Joint pilot and precoder design for optimal throughput

Abstract

For single-user, multiple-input multiple-output (MIMO) channels with Rayleigh fading correlated at the transmitter side, and where the receiver only has partial channel knowledge in form of an MMSE channel estimate, we study the joint optimization of the linear precoder and the pilot (training) sequence under the constraint of prescribed transmit power and training energy budgets. Although this joint problem is generally not convex itself, we can show that the two marginal problems of optimizing either the pilot sequence or the precoder when the other variable is fixed, are convex. Furthermore, we characterize the jointly optimal transmit and training directions. Finally, we propose a full characterization of the Pareto efficient joint power loading strategies for the case of two transmit antennas, and illustrate the behavior of the jointly optimal solution.

Optimal pilot design and power control in correlated MISO links

“…Namely, we want to determine a pilot Gram P and a mappingŵ → Q(ŵ) that solve the full problem max P 0 : tr(P )≤μP max w →Q(ŵ) : Eŵ tr(Q(ŵ))≤μQ Eŵ log(1 +ŵ † Φŵ). (9) The sum energy of the pilot symbols is limited by the energy budget μ P , while the average energy per channel access (i.e., power) available for data symbols isμ Q . Following an approach from [4], we split the variational problem of finding the optimal functionŵ → Q(ŵ) into one of temporal power control, and one of spatial transmit covariance design:…”

“…Since the latter holds for any power controlŵ → μ Q (ŵ), it also holds in general for the full-fledged problem (9). Plugging the optimal Q = μ Q vv † [cf.…”

“…The above Lemma V.1 is employed in [9], [14] to prove the eigenbasis alignment property col(U P ) ⊆ col(U R ) for the case of statistical feedback, but it is powerful enough to also cover the case of instantaneous feedback, as is being treated here. Note also that this alignment property can be straightforwardly extended to transmit-side correlated MIMO Rayleigh fading channels.…”

“…In the present article, we assume instead that the CSIR is acquired during a training procedure, in which a sequence of pilot symbols known by the receiver is transmitted. Instead of transmitting generic pilot sequences which make no assumptions on channel specificities, a case is made in [9] for designing the pilot sequence jointly with the linear precoder when the transmitter has statistical CSI.…”

“…In the present study, we modify the setup from [9] to include a delay-free feedback link. This way, the transmitter is fully cognizant of the current channel estimate and can adapt its transmit covariance accordingly in order to maximize the instantaneous achievable rate.…”