Dense Delta-Sigma Phased Arrays

Abstract

The high cost of high-resolution phase shifters required to maintain precise control over the array beam pattern in traditional phased arrays preclude their use in a variety of emerging millimeter-wave applications. We develop a phased array architecture that obviates the need for such precise phase shifters, based on the use of sub-half-wavelength array element spacing and novel spatial domain delta-sigma processing. We characterize the performance of this architecture in terms of the array signal-to-quantization-noise ratio (SQNR) and the array power transfer efficiency, and demonstrate a tradeoff between these two metrics. As an illustrative design, we show that when constrained to two-bit phase shifters, a four-fold increase in the array density can provide a roughly 6 dB improvement in SQNR over standard design techniques, with an average efficiency loss of less than 1.5 dB with respect to a perfectly tuned ideal array. In our analysis, we account for the effects of mutual coupling, and describe a simple, practical impedance matching network for this architecture. The resulting framework allows a system designer with a given set of circuit, device, and antenna fabrication and integration technologies to choose from a spectrum of tradeoffs between array density and RF component complexity.

One-Bit Sigma-Delta MIMO Precoding

“…Proof: From (27)- (28), we see that the problem is to analyze A † Ds IQ−∞ . Let · p denote either the p-norm for vectors or the induced p-norm for matrices.…”

Personal Mobile Radars with Millimeter-Wave Massive Arrays for Indoor Mapping

“…They are even more pronounced when working at very high frequencies due to technological and cost constraints [30]. This section deals with the effects of phase quantization errors and large signal bandwidth.…”

“…Digitally controlled phase shifters implementing a discrete set of phase shifts represent a cheaper alternative at the expense of quantization errors [20]. Some new solutions have been investigated in [30] to find a compromise between the number of elements and the phase shifters accuracy.…”

“…Note that in the model herein adopted we neglect the dependency of m i (k) from the frequency and the environment is assumed stationary. where e bs (k) is given by (30). As shown in the previous section, e bs (k) is proportional to a non-central Chisquare distributed RV that makes the formulation of the observation model challenging.…”

Spectral Efficiency of Mixed-ADC Massive MIMO

“…Relatively little research has focused on the spatial Σ∆ architecture. Prior related work has dealt with phased-array beamforming [31], [32], generalized structures for interference cancellation [33], and circuit implementations [34], [35]. Applications of the idea to massive MIMO were first presented in [36], [37], and more recently algorithms have been developed for channel estimation [38] and transmit precoding using Σ∆ DACs [39].…”