On Ultra-Wideband MIMO Systems with 1-bit Quantized Outputs: Performance Analysis and Input Optimization

Abstract

We study the performance of multi-input multioutput (MIMO) channels with coarsely quantized outputs in the low signal-to-noise ratio (SNR) regime, where the channel is perfectly known at the receiver. This analysis is of interest in the context of Ultra-Wideband (UWB) communications from two aspects. First the available power is spread over such a large frequency band, that the power spectral density is extremely low and thus the SNR is low. Second the analogto-digital converters (ADCs) for such high bandwidth signals should be low-resolution, in order to reduce their cost and power consumption. In this paper we consider the extreme case of only 1-bit ADC for each receive signal component. We compute the mutual information up to second order in the SNR and study the impact of quantization. We show that, up to first order in SNR, the mutual information of the 1-bit quantized system degrades only by a factor of 2 compared to the system with infinite resolution independent of the actual MIMO channel realization. With Channel State Information (CSI) only at receiver, we show that QPSK is, up to the second order, the best among all distributions with independent components. We also elaborate on the ergodic capacity under this scheme in a Rayleigh flat-fading environment.

Chip-to-Chip and On-Chip Communications

“…This shows that mono-bit ADCs may be used to save system power without an excessive degradation in performance, and confirms the significant potential of the coarsely quantized UWB MIMO channel. Using a different approach, [40] presented a similar result, and showed that the above approximation is asymptotically exact.…”

“…Therefore, the coding schemes which are needed are non-linear and -for having good performance and, at the same time, a low complexity -for instance have memory of order one. In [51][52][53], an information-theoretic framework was developed as a practical design guideline for novel codes. To this end, the following optimization has been considered in [52] …”

“…section 4), in order to reach information rates (well) above the i.u.d. capacity [53]. (6) is non-convex but can be solved by an efficient greedy algorithm [52] that delivers an optimized transition probability matrix P =[ P i,j ] that maximizes the mutual information between the input and the output.…”

“…For a wide range of LDPC codes with code complexities n · d V between 300 and 24,000 the ratio varies only between 0.30 and 0.37. Approximating the ratio of the average to the maximum Manhattan length with 0.35 and using (40), the required Manhattan length can be estimated based on the decoder side length as…”

Millimeter wave receive beamforming with one-bit quantization

“…Ref. [5] analyzed the capacity using a one-bit ADC in a low SNR (Signal to Noise Ratio) regime while Ref. [6] analyzed the capacity in a high SNR regime.…”