Expeditious Estimation of Angle-of-Arrival for Hybrid Butler Matrix Arrays

Expeditious Estimation of Angle-of-Arrival for Hybrid Butler Matrix Arrays

Abstract: Arrays of Butler matrices provide a promising frontend design for massive MIMO transceivers with low cost and low complexity. However, this advanced design does not necessarily translate to effective applications, unless the angle-of-arrival (AoA) of signals avails to the Butler matrices. This paper presents an efficient approach to the unprecedented AoA estimation for the arrays of Butler matrices.

Specifically, we design a new beam synthesis method to recursively narrow down and increasingly focus on the angular region of interest, hence achieving robust estimation of the phase offset between Butler matrices. With the phase offset canceled in the received signals, we are able to identify the set of critical Butler beams with the dominating effect on the AoA estimation, and estimate the AoA accordingly with the minimum signaling. The mean squared error of the proposed estimation is analyzed in the presence of non-negligible noises, with closed-form lower bounds derived. Validated by simulations, the proposed algorithm is able to indistinguishably approach the lower bounds, and significantly outperform the state of the art developed for discrete antenna arrays by orders of magnitude in terms of accuracy especially in low signal-to-noise regimes.

Existing system:

There is no existing research on the AoA estimation for BMAs which are specially designed hybrid antenna arrays. The existing AoA estimation algorithms developed for general hybrid antenna arrays, i.e., DAAs, are either inapplicable to BMAs, or not tailored according to the properties of BMAs to fulfill the full potential of the BMAs. Earlier AoA approaches for DAAs were based on beam search, such. In some of the approaches, the beams were increasingly narrowed down by designing the analog phase shifts of the DAAs. The phase shifts, referred to as “codebook�, were optimized offline. In other approaches, the phase offset between adjacent analog sub arrays was first estimated, resulting in multiple potential estimates of the AoA; and each of the potential estimates was then probed for validation. These techniques require analog beam forming, and are inapplicable to BMAs. Proposed system: By differentially weighting the DFT beams of BMAs, a new beam synthesis technique is proposed to synthesize the DFT beams in the analog domain to produce steerable beams with reconfigurable beam widths and improved main lobe-to-side lobe ratios (MSRs). Empowered by the new beam synthesis, we propose to increasingly narrow down the search of the incident signal to estimate the phase offset between adjacent Butler matrices, Nau, with up to logNa NrNm symbols (c.f., Na NrNm symbols). u is the AoA to be estimated, Nm is the number of Butler matrices, and Nr is the number of RF chains per Butler matrix. We prove that, in the presence of a dominant LoS path, Nm DFT beams dominate the estimation of u, and the contribution of the rest of the beams is asymptotically negligible. Only the received signals of the Nm DFT beams need to be collected and, with the phase offset between Butler matrices canceled, transformed to the spatial-angular domain for fast and accurate AoA estimation.

Advantages: The received signals can be written as the product of a linearly independent coefficient matrix constituted of the phase shifts, as well as the steering matrix on which the standard MUSIC operations can be executed.

The methods can be applied to BMAs, in which case the coefficient matrix is the DFT matrix (which is linearly independent) and can be decoupled from the

steering matrix. However, the methods are computationally expensive due to the use of SVD and susceptible to low SNRs, as classical MUSIC. Disadvantages: In, the channel estimation in DAAs was formulated as a sparse recovery problem, and the AoA was estimated through recovering the support of the sparse vector zed channel matrix.

The hybrid precoder/combiner was designed by first solving the optimal precoder/combiner to maximize the mutual information of a MIMO channel, and then decomposing the optimal pre coder/combiner for analog and digital implementations through sparse reconstruction.

Modules: Signal transform: A few recent AoA estimation approaches developed for DAAs, can be potentially applied to BMAs, where the phase offset between analog sub arrays is first estimated by producing DFT beams and canceled in the received signals of sub arrays. By using inverse DFT (IDFT), the signals can be then transformed from the beam space domain and the spatial-angular domain to estimate the AoA. However, the phase offset between sub arrays has to be exhaustively searched with DFT beams to prevent misdetection, incurring conversely inefficiency and latency. This paper presents a new approach which, tailored according to the properties of BMAs, is able to accurately and efficiently estimates the AoA for BMAs under a far smaller number of RF chains than antennas and the obscurity.

Singular value decomposition: The popular spatial spectrum analysis designed for digital arrays, such as MUSIC and ESPRIT, cannot be directly applied to DAAs, due to the RF combining at analog sub arrays and the resultant obscurity of the phase offset information on individual antennas. In, MUSIC and ESPRIT were extended to DAAs by using linearly independent phase shifts for the sub arrays, and can be potentially applied to BMAs since a Butler matrix implements a linearly independent DFT matrix.

However, singular value decomposition (SVD) was required, and the complexity

of the algorithm would grow cubically with the number of antennas and can be computationally prohibitive, as will be analyzed later in the paper.

Massive multiple – input – multiple –output: Massive multiple-input-multiple-output (MIMO) has been widely accepted as an enabling technology for the fifth generation (5G) communications. One reason is because the scarcity of communication spectrum pushes 5G towards millimeter wave (mm Wave) frequencies. Another reason is that the short wavelength of mm Wave allows for integrations of large numbers, i.e., up to hundreds, of miniaturized antennas in limited space, exploiting array gain to compensate for poor radio propagations of mm Wave, and allowing tens of terminals to be served simultaneously. On the other hand, the physical sizes of radio frequency (RF) chains, consisting of analog-to-digital and digital-to-analog converters (ADC/DAC).

Angle – Of – Arrival: A Butler matrix is more energy-efficient than a conventional DAA. A Nadimensional Butler matrix can readily produce Na Butler beams, while an Nadimensional linear DAA requires N2 a number of log Na 2 -bit phase shifters to generate Na DFT beams. The Butler matrix can also provide effective spatial interference suppression, and separate signals with different angle-of-arrivals (AoAs) by exploiting different main lobes of the Butler beams.1 An array of Butler matrices can readily form a massive MIMO transceiver, as shown. This can help by either reducing the numbers of antennas and beam ports of each Butler matrix, or improving the array gain, as compared to a single large-dimensional Butler matrix. The reduced number of antennas and beam ports can also reduce crossovers and mutual couplings. To fulfill the expected benefits of Butler matrix arrays (BMAs), accurate estimations of AoAs of incident paths are the key.