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Register a new userCapacity and Modulations with Peak Power Constraint
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Added by
Shiro Ikeda Dr.
Publication date
2010
fields
Informatics Engineering
and research's language is
English
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A practical communication channel often suffers from constraints on input other than the average power, such as the peak power constraint. In order to compare achievable rates with different constellations as well as the channel capacity under such constraints, it is crucial to take these constraints into consideration properly. In this paper, we propose a direct approach to compare the achievable rates of practical input constellations and the capacity under such constraints. As an example, we study the discrete-time complex-valued additive white Gaussian noise (AWGN) channel and compare the capacity under the peak power constraint with the achievable rates of phase shift keying (PSK) and quadrature amplitude modulation (QAM) input constellations.
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A discrete-time single-user scalar channel with temporally correlated Rayleigh fading is analyzed. There is no side information at the transmitter or the receiver. A simple expression is given for the capacity per unit energy, in the presence of a peak constraint. The simple formula of Verdu for capacity per unit cost is adapted to a channel with memory, and is used in the proof. In addition to bounding the capacity of a channel with correlated fading, the result gives some insight into the relationship between the correlation in the fading process and the channel capacity. The results are extended to a channel with side information, showing that the capacity per unit energy is one nat per Joule, independently of the peak power constraint. A continuous-time version of the model is also considered. The capacity per unit energy subject to a peak constraint (but no bandwidth constraint) is given by an expression similar to that for discrete time, and is evaluated for Gauss-Markov and Clarke fading channels.
Flat-fading channels that are correlated in time are considered under peak and average power constraints. For discrete-time channels, a new upper bound on the capacity per unit time is derived. A low SNR analysis of a full-scattering vector channel is used to derive a complimentary lower bound. Together, these bounds allow us to identify the exact scaling of channel capacity for a fixed peak to average ratio, as the average power converges to zero. The upper bound is also asymptotically tight as the average power converges to zero for a fixed peak power. For a continuous time infinite bandwidth channel, Viterbi identified the capacity for M-FSK modulation. Recently, Zhang and Laneman showed that the capacity can be achieved with non-bursty signaling (QPSK). An additional contribution of this paper is to obtain similar results under peak and average power constraints.
This paper investigates the capacity and capacity per unit cost of Gaussian multiple access-channel (GMAC) with peak power constraints. We first devise an approach based on Blahut-Arimoto Algorithm to numerically optimize the sum rate and quantify the corresponding input distributions. The results reveal that in the case with identical peak power constraints, the user with higher SNR is to have a symmetric antipodal input distribution for all values of noise variance. Next, we analytically derive and characterize an achievable rate region for the capacity in cases with small peak power constraints, which coincides with the capacity in a certain scenario. The capacity per unit cost is of interest in low power regimes and is a target performance measure in energy efficient communications. In this work, we derive the capacity per unit cost of additive white Gaussian channel and GMAC with peak power constraints. The results in case of GMAC demonstrate that the capacity per unit cost is obtained using antipodal signaling for both users and is independent of users rate ratio. We characterize the optimized transmission strategies obtained for capacity and capacity per unit cost with peak-power constraint in detail and specifically in contrast to the settings with average-power constraints.
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.
Effective capacity (EC) determines the maximum communication rate subject to a particular delay constraint. In this work, we analyze the EC of ultra reliable Machine Type Communication (MTC) networks operating in the finite blocklength (FB) regime. First, we present a closed form approximation for EC in quasi-static Rayleigh fading channels. Our analysis determines the upper bounds for EC and delay constraint when varying transmission power. Finally, we characterize the power-delay trade-off for fixed EC and propose an optimum power allocation scheme which exploits the asymptotic behavior of EC in the high SNR regime. The results illustrate that the proposed scheme provides significant power saving with a negligible loss in EC.
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