Capacity of SIMO and MISO Phase-Noise Channels With Common/Separate Oscillators

Abstract

Abstract-In multiple antenna systems, phase noise due to instabilities of the radio-frequency (RF) oscillators, acts differently depending on whether the RF circuitries connected to each antenna are driven by separate (independent) local oscillators (SLO) or by a common local oscillator (CLO). In this paper, we investigate the high-SNR capacity of single-input multiple-output (SIMO) and multiple-output single-input (MISO) phase-noise channels for both the CLO and the SLO configurations.Our results show that the first-order term in the high-SNR capacity expansion is the same for all scenarios (SIMO/MISO and SLO/CLO), and equal to 0.5 ln(ρ), where ρ stands for the SNR. On the contrary, the second-order term, which we refer to as phasenoise number, turns out to be scenario-dependent. For the SIMO case, the SLO configuration provides a diversity gain, resulting in a larger phase-noise number than for the CLO configuration. For the case of Wiener phase noise, a diversity gain of at least 0.5 ln(M ) can be achieved, where M is the number of receive antennas. For the MISO, the CLO configuration yields a higher phase-noise number than the SLO configuration. This is because with the CLO configuration one can obtain a coherent-combining gain through maximum ratio transmission (a.k.a. conjugate beamforming). This gain is unattainable with the SLO configuration.

Receiver Algorithm Based on Differential Signaling for SIMO Phase Noise Channels with Common and Separate Oscillator Configurations

“…As can be seen in (16), this manifests as a reduction of the effective variance of the noise that distorts the phase of the signal. Similar observations have been reported in the capacity calculations for the SIMO phase noise channel [10]. However at low SNR, the proposed differential method performs worse in the SLO configuration.…”

“…Furthermore, the performance of the studied method in SLO configuration improves by increasing the number of antennas till it achieves an error floor that is a function of the level of phase noise at the transmitter. This observation is in line with the results from prior work on the performance of uplink transmissions in presence of phase noise (see e.g., [10], [17], [22]). …”

“…Then the transmitted signal amplitude, as determined by the amplitude detector, is used along with the phase of the received signals at each antenna in order to perform differential maximum likelihood (ML) phase detection. It is straightforward to show that given r k , t k = y k 2 follows a noncentral chi-squared distribution with 2M degrees of freedom and noncentrality parameter r 2 k h 2 [10], i.e.,…”

“…Although the CLO configuration is of lower implementation complexity, the SLO configuration is unavoidable when a spacing, as large as a few meters, is needed between the antennas in order to exploit the available spatial degrees of freedom for higher multiplexing or diversity gains [6]- [10].…”

On discrete-time modeling of the filtered and symbol-rate sampled continuous-time signal affected by Wiener phase noise

“…Also, schemes based on time domain interleaving of robust modulation formats and less robust, but more spectrally efficient modulation formats, are proposed in [20,21]. The information rate transferred through 20 the discrete-time phase noise channel is studied in [22][23][24][25][26] while that associated with multiple-input multiple-output channels is considered in [27,28]. With reference to Fig.…”