7 research outputs found
Unitary isotropically distributed inputs are not capacity-achieving for large-MIMO fading channels
We analyze the capacity of Rayleigh block-fading multiple-input multiple-output (MIMO) channels in the noncoherent setting and prove that unitary space-time modulation (USTM) is not capacity-achieving when the total number of antennas exceeds the coherence time of the fading channel. This situation is relevant for MIMO systems with large antenna arrays (large-MIMO systems). Our result settles a conjecture by Zheng & Tse (2002) in the affirmative. The capacity-achieving input signal, which we refer to as Beta-variate space-time modulation (BSTM), turns out to be the product of a unitary isotropically distributed random matrix, and a diagonal matrix whose nonzero entries are distributed as the eigenvalues of a Beta-distributed random matrix of appropriate size. Numerical results illustrate that using BSTM instead of USTM in large-MIMO systems yields a rate gain as large as 13% for SNR values of practical interest
Unified Capacity Limit of Non-coherent Wideband Fading Channels
In non-coherent wideband fading channels where energy rather than spectrum is
the limiting resource, peaky and non-peaky signaling schemes have long been
considered species apart, as the first approaches asymptotically the capacity
of a wideband AWGN channel with the same average SNR, whereas the second
reaches a peak rate at some finite critical bandwidth and then falls to zero as
bandwidth grows to infinity. In this paper it is shown that this distinction is
in fact an artifact of the limited attention paid in the past to the product
between the bandwidth and the fraction of time it is in use. This fundamental
quantity, called bandwidth occupancy, measures average bandwidth usage over
time. For all signaling schemes with the same bandwidth occupancy, achievable
rates approach to the wideband AWGN capacity within the same gap as the
bandwidth occupancy approaches its critical value, and decrease to zero as the
occupancy goes to infinity. This unified analysis produces quantitative
closed-form expressions for the ideal bandwidth occupancy, recovers the
existing capacity results for (non-)peaky signaling schemes, and unveils a
trade-off between the accuracy of approximating capacity with a generalized
Taylor polynomial and the accuracy with which the optimal bandwidth occupancy
can be bounded.Comment: Accepted for publication in IEEE Transactions on Wireless
Communications. Copyright may be transferred without notic
On the Capacity of Large-MIMO Block-Fading Channels
We characterize the capacity of Rayleigh block-fading multiple-input
multiple-output (MIMO) channels in the noncoherent setting where transmitter
and receiver have no a priori knowledge of the realizations of the fading
channel. We prove that unitary space-time modulation (USTM) is not
capacity-achieving in the high signal-to-noise ratio (SNR) regime when the
total number of antennas exceeds the coherence time of the fading channel
(expressed in multiples of the symbol duration), a situation that is relevant
for MIMO systems with large antenna arrays (large-MIMO systems). This result
settles a conjecture by Zheng & Tse (2002) in the affirmative. The
capacity-achieving input signal, which we refer to as Beta-variate space-time
modulation (BSTM), turns out to be the product of a unitary isotropically
distributed random matrix, and a diagonal matrix whose nonzero entries are
distributed as the square-root of the eigenvalues of a Beta-distributed random
matrix of appropriate size. Numerical results illustrate that using BSTM
instead of USTM in large-MIMO systems yields a rate gain as large as 13% for
SNR values of practical interest.Comment: To appear in IEEE Journal on Selected Areas in Communicatio
Noncoherent Capacity of Underspread Fading Channels
We derive bounds on the noncoherent capacity of wide-sense stationary
uncorrelated scattering (WSSUS) channels that are selective both in time and
frequency, and are underspread, i.e., the product of the channel's delay spread
and Doppler spread is small. For input signals that are peak constrained in
time and frequency, we obtain upper and lower bounds on capacity that are
explicit in the channel's scattering function, are accurate for a large range
of bandwidth and allow to coarsely identify the capacity-optimal bandwidth as a
function of the peak power and the channel's scattering function. We also
obtain a closed-form expression for the first-order Taylor series expansion of
capacity in the limit of large bandwidth, and show that our bounds are tight in
the wideband regime. For input signals that are peak constrained in time only
(and, hence, allowed to be peaky in frequency), we provide upper and lower
bounds on the infinite-bandwidth capacity and find cases when the bounds
coincide and the infinite-bandwidth capacity is characterized exactly. Our
lower bound is closely related to a result by Viterbi (1967).
The analysis in this paper is based on a discrete-time discrete-frequency
approximation of WSSUS time- and frequency-selective channels. This
discretization explicitly takes into account the underspread property, which is
satisfied by virtually all wireless communication channels.Comment: Submitted to the IEEE Transactions on Information Theor
Information Theory of underspread WSSUS channels
The chapter focuses on the ultimate limit on the rate of reliable communication through Rayleigh-fading channels that satisfy the wide-sense stationary (WSS) and uncorrelated scattering (US) assumptions and are underspread. Therefore, the natural setting is an information-theoretic one, and the performance metric is channel capacity. The family of Rayleigh-fading underspread WSSUS channels constitutes a good model for real-world wireless channels: their stochastic properties, like amplitude and phase distributions match channel measurement results. The Rayleigh-fading and the WSSUS assumptions imply that the stochastic properties of the channel are fully described by a two-dimensional power spectral density (PSD) function, often referred to as scattering function. The underspread assumption implies that the scattering function is highly concentrated in the delay-Doppler plane. Two important aspects need to be accounted for by a model that aims at being realistic: neither the transmitter nor the receiver knows the realization of the channel; and the peak power of the transmit signal is limited. Based on these two aspects the chapter provides an information-theoretic analysis of Rayleigh-fading underspread WSSUS channels in the noncoherent setting, under the additional assumption that the transmit signal is peak-constrained