SEP Analysis of a Low-Resolution SIMO System with M-PSK over Fading Channels
Amila Ravinath, Minhua Ding, Bikshapathi Gouda, Italo Atzeni, Antti Tölli
TL;DR
This work analyzes the symbol-error probability (SEP) of a phase-quantized SIMO system employing M-PSK over Rayleigh fading with perfect and limited CSIR. A novel approach that leverages circular symmetry converts the SEP analysis into an equivalent single-channel problem, enabling exact SEP expressions for QPSK with n-bit phase quantization under SIMO-MRC, along with closed-form high-SNR diversity and coding gains. The paper also establishes a duality between SIMO-MRC and MISO-MRT systems under the same quantization and modulation, enabling transfer of results across frontiers of uplink and downlink configurations, and extends the SEP analysis to 2-bit limited CSIR with explicit diversity losses. Additional contributions include exact results for n=1, n=2, and n>=3, an accurate approximate closed-form for 2-bit quantization, and high-SNR characterizations for SIMO-SC. Practical implications include insights into how quantization and CSI limitations impact reliability in low-resolution multi-antenna systems and guidance for system design under hardware constraints.
Abstract
In this paper, the average symbol error probability (SEP) of a phase-quantized single-input multiple-output (SIMO) system with M-ary phase-shift keying (PSK) modulation is analyzed under Rayleigh fading and additive white Gaussian noise. By leveraging a novel method, we derive exact SEP expressions for a quadrature PSK (QPSK)-modulated n-bit phase-quantized SIMO system with maximum ratio combining (SIMO-MRC), along with the corresponding high signal-to-noise ratio (SNR) characterizations in terms of diversity and coding gains. For a QPSK-modulated 2-bit phase-quantized SIMO system with selection combining, the diversity and coding gains are further obtained for an arbitrary number of receive antennas, complementing existing results. Interestingly, the proposed method also reveals a duality between a SIMO-MRC system and a phase-quantized multiple-input single-output (MISO) system with maximum ratio transmission, when the modulation order, phase-quantization resolution, antenna configuration, and the channel state information (CSI) conditions are reciprocal. This duality enables direct inference to obtain the diversity of a general M-PSK-modulated n-bit phase-quantized SIMO-MRC system, and extends the results to its MISO counterpart. All the above results have been obtained assuming perfect CSI at the receiver (CSIR). Finally, the SEP analysis of a QPSK-modulated 2-bit phase-quantized SIMO system is extended to the limited CSIR case, where the CSI at each receive antenna is represented by only 2 bits of channel phase information. In this scenario, the diversity gain is shown to be further halved in general.