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Register a new userOn Multiuser Gain and the Constant-Gap Sum Capacity of the Gaussian Interfering Multiple Access Channel
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Added by
Rick Fritschek
Publication date
2017
fields
Informatics Engineering
and research's language is
English
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Recent investigations have shown sum capacity results within a constant bit-gap for several channel models, e.g. the two-user Gaussian interference channel (G-IC), k-user G-IC or the Gaussian X-channel. This has motivated investigations of interference-limited multi-user channels, for example, the Gaussian interfering multiple access channel (G-IMAC). Networks with interference usually require the use of interference alignment (IA) as a technique to achieve the upper bounds of a network. A promising approach in view of constant-gap capacity results is a special form of IA called signal-scale alignment, which works for time-invariant, frequency-flat, single-antenna networks. However, until now, results were limited to the many-to-one interference channel and the Gaussian X-channel. To make progress on this front, we investigate signal-scale IA schemes for the G-IMAC and aim to show a constant-gap capacity result for the G-IMAC. We derive a constant-gap sum capacity approximation for the lower triangular deterministic (LTD)-IMAC and see that the LTD model can overcome difficulties of the linear deterministic model. We show that the schemes can be translated to the Gaussian IMAC and that they achieve capacity within a constant gap. We show that multi-user gain is possible in the whole regime and provide a new look at cellular interference channels.
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We study a deterministic approximation of the two-user multiple access wiretap channel. This approximation enables results beyond the recently shown $tfrac{2}{3}$ secure degrees of freedom (s.d.o.f.) for the Gaussian multiple access channel. While the s.d.o.f. were obtained by real interference alignment, our approach uses signal-scale alignment. We show an achievable scheme which is independent of the rationality of the channel gains. Moreover, our result can differentiate between channel strengths, in particular between both users, and establishes a secrecy rate dependent on this difference. We can show that the resulting achievable secrecy rate tends to the s.d.o.f. for vanishing channel gain differences. Moreover, we extend the s.d.o.f. bound towards a general bound for varying channel strengths and show that our achievable scheme reaches the bound for certain channel gain parameters. We believe that our analysis is the first step towards a constant-gap analysis of the Gaussian multiple access wiretap channel.
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.
The feedback sum-rate capacity is established for the symmetric $J$-user Gaussian multiple-access channel (GMAC). The main contribution is a converse bound that combines the dependence-balance argument of Hekstra and Willems (1989) with a variant of the factorization of a convex envelope of Geng and Nair (2014). The converse bound matches the achievable sum-rate of the Fourier-Modulated Estimate Correction strategy of Kramer (2002).
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This paper studies the capacity of the peak-and-average-power-limited Gaussian channel when its output is quantized using a dithered, infinite-level, uniform quantizer of step size $Delta$. It is shown that the capacity of this channel tends to that of the unquantized Gaussian channel when $Delta$ tends to zero, and it tends to zero when $Delta$ tends to infinity. In the low signal-to-noise ratio (SNR) regime, it is shown that, when the peak-power constraint is absent, the low-SNR asymptotic capacity is equal to that of the unquantized channel irrespective of $Delta$. Furthermore, an expression for the low-SNR asymptotic capacity for finite peak-to-average-power ratios is given and evaluated in the low- and high-resolution limit. It is demonstrated that, in this case, the low-SNR asymptotic capacity converges to that of the unquantized channel when $Delta$ tends to zero, and it tends to zero when $Delta$ tends to infinity. Comparing these results with achievability results for (undithered) 1-bit quantization, it is observed that the dither reduces capacity in the low-precision limit, and it reduces the low-SNR asymptotic capacity unless the peak-to-average-power ratio is unbounded.
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