Linear CE and 1-bit Quantized Precoding With Optimized Dithering

Abstract

High power amplifiers (HPA), used at transmission, add nonlinear impairments to the output signals. Through Constant envelope (CE) transmission, distortion in the signal can be avoided without wasting power on PA linearization. A more restricted form of CE transmission, 1-bit quantized transmission, further simplifies the RF chain and reduces the DAC power consumption. In this paper, for CE transmission and 1-bit quantized transmission at the BS antennas, we analyze downlink transmission for low complexity linear precoding. We observe that for small numbers of users in the downlink, correlation among the quantization error components across BS antennas is high, deteriorating the performance rapidly as number of users become smaller. To improve performance for smaller numbers of downlink users, we propose the addition of correlated Gaussian dither to the precoded signal before quantization and subsequent transmission. We observe that the receive SQINR peaks for finite non-trivial dither power. For given value of transmit power, number of BS antennas and number of users, SQINR is maximized analytically by the transmitter, to find the optimum dither power, using the Bussgang decomposition. We observe that with the implementation of optimized dithering, the error floor in the coded BER at high transmit power, for CE and 1-bit quantized transmissions, is pushed down significantly. We also observe that optimum dither power increases monotonically with transmit power, with rate of increase decreasing with increasing transmit power. Further, the optimum dither power strictly increases with number of BS antennas.

Low-Resolution Precoding for Multi-Antenna Downlink Channels and OFDM

“…Most works consider discrete alphabet signaling. Perhaps the simplest approach, called quantized linear precoding (QLP), applies a linear precoder followed by one lowresolution quantizer per antenna [8][9][10][11][12][13][14][15]. Our focus is on zero forcing (ZF), and we use the acronyms LP-ZF and QLP-ZF, respectively, for unquantized ZF and the QLP version of ZF.…”

Massive MIMO with Dense Arrays and 1-bit Data Converters

“…A generalization to be applied for planar arrays is rather not straightforward due the sequential precoding. Instead, we will use the technique of dithering [40], [41] to whiten the quatization error by adding a random signal prior to the 1-bit quatizer. Furthermore, to avoid injecting interference in the environments, we propose the concept of non-radiating dithering, where the dither signal lies mainly on the null space of the coupling matrix B(f ) .…”

“…It has to be large enough to reduce the quantization noise correlation but excessive values would lead to a penalty as shown in the rate formula (44). This trade-off and the corresponding optimization of σ 2 d have been considered for the case of conventional antenna arrays in [40], [41]. In our setting, the optimal value for σ 2 d will depend on the number of users, antennas, and antenna spacing.…”

Massive MIMO Precoding and Spectral Shaping with Low Resolution Phase-only DACs and Active Constellation Extension

“…DACs. Besides the linear precoding techniques that have been considered in [20]- [27], several nonlinear precoding algorithms based on different criteria has been proposed in flat fading channel [1]- [3], [28]- [37]. In this context, the uncoded symbol error rate (SER) is a widely used design criterion [1], [3], [28], [31]- [34], [38], [39] and is claimed to be more appropriate than the mean squared error (MSE) criterion.…”