Low SNR Capacity of Noncoherent Fading Channels

Discrete-time Rayleigh fading single-input single-output (SISO) and multiple-input multiple-output (MIMO) channels are considered, with no channel state information at the transmitter or the receiver. The fading is assumed to be stationary and correlated in time, but independent from antenna to antenna. Peak-power and average-power constraints are imposed on the transmit antennas. For MIMO channels, these constraints are either imposed on the sum over antennas, or on each individual antenna. For SISO channels and MIMO channels with sum power constraints, the asymptotic capacity as the peak signal-to-noise ratio tends to zero is identified; for MIMO channels with individual power constraints, this asymptotic capacity is obtained for a class of channels called transmit separable channels. The results for MIMO channels with individual power constraints are carried over to SISO channels with delay spread (i.e. frequency selective fading).Comment: submitted to IEEE I

A Queueing Characterization of Information Transmission over Block Fading Rayleigh Channels in the Low SNR

Unlike the AWGN (additive white gaussian noise) channel, fading channels suffer from random channel gains besides the additive Gaussian noise. As a result, the instantaneous channel capacity varies randomly along time, which makes it insufficient to characterize the transmission capability of a fading channel using data rate only. In this paper, the transmission capability of a buffer-aided block Rayleigh fading channel is examined by a constant rate input data stream, and reflected by several parameters such as the average queue length, stationary queue length distribution, packet delay and overflow probability. Both infinite-buffer model and finite-buffer model are considered. Taking advantage of the memoryless property of the service provided by the channel in each block in the the low SNR (signal-to-noise ratio) regime, the information transmission over the channel is formulated as a \textit{discrete time discrete state} $D/G/1$ queueing problem. The obtained results show that block fading channels are unable to support a data rate close to their ergodic capacity, no matter how long the buffer is, even seen from the application layer. For the finite-buffer model, the overflow probability is derived with explicit expression, and is shown to decrease exponentially when buffer size is increased, even when the buffer size is very small.Comment: 29 pages, 11 figures. More details on the proof of Theorem 1 and proposition 1 can be found in "Queueing analysis for block fading Rayleigh channels in the low SNR regime ", IEEE WCSP 2013.It has been published by IEEE Trans. on Veh. Technol. in Feb. 201

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

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

Real-world wireless communication channels are typically highly underspread: their coherence time is much greater than their delay spread. In such situations it is common to assume that, with sufficiently high bandwidth, the capacity without Channel State Information (CSI) at the receiver (termed the noncoherent channel capacity) is approximately equal to the capacity with perfect CSI at the receiver (termed the coherent channel capacity). In this paper, we propose a lower bound on the noncoherent capacity of highly underspread fading channels, which assumes only that the delay spread and coherence time are known. Furthermore our lower bound can be calculated recursively, with each increment corresponding to a step increase in bandwidth. These properties, we contend, make our lower bound an excellent candidate as a simple method to verify that the noncoherent capacity is indeed approximately equal to the coherent capacity for typical wireless communication applications. We precede the derivation of the aforementioned lower bound on the information capacity with a rigorous justification of the mathematical representation of the channel. Furthermore, we also provide a numerical example for an actual wireless communication channel and demonstrate that our lower bound does indeed approximately equal the coherent channel capacity.The work of T. H. Loh was supported by the 2013 - 2017 Electromagnetics and Time Metrology Programme of the National Measurement Office, an Executive Agency of the U.K. Department for Business, Innovation and Skills, under Projects EMT13018This is the author accepted manuscript. The final version is available from IEEE via http://dx.doi.org/10.1109/TWC.2016.253167