Asymptotic Capacity of Massive MIMO With 1-Bit ADCs and 1-Bit DACs at the Receiver and at the Transmitter

Abstract

In this paper, we investigate the capacity of massive multiple-input multiple-output (MIMO) systems corrupted by complex-valued additive white Gaussian noise (AWGN) when both the transmitter and the receiver employ 1-bit digital-to-analog converters (DACs) and 1-bit analog-to-digital-converters (ADCs). As a result of 1-bit DACs and ADCs, the transmitted and received symbols, as well as the transmit-and receive-side noisy channel state information (CSI) are assumed to be quantized to 1-bit of information. The derived results, applicable to both single-user and multi-user MIMO, show that the capacity of the considered massive MIMO system is 2N and 2M bits per channel use when N is fixed and M goes to infinity and when M is fixed and N goes to infinity, respectively, where M and N denote the number of transmit and receive antennas, respectively. These coincide with the respective capacities with full and noise-free CSI at both the transmitter and the receiver. In both cases, we showed that the derived capacities can be achieved with noisy 1-bit CSI at the massive-side and without any CSI at the other end. Moreover, we showed that the capacity can be achieved in one channel use without employing channel coding, which results in a latency of one channel use.

Uplink Data Detection Analysis of 1-Bit Quantized Massive MIMO

“…Note that, when K < N (i.e., when the number of data streams is strictly smaller than the number of transmit antennas, which is generally the case in downlink massive MIMO systems), C x in ( 8) is rank-deficient and G TX cannot be computed as in (11); 2 nonetheless, it can still be obtained via (13), which does not involve the inversion of C x . Furthermore, C t in ( 9) can be computed in closed form as in ( 14) at the top of the page [5].…”

“…For instance, [10] studied the 1-bit multiple-input single-output capacity with perfect channel state information (CSI) at both the transmitter and receiver. Moreover, [11] described the 1-bit MIMO capacity with imperfect CSI assuming that the number of transmit or receive antennas tends to infinity. Lastly, [12] showed that a proper combination of transmit beamforming and equiprobable signaling allows the system to operate close to the 1-bit MIMO capacity.…”

1-Bit MIMO for Terahertz Channels

“…where P ∩ (i, j) is given by (59). The bounds specified by ( 57)-( 59) are readily computable even for very large numbers of antennas.…”

“…Most importantly, because the entries of h are IID, the position of those −1 values is immaterial and only their totals i and j matter. Altogether, the joint distribution of ℜ{a k }, ℑ{a k }, ℜ{a 1 } and ℑ{a 1 } is as in (93) and, plugging it in (88) and tediously integrating over two of the dimensions, what emerges is (59) with the dependence on i and j made explicit and with erfc(•) the complementary error function.…”

“…Altogether, 1-bit MIMO architectures might feature prominently in future wireless systems, and not only for mmWave or terahertz operation: these architectures are also a sensible way forward for lower-frequency extreme massive MIMO, with antenna counts in the hundreds or even thousands [14]. All this interest is evidenced by the extensive literature on transmission strategies and the ensuing performance with 1-bit converters at the transmitter or receiver only (see [15]- [45] and references therein), and by the smaller but growing body of work that considers 1-bit converters at both ends [46]- [59]. Chief among the difficulties in this most stringent case stand (i) computing the information-theoretic performance limits for moderate and large antenna counts, and (ii) precoding to generate signals that can approach those limits.…”