Randomized Kaczmarz algorithm for massive MIMO systems with channel estimation and spatial correlation

Abstract

Summary To exploit the benefits of massive multiple‐input multiple‐output (M‐MIMO) technology in scenarios where base stations (BSs) need to be cheap and equipped with simple hardware, the computational complexity of classical signal processing schemes for spatial multiplexing of users shall be reduced. This calls for suboptimal designs that perform well the combining/precoding steps and simultaneously achieve low computational complexities. An approach on the basis of the iterative Kaczmarz algorithm (KA) has been recently investigated, assuring well execution without the knowledge of second order moments of the wireless channels in the BS, and with easiness since no tuning parameters, besides the number of iterations, are required. In fact, the randomized version of KA (rKA) has been used in this context because of global convergence properties. Herein, modifications are proposed on this first rKA‐based attempt, aiming to improve its performance‐complexity trade‐off solution for M‐MIMO systems. We observe that long‐term channel effects degrade the rate of convergence of the rKA‐based schemes. This issue is then tackled herein by means of a hybrid rKA initialization proposal, which lands within the region of convexity of the algorithm and assures fairness to the communication system. The effectiveness of our proposal is illustrated through numerical results, which bring more realistic system conditions in terms of channel estimation and spatial correlation than those used so far. We also characterize the computational complexity of the proposed rKA scheme, deriving upper bounds for the number of iterations. A case study focused on a dense urban application scenario is used to gather new insights on the feasibility of the proposed scheme to cope with the inserted BS constraints.

Intercarrier interference analysis for massive MIMO fractional Fourier transform‐OFDM systems over time‐varying channels

“…The relation between sampling time and sampling frequency in fractional is ∆u∆t = 2 π sin( α ))/ N . When the transmitted signal interacted with the time‐varying frequency selective channel h , the received signal y in time domain is expressed as 9,15 where * is convolution between channel and transmitted data, subscript () u denotes uplink, h u ∈∁ K XM is the time‐domain channel matrix between K transmitting antenna and M receiving antenna, x u ∈ ∁ Kx 1 is the transmitted signal form K single antenna user terminals, f d is Doppler frequency, z u ∈ ∁ MX 1 is independent identically distributed additive white Gaussian noise matrix with mean equal to 0, and i u ∈ ∁ MX 1 is self‐interference introduced due to frequency offset. By using the convolution theorem of FrFT, 16 the received signal can also be expressed in frequency domain as where is frequency domain channel matrix between K transmitting antenna and M receiving antenna, X u ∈ ∁ 1 xK is the frequency domain transmitted signal form K single antenna user terminals, is frequency domain independent identically distributed additive white Gaussian noise matrix with mean equals to 0, and is self‐interference introduced due to frequency offset.…”

Hanger forces optimization of ground test device on deployable structure

“…[22][23][24] MATLAB has a strong matrix computing capability, and its programming environment is friendly, very suitable for the preparation and operation of all kinds of optimization algorithms. [25][26][27] Therefore, this article will combine the advantages of these two software to provide a hanger forces optimization allocation strategy based on AGA.…”

Efficient receivers for cellular massive mimo systems and random access in cell-free networks.

“…The rKA is an iterative algorithm that solves systems of linear equations (SLEs) and has been recently applied to efficiently tackle the problem of relaxing linear signal processing schemes in the context of M-MIMO. This procedure was first presented in [55] and deepened in [57,58]. The randomization in rKA is related to the order in which the SLE equations are being selected when solved.…”

“…Contributions: Inspired by the promising results obtained for M-MIMO [55,57,58], this work proposes the application of the randomized Kaczmarz algorithm (rKA) as a way to circumvent the high-dimensional matrix inversion that comes with zero-forcing (ZF) and regularized zero-forcing (RZF) schemes when these are applied to recover the signal estimates of a crowded XL-MIMO scenario [8]. The contributions are listed as follows: (i) extension of rKA to resemble the performance of ZF and RZF schemes for a XL-MIMO system with a fixed number of subarrays; (ii) consideration of non-stationary properties through the concept of visibility regions (VRs) when taking into account two different power normalization methods of non-stationary channels [19]; (iii) exploitation of non-stationary features in the randomness design of rKA; (iv) complexity analysis considering the different random variants of the proposed algorithm.…”

“…Simplicity: the only tuning parameter needed to be set is the number of iterations at each subarray. The others stem from network design choices and environment characteristics, which obviously affect the convergence of the algorithm, as discussed in [55], [57], and [58]. In opposite to that, this also means that a convergence analysis is sufficient to characterize the efficiency of the algorithm in achieving its goal.…”