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Register a new userCapacity scaling in a Non-coherent Wideband Massive SIMO Block Fading Channel
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Added by
Felipe G\\'omez-Cuba
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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The scaling of coherent and non-coherent channel capacity is studied in a single-input multiple-output (SIMO) block Rayleigh fading channel as both the bandwidth and the number of receiver antennas go to infinity jointly with the transmit power fixed. The transmitter has no channel state information (CSI), while the receiver may have genie-provided CSI (coherent receiver), or the channel statistics only (non-coherent receiver). Our results show that if the available bandwidth is smaller than a threshold bandwidth which is proportional (up to leading order terms) to the square root of the number of antennas, there is no gap between the coherent capacity and the non-coherent capacity in terms of capacity scaling behavior. On the other hand, when the bandwidth is larger than this threshold, there is a capacity scaling gap. Since achievable rates using pilot symbols for channel estimation are subject to the non-coherent capacity bound, this work reveals that pilot-assisted coherent receivers in systems with a large number of receive antennas are unable to exploit excess spectrum above a given threshold for capacity gain.
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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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An uplink system with a single antenna transmitter and a single receiver with a large number of antennas is considered. We propose an energy-detection-based single-shot noncoherent communication scheme which does not use the instantaneous channel state information (CSI), but rather only the knowledge of the channel statistics. The suggested system uses a transmitter that modulates information on the power of the symbols, and a receiver which measures only the average energy across the antennas. We propose constellation designs which are asymptotically optimal with respect to symbol error rate (SER) with an increasing number of antennas, for any finite signal to noise ratio (SNR) at the receiver, under different assumptions on the availability of CSI statistics (exact channel fading distribution or the first few moments of the channel fading distribution). We also consider the case of imperfect knowledge of the channel statistics and describe in detail the case when there is a bounded uncertainty on the moments of the fading distribution. We present numerical results on the SER performance achieved by these designs in typical scenarios and find that they may outperform existing noncoherent constellations, e.g., conventional Amplitude Shift Keying (ASK), and pilot-based schemes, e.g., Pulse Amplitude Modulation (PAM). We also observe that an optimized constellation for a specific channel distribution makes it very sensitive to uncertainties in the channel statistics. In particular, constellation designs based on optimistic channel conditions could lead to significant performance degradation in terms of the achieved symbol error rates.
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