bounds for peak-constrained multiantenna wideband channels

Abstract

We derive bounds on the noncoherent capacity of a very general class of multiple-input multiple-output channels that allow for selectivity in time and frequency as well as for spatial correlation. The bounds apply to peak-constrained inputs; they are explicit in the channel's scattering function, are useful for a large range of bandwidth, and allow to coarsely identify the capacityoptimal combination of bandwidth and number of transmit antennas. Furthermore, we obtain a closed-form expression for the first-order Taylor series expansion of capacity in the limit of infinite bandwidth. From this expression, we conclude that in the wideband regime: (i) it is optimal to use only one transmit antenna when the channel is spatially uncorrelated; (ii) rank-one statistical beamforming is optimal if the channel is spatially correlated; and (iii) spatial correlation, be it at the transmitter, the receiver, or both, is beneficial.Index Terms-Noncoherent capacity, MIMO systems, underspread channels, wideband channels. Contributions:We consider a point-to-point MIMO channel model where each component channel between a given transmit antenna and a given receive antenna is underspread [13] and satisfies the standard wide-sense stationary uncorrelatedscattering (WSSUS) assumption [14]; hence, our channel model allows for selectivity in time and frequency. We assume that the component channels are spatially correlated according to the separable correlation model [8], [9] and that they are characterized by the same scattering function; furthermore, the transmit signal is peak constrained. On the basis of a discrete-time, discretefrequency approximation of said channel model that is enabled by the underspread property [15], we obtain the following results:

Single-User Beamforming in Large-Scale MISO Systems with Per-Antenna Constant-Envelope Constraints: The Doughnut Channel

“…We propose to use g(z) = 2βe −π 3 β 2 |z| 4 , β > 0. With this choice of g(z) in (26), we have 10 With N > 1, a condition that is required for the usage of EPI to be valid is that M (h) > m(h), since otherwise the set M(h) has a zero Lebesgue measure leading to an undefined h(u). From Lemma 2 and 3 it follows that the condition…”

“…In [9], the author has derived a closed-form expression for the capacity of a single-user MISO channel with a per-antenna average power constraint at the TX. In [10], the authors compute bounds on the capacity of a noncoherent single-user MIMO channel with peak per-antenna power constraints at the TX.…”

Information Theory of Underspread WSSUS Channels

“…Our focus here will be on the engineering insights that can be obtained from the bounds; we will give a flavor of the derivations and refer the reader to [DSBS10,SDBP09] for detailed derivations.…”

“…where, for each slot A detailed discussion and formal description of the MIMO extension just outlined can be found in [Sch09,SDBP09].…”

“…The resulting upper and lower bounds are presented in Theorems 3 and 4 below. A detailed derivation of these bounds can be found in [Sch09,SDBP09].…”