On the Sensitivity of Continuous-Time Noncoherent Fading Channel Capacity

Durisi, Giuseppe; Bölcskei, Helmut

doi:10.1109/tit.2012.2207089

Cited by 38 publications

(17 citation statements)

References 33 publications

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“…1 The equivalence between the discrete-time and continuous-time channel models for SISO is established in [20] using sampling and DFT, and in [21] using pulse shaping filter banks with Weyl-Heisenberg projection. Our result uses MIMO in a rich scattering environment and we provide explicit mapping of the channel coefficients between two different discrete-time models.…”

Section: System Modelmentioning

confidence: 99%

Unified Capacity Limit of Non-Coherent Wideband Fading Channels

Gómez-Cuba

Médard

et al. 2017

IEEE Trans. Wireless Commun.

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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.

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Section: System Modelmentioning

confidence: 99%

Unified Capacity Limit of Non-Coherent Wideband Fading Channels

Gómez-Cuba

Médard

et al. 2017

IEEE Trans. Wireless Commun.

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“…1. The reader is referred to [25], [40], [41] for a detailed exposition and a technical discussion of the mapping from the continuous to the discrete representations.…”

Section: A Signal Modelmentioning

confidence: 99%

Revisiting the Capacity of Noncoherent Fading Channels in mmWave System

Ferrante¹,

Quek²,

Win³

2024

IEEE Trans. Commun.

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Millimeter wave communications will use large bandwidth and experience severe propagation due to pathloss and blockages. The two above conditions may force the communication system to enter the so-called wideband regime, where signals must be increasingly "peaky" in order to attain a large fraction of the wideband capacity with no peak constraint, especially in the presence of non-line-of-sight propagation. This paper investigates the noncoherent capacity of millimeter wave channels with average and peak power constrained inputs as a function of bandwidth. Capacity upper and lower bounds are provided, and the impact of features peculiar of millimeter wave channels is investigated. Numerical results for a practical scenario based on recent experimental campaigns are provided. It is shown that the achievable rate of a large fraction of users in a typical millimeter wave cell may be bounded far from the wideband capacity without peak constraint because signaling is dense, hence suggesting to reconsider the role of signaling sparsity in future millimeter wave communications.

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“…Here, b j , j = 1, ..., S, are (complex-valued) attenuation factors associated with the delay-Doppler pair (τ j ,ν j ). With (18), (17) reduces to the input-output relation (1) stated in the introduction, i.e., to…”

Section: Relationship Between the Continuous Time And Discrete Time Mmentioning

confidence: 99%

“…and approximately time-limited to [−2T, 2T ]. According to the 2W T -Theorem [40,17], Hx has on the order of BT degrees of freedom so that one can think of Hx as having effective dimensionality on the order of BT . Therefore, by sampling Hx at rate 1/B in the interval [−T /2, T /2], we collect the number of samples that matches the dimensionality of Hx up to a constant.…”

Section: Sampling the Outputmentioning

confidence: 99%

Super-resolution radar

Heckel

Soltanolkotabi

2016

Information and Inference

Self Cite

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In this paper we study the identification of a time-varying linear system from its response to a known input signal. More specifically, we consider systems whose response to the input signal is given by a weighted superposition of delayed and Doppler shifted versions of the input. This problem arises in a multitude of applications such as wireless communications and radar imaging. Due to practical constraints, the input signal has finite bandwidth B, and the received signal is observed over a finite time interval of length T only. This gives rise to a delay and Doppler resolution of 1/B and 1/T . We show that this resolution limit can be overcome, i.e., we can exactly recover the continuous delay-Doppler pairs and the corresponding attenuation factors, by solving a convex optimization problem. This result holds provided that the distance between the delay-Doppler pairs is at least 2.37/B in time or 2.37/T in frequency. Furthermore, this result allows the total number of delay-Doppler pairs to be linear up to a log-factor in BT , the dimensionality of the response of the system, and thereby the limit for identifiability. Stated differently, we show that we can estimate the time-frequency components of a signal that is S-sparse in the continuous dictionary of time-frequency shifts of a random window function, from a number of measurements, that is linear up to a log-factor in S.

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On the Sensitivity of Continuous-Time Noncoherent Fading Channel Capacity

Cited by 38 publications

References 33 publications

Unified Capacity Limit of Non-Coherent Wideband Fading Channels

Unified Capacity Limit of Non-Coherent Wideband Fading Channels

Revisiting the Capacity of Noncoherent Fading Channels in mmWave System

Super-resolution radar

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