Oversampling Increases the Pre-Log of Noncoherent Rayleigh Fading Channels

We analyze the capacity of a continuous-time, time-selective, Rayleigh block-fading channel in the high signal-to-noise ratio (SNR) regime. The fading process is assumed stationary within each block and to change independently from block to block; furthermore, its realizations are not known a priori to the transmitter and the receiver (noncoherent setting). A common approach to analyzing the capacity of this channel is to assume that the receiver performs matched filtering followed by sampling at symbol rate (symbol matched filtering). This yields a discrete-time channel in which each transmitted symbol corresponds to one output sample. Liang & Veeravalli (2004) showed that the capacity of this discrete-time channel grows logarithmically with the SNR, with a capacity pre-log equal to $1-{Q}/{N}$. Here, $N$ is the number of symbols transmitted within one fading block, and $Q$ is the rank of the covariance matrix of the discrete-time channel gains within each fading block. In this paper, we show that symbol matched filtering is not a capacity-achieving strategy for the underlying continuous-time channel. Specifically, we analyze the capacity pre-log of the discrete-time channel obtained by oversampling the continuous-time channel output, i.e., by sampling it faster than at symbol rate. We prove that by oversampling by a factor two one gets a capacity pre-log that is at least as large as $1-1/N$. Since the capacity pre-log corresponding to symbol-rate sampling is $1-Q/N$, our result implies indeed that symbol matched filtering is not capacity achieving at high SNR.Comment: To appear in the IEEE Transactions on Information Theor

Capacity bounds for MIMO microwave backhaul links affected by phase noise

We present bounds and a closed-form high-SNR expression for the capacity of multiple-antenna systems affected by Wiener phase noise. Our results are developed for the scenario where a single oscillator drives all the radio-frequency circuitries at each transceiver (common oscillator setup), the input signal is subject to a peak-power constraint, and the channel matrix is deterministic. This scenario is relevant for line-of-sight multiple-antenna microwave backhaul links with sufficiently small antenna spacing at the transceivers. For the 2 by 2 multiple-antenna case, for a Wiener phase-noise process with standard deviation equal to 6 degrees, and at the medium/high SNR values at which microwave backhaul links operate, the upper bound reported in the paper exhibits a 3 dB gap from a lower bound obtained using 64-QAM. Furthermore, in this SNR regime the closed-form high-SNR expression is shown to be accurate.Comment: 10 pages, 2 figures, to appear in IEEE Transactions on Communication

On the Capacity of the Wiener Phase-Noise Channel: Bounds and Capacity Achieving Distributions

In this paper, the capacity of the additive white Gaussian noise (AWGN) channel, affected by time-varying Wiener phase noise is investigated. Tight upper and lower bounds on the capacity of this channel are developed. The upper bound is obtained by using the duality approach, and considering a specific distribution over the output of the channel. In order to lower-bound the capacity, first a family of capacity-achieving input distributions is found by solving a functional optimization of the channel mutual information. Then, lower bounds on the capacity are obtained by drawing samples from the proposed distributions through Monte-Carlo simulations. The proposed capacity-achieving input distributions are circularly symmetric, non-Gaussian, and the input amplitudes are correlated over time. The evaluated capacity bounds are tight for a wide range of signal-to-noise-ratio (SNR) values, and thus they can be used to quantify the capacity. Specifically, the bounds follow the well-known AWGN capacity curve at low SNR, while at high SNR, they coincide with the high-SNR capacity result available in the literature for the phase-noise channel.Comment: IEEE Transactions on Communications, 201

On an Achievable Rate of Large Rayleigh Block-Fading MIMO Channels with No CSI

Training-based transmission over Rayleigh block-fading multiple-input multiple-output (MIMO) channels is investigated. As a training method a combination of a pilot-assisted scheme and a biased signaling scheme is considered. The achievable rates of successive decoding (SD) receivers based on the linear minimum mean-squared error (LMMSE) channel estimation are analyzed in the large-system limit, by using the replica method under the assumption of replica symmetry. It is shown that negligible pilot information is best in terms of the achievable rates of the SD receivers in the large-system limit. The obtained analytical formulas of the achievable rates can improve the existing lower bound on the capacity of the MIMO channel with no channel state information (CSI), derived by Hassibi and Hochwald, for all signal-to-noise ratios (SNRs). The comparison between the obtained bound and a high SNR approximation of the channel capacity, derived by Zheng and Tse, implies that the high SNR approximation is unreliable unless quite high SNR is considered. Energy efficiency in the low SNR regime is also investigated in terms of the power per information bit required for reliable communication. The required minimum power is shown to be achieved at a positive rate for the SD receiver with no CSI, whereas it is achieved in the zero-rate limit for the case of perfect CSI available at the receiver. Moreover, numerical simulations imply that the presented large-system analysis can provide a good approximation for not so large systems. The results in this paper imply that SD schemes can provide a significant performance gain in the low-to-moderate SNR regimes, compared to conventional receivers based on one-shot channel estimation.Comment: re-submitted to IEEE Trans. Inf. Theor

The fading number of multiple-input multiple-output fading channels with memory

Abstract—The fading number of a general (not necessarily Gaussian) regular multiple-input multiple-output (MIMO) fading channel with arbitrary temporal and spatial memory is derived. The channel is assumed to be non-coherent, i.e., neither receiver nor transmitter have knowledge about the channel state, but they only know the probability law of the fading process. The fading number is the second term in the asymptotic expansion of channel capacity when the signal-to-noise ratio (SNR) tends to infinity. It is shown that the fading number can be achieved by an input that is the product of two independent processes: a stationary and circularly symmetric direction- (or unit-) vector process whose distribution needs to be chosen such that it maximizes the fading number, and a non-negative magnitude process that is independent and identically distributed (IID) and that escapes to infinity. Additionally, in the more general context of an arbitrary stationary channel model satisfying some weak conditions on the channel law, it is shown that the optimal input distribution is stationary apart from some edge effects. I

Analysis and Design of Line of Sight MIMO transmission systems

A cost-effective solution to the problem of guaranteeing backhaul connectivity in mobile cellular networks is the use of point-to-point microwave links in the Q-Band and E-Band. The always increasing rate in mobile data traffic makes these microwave radio links a potential bottleneck in the deployment of high-throughput cellular networks. A fundamental way to characterize the impact of phase noise on the throughput of these systems is to study their Shannon capacity. Unfortunately, the capacity of the phase-noise channel is not known in closed-form, even for simple channel models. The effect of phase noise in telecommunication systems is more evident in presence of multiple antennas at transmitter and receiver because of the overlapping of phase noise contribution in receivers. We propose a simulated-based tool to compute a lower bound to channel capacity for SISO and MIMO systems in presence of phase noise with one oscillator shared among the antennas per side and we give a non asymptotic expression of an upper bound to capacity always for SISO and MIMO channels. Finally we present a low complex phase detector based on combination of Phase Locked Loop (PLL) exploiting the decisions made by a turbo decoder. The aim of this work is showing a way to bound the channel capacity for single antenna and multiple antennas channels impaired by phase noise generated by instabilities in oscillators driving all the transceivers, and compare the performance of the proposed phase detector to those theoretical limits