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Register a new userUpper and Lower Bounds on the Capacity of Amplitude-Constrained MIMO Channels
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Added by
Mario Goldenbaum
Publication date
2017
fields
Informatics Engineering
and research's language is
English
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In this work, novel upper and lower bounds for the capacity of channels with arbitrary constraints on the support of the channel input symbols are derived. As an immediate practical application, the case of multiple-input multiple-output channels with amplitude constraints is considered. The bounds are shown to be within a constant gap if the channel matrix is invertible and are tight in the high amplitude regime for arbitrary channel matrices. Moreover, in the high amplitude regime, it is shown that the capacity scales linearly with the minimum between the number of transmit and receive antennas, similarly to the case of average power-constrained inputs.
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The capacity-achieving input distribution of the discrete-time, additive white Gaussian noise (AWGN) channel with an amplitude constraint is discrete and seems difficult to characterize explicitly. A dual capacity expression is used to derive analytic capacity upper bounds for scalar and vector AWGN channels. The scalar bound improves on McKellips bound and is within 0.1 bits of capacity for all signal-to-noise ratios (SNRs). The two-dimensional bound is within 0.15 bits of capacity provably up to 4.5 dB, and numerical evidence suggests a similar gap for all SNRs.
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 channels scattering function, are useful for a large range of bandwidth, and allow to coarsely identify the capacity-optimal 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.
This paper studies the capacity of a general multiple-input multiple-output (MIMO) free-space optical intensity channel under a per-input-antenna peak-power constraint and a total average-power constraint over all input antennas. The focus is on the scenario with more transmit than receive antennas. In this scenario, different input vectors can yield identical distributions at the output, when they result in the same image vector under multiplication by the channel matrix. We first determine the most energy-efficient input vectors that attain each of these image vectors. Based on this, we derive an equivalent capacity expression in terms of the image vector, and establish new lower and upper bounds on the capacity of this channel. The bounds match when the signal-to-noise ratio (SNR) tends to infinity, establishing the high-SNR asymptotic capacity. We also characterize the low-SNR slope of the capacity of this channel.
The channel law for amplitude-modulated solitons transmitted through a nonlinear optical fibre with ideal distributed amplification and a receiver based on the nonlinear Fourier transform is a noncentral chi-distribution with $2n$ degrees of freedom, where $n=2$ and $n=3$ correspond to the single- and dual-polarisation cases, respectively. In this paper, we study capacity lower bounds of this channel under an average power constraint in bits per channel use. We develop an asymptotic semi-analytic approximation for a capacity lower bound for arbitrary $n$ and a Rayleigh input distribution. It is shown that this lower bound grows logarithmically with signal-to-noise ratio (SNR), independently of the value of $n$. Numerical results for other continuous input distributions are also provided. A half-Gaussian input distribution is shown to give larger rates than a Rayleigh input distribution for $n=1,2,3$. At an SNR of $25$ dB, the best lower bounds we developed are approximately $3.68$ bit per channel use. The practically relevant case of amplitude shift-keying (ASK) constellations is also numerically analysed. For the same SNR of $25$ dB, a $16$-ASK constellation yields a rate of approximately $3.45$ bit per channel use.
In this work we consider the communication of information in the presence of a causal adversarial jammer. In the setting under study, a sender wishes to communicate a message to a receiver by transmitting a codeword $(x_1,...,x_n)$ bit-by-bit over a communication channel. The sender and the receiver do not share common randomness. The adversarial jammer can view the transmitted bits $x_i$ one at a time, and can change up to a $p$-fraction of them. However, the decisions of the jammer must be made in a causal manner. Namely, for each bit $x_i$ the jammers decision on whether to corrupt it or not must depend only on $x_j$ for $j leq i$. This is in contrast to the classical adversarial jamming situations in which the jammer has no knowledge of $(x_1,...,x_n)$, or knows $(x_1,...,x_n)$ completely. In this work, we present upper bounds (that hold under both the average and maximal probability of error criteria) on the capacity which hold for both deterministic and stochastic encoding schemes.
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