On The Stability of Approximate Message Passing with Independent Measurement Ensembles

Approximate message passing (AMP) is a scalable, iterative approach to signal recovery. For structured random measurement ensembles, including independent and identically distributed (i.i.d.) Gaussian and rotationally-invariant matrices, the performance of AMP can be characterized by a scalar recursion called state evolution (SE). The pseudo-Lipschitz (polynomial) smoothness is conventionally assumed. In this work, we extend the SE for AMP to a new class of measurement matrices with independent (not necessarily identically distributed) entries. We also extend it to a general class of functions, called controlled functions which are not constrained by the polynomial smoothness; unlike the pseudo-Lipschitz function that has polynomial smoothness, the controlled function grows exponentially. The lack of structure in the assumed measurement ensembles is addressed by leveraging Lindeberg-Feller. The lack of smoothness of the assumed controlled function is addressed by a proposed conditioning technique leveraging the empirical statistics of the AMP instances. The resultants grant the use of the SE to a broader class of measurement ensembles and a new class of functions.

True-Time Delay-Based Hybrid Precoding Under Time Delay Constraints in Wideband THz Massive MIMO Systems

The beam squint effect that arises in the wideband Terahertz (THz) massive multiple-input multiple-output (MIMO) communication produces a serious array gain loss. True-time delay (TTD)-based hybrid precoding has been considered to compensate for the beam squint effect. By fixing the phase shifter (PS) precoder, a common strategy has been designing TTD precoder under the assumption of unbounded time delay values. In this paper, we present a new approach to the problem of beam squint compensation, based on the joint optimization of the TTD and PS precoders under per TTD device time delay constraints. We first derive a lower bound of the achievable rate and show that in the large system limit the ideal analog precoder that completely compensates for the beam squint is equivalent to the one that maximizes the achievable rate lower bound. Unlike the prior approaches, our approach does not require the unbounded time delay assumption; the range of time delay values that a TTD can produce is strictly limited in our approach. Instead of focusing on the design of TTD values only, we jointly optimize both the TTD and PS values to effectively cope with the practical time delay constraints. Taking the advantage of the proposed joint TTD and PS precoder optimization approach, we quantify the minimum number of TTDs required to produce a predefined array gain performance. The simulation results illustrate the substantially improved performance with the array gain performance guarantee of the proposed joint optimization method.

Joint Delay and Phase Precoding Under True-Time Delay Constraint for THz Massive MIMO

A new approach is presented to the problem of compensating the beam squint effect arising in wideband terahertz (THz) hybrid massive multiple-input multiple-output (MIMO) systems, based on the joint optimization of the phase shifter (PS) and true-time delay (TTD) values under per-TTD device time delay constraints. Unlike the prior approaches, the new approach does not require the unbounded time delay assumption; the range of time delay values that a TTD device can produce is strictly limited in our approach. Instead of focusing on the design of TTD values, we jointly optimize both the TTD and PS values to effectively cope with the practical time delay constraint. Simulation results that illustrate the performance benefits of the new method for the beam squint compensation are presented. Through simulations and analysis, we show that our approach is a generalization of the prior TTD-based precoding approaches.