This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. 1 Dense Delta-Sigma Phased Arrays

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.