Abstract
The channel capacity of noncoherent reception of multi-level one-sided amplitude-shift keying (ASK), which is an asymmetric constellation, in Rayleigh fading with receive diversity and energy detection is considered. The asymmetries result in capacity achieving input probability distributions, that is, a priori probability distributions, that deviate from uniformity. An analytical expression for the mutual information in terms of a single integral is derived, and from it the set of equations, which can be solved to obtain the optimum or capacity achieving input probabilities, is obtained. High and low signal-to-noise ratio (SNR) approximations of the optimum input probabilities and the capacity are derived next. Furthermore, a logarithmic upper bound on the mutual information is obtained. Numerical results confirm that the uniform distribution of input probabilities is not capacity achieving. For example, with average SNR per symbol per branch of 6 dB, the relative deviation of the mutual information (with uniform input distribution) from the capacity is nearly 20% for 4-level ASK with one transmit diversity branch and two receive diversity branches. Furthermore, the derived high and low SNR approximations to the capacity are shown to be reasonably accurate.
Highlights
R ECENT interest in noncoherent communication has focused on its application to the internet of things (IoT) [1] and future wireless communication systems [2]
The channel capacity is the maximum of the mutual information between the transmitted amplitude-shift keying (ASK) symbol s and the received signal vector r over the input probability distribution, that is, the a priori probability distribution, {p1, . . . , pL}
Substituting (31) in (60), we find that the limiting capacity upper bound under the infinite signal-to-noise ratio (SNR) condition (29) is CLUB,SNR→∞ = log2L, which is the same as the limiting capacity given by (32)
Summary
R ECENT interest in noncoherent communication has focused on its application to the internet of things (IoT) [1] and future wireless communication systems [2]. Few results for capacity are available for noncoherent systems when energy detection is utilized and block fading is not assumed [12] One reason for this is that without any CSI, it is impossible to separate out the MIMO channels [19]–[21]. Previous work has focused on energy detection MIMO when partial channel knowledge is available [22], for which fundamental limits on system performance including capacity and diversity have been obtained [23], [24]. These reveal that capacity and diversity order are approximately halved compared to coherent MIMO systems.
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