Angular Domain Channel Estimation for Symmetrical Nonuniform Linear Array in Communication Systems

This paper deals with the problem of the Direction Of Arrival (DOA) estimation with nonuniform linear arrays. The proposed method is based on the Expectation Maximization method where ESPRIT is used in the maximization step. The key idea is to iteratively interpolate the data to a virtual uniform linear array in order to apply ESPRIT to estimate the DOA. The iterative approach allows one to improve the interpolation using the previously estimated DOA. One of this method’s novelties lies in its capacity of dealing with any nonuniform array geometry. This technique manifests significant performance and computational advantages over previous algorithms such as Spectral MUSIC, EM-IQML and the method based on manifold separation technique. EM-ESPRIT is shown to be more robust to additive noise. Furthermore, EM-ESPRIT fully exploits the advantages of using a nonuniform array over a uniform array: simulations show that for the same aperture and with a smaller number of sensors, the nonuniform array presents almost identical performance as the equivalent uniform array.

Millimeter wave (mmWave) communication is a promising technology in the 5G and beyond communications. Because of the ultra-high frequency, the mmWave communication suffers from significant path loss and the number of paths from users to the base station (BS) is much fewer than that in the conventional wireless communications systems. These problems can be mitigated by exploiting massive multi-input multi-output (MIMO) and beamforming techniques. To obtain the channel information for MIMO systems, the pilot-based channel estimation may incur a large overhead as the numbers of users and antennas increase. In this paper, we propose a blind channel estimation method for mmWave uplink that avoids using pilot signals. With the number of users unknown, we first estimate the number of users by the rank of the correlation matrix of the signal received at the base station (BS). Then, the compressed sensing (CS) technique is utilized to estimate the direction-of-arrival (DOA) of each path. At last, we take advantage of the special structure of the fading channel matrix to eliminate the spurious DOAs and estimate the fading gain of each path at the same time. A special case with only one path from each user to the BS is also discussed, and we exploit the multiple signal classification (MUSIC) algorithm to reduce the complexity. A non-uniform antenna array called the nested array is utilized to increase the array aperture for both the single-path per user and the general cases.

In this study, isotropic V-shaped uniform and nonuniform arrays are considered. An isotropic array has the same value for the Cramer-Rao bound (CRB) for all direction of arrival (DOA) angles. The conditions for isotropic V-shaped arrays are presented and closed form expressions for V-shaped uniform and nonuniform arrays are found. These expressions return the V-angle for the array. Therefore, given the number of sensors and sensor displacements, isotropic performance V-angle can be found easily. V-shaped arrays are compared with circular arrays and it is also shown that both uniform and nonuniform V-shaped arrays have certain advantages.

The effects of amplitude and phase errors are determined for symmetric and asymmetric linear predictive array processors. The maximum entropy method (MEM) corresponds to linear prediction in the asymmetric case of a line array of equispaced elements with an end reference. A comparison to conventional beamforming and maximum-likelihood processing shows that they have the same peak location as the symmetric linear predictive array processor. >

This paper investigates the localization of multiple near-field narrowband signals impinging on a symmetrical uniform linear array (ULA), and a new computationally efficient subspace-based method is proposed. The directions-of-arrival (DOAs) and ranges are estimated separately with a one-dimensional (1-D) subspaced-based estimation technique without eigendecomposition, where the null spaces are obtained through a linear operation of the matrices formed from the anti-diagonal elements of the noiseless array covariance matrix, and the estimated DOAs and ranges are automatically paired without any additional processing. Furthermore, the statistical analysis of the proposed method is studied, and the asymptotic mean-square-error (MSE) expressions of the estimation errors are derived. The effectiveness and the theoretical analysis of the proposed method are verified through numerical examples, and the simulation results show that our method provides good estimation performance for both the DOAs and ranges.

This paper deals with the problem of the Direction Of Arrival (DOA) estimation with nonuniform linear arrays (NLA). We show that the Root-MUSIC algorithm can be directly applied in the case of the non uniform array. Moreover, we show that the elimination of a certain sensors of a uniform array degrades only very slightly the performance thanks to the use of the high-resolution(HR) methods like Root-MUSIC. We also show that root-MUSIC presents good performances, and does not require any additional data transformation. In addition, an analytical expression from the estimator variance are derived in order to support our simulation results and to show the advantages of the NLA.

The performance of wideband array signal processing algorithms is dependant on the noise level in the system. In this thesis, a method is proposed for reducing the level of white noise in wideband arrays via a judiciously designed spatial transformation followed by a bank of high-pass filters. The method is initially introduced for uniform linear arrays (ULAs) and analysed in detail. The spectrum of the signal and noise after being processed by the proposed noise reduction method is analysed, and the correlation matrix of the processed noise is derived. The reduced noise level leads to a higher signal-to-noise ratio (SNR) for the system, which can have a significant effect on the performance improvement of various beamforming methods and other array signal processing applications such as direction of arrival (DOA) estimation. The performance of two well-known beamformers, the reference signal based (RSB) beamformer and the linearly constrained minimum variance (LCMV) beamformer is reviewed. Then, the theoretical effect of applying the proposed noise reduction method as a pre-processing step on the performance enhancement of RSB and LCMV beamformers is studied. The theoretical results are then confirmed by simulation. As a representative example of wideband DOA estimation application, a compressive sensing-based DOA estimation method is employed to demonstrate the improved estimation by applying the pre-processing noise reduction method, which is confirmed by simulation. Next, the idea is extended to wideband non-uniform linear arrays (NLAs). Since, NLA does not have a uniform spacing, the beam response of the row vectors of the transformation is distorted. Therefore, the transformation is re-designed using the least squares method to satisfy the band-pass requirements of the transformation. Simulation results show a satisfactory improvement in the the performance of RSB and LCMV beamformers for the NLA structure. The idea is further extended to uniform rectangular arrays (URAs) and uniform circular arrays (UCAs), as two major types of the planar arrays. Two methods are proposed for reducing the effect of white noise in wideband URAs and for each one, a different transformation is designed. The first one is based on a two-dimensional (2D) transformation and the second one is an adaptation of the method developed for the ULA case. The developed method for the UCA structure is based on a one-dimensional (1D) transformation, with modified modulation for the transformation to satisfy the required band-pass characteristics of the transformation. Same as linear array structures, the RSB and LCMV beamformers are used to demonstrate the performance enhancement of the method for planar arrays.

Estimating the bearing of a narrowband sound source using a towed horizontal array is a common array processing problem. This paper designs nonuniform linear symmetric arrays of fixed apertures for estimating the bearing of a sound source. Specifically, the hydrophone spacings for a symmetric linear array are chosen to maximize the upper bound on the mutual information between the true bearing and the estimated bearing in spatially white noise. The arrays maximizing the mutual information while nulling the forward endfire direction look significantly different from the uniform arrays commonly used in towed systems. Arrays maximizing mutual information are helpful when bearing estimation is considered as a quantization problem to assign the source to the correct partition. The optimal partitions for the array are designed using the Lloyd algorithm with an inner product distortion metric based on maximizing the likelihood function of the observations. In these approaches, increasing the mutual information and optimizing the partitions should reduce the probability of error (P(e)) in choosing the partition containing an unknown source. Simulation results with MAP and ML estimators demonstrate that the optimum arrays and partitions proposed here have a much lower P(e) than the uniform array and uniform partitions.

A fast gridless mmWave full-dimensional MIMO channel estimation method

This paper presents a system-oriented convex optimization framework for beam synthesis problems for both uniform and non-uniform arrays in smart antenna applications. The signal propagation through different antenna elements is modeled by the Pade approximation. The array linear system model is used to formulate a semi-definite convex formulation to optimize the antenna weight coefficients. The numerical solutions demonstrate the efficiency of the proposed approach. Furthermore, the proposed convex framework solves a currently non-convex beam synthesis problem for non-uniform antenna arrays, yields low computational complexity and maintains the highest possible degrees of freedom.

We consider the problem of direction of arrival (DOA) estimation based on a nonuniform linear nested array, which is known to provide $O(N^2)$ degrees of freedom (DOFs) using only $N$ sensors. Both subspace-based and sparsity-based algorithms require certain modeling assumptions, e.g., exactly known array geometry, including sensor gain and phase. In practice, however, the actual sensor gain and phase are often perturbed from their nominal values, which disrupts the existing DOA estimation algorithms. In this paper, we investigate the self-calibration problem for perturbed nested arrays, proposing corresponding robust algorithms to estimate both the model errors and the DOAs. The partial Toeplitz structure of the covariance matrix is employed to estimate the gain errors, and the sparse total least squares (STLS) is used to deal with the phase error issue. In addition, we provide the Cramer-Rao bound (CRB) to analyze the robustness of the estimation performance of the proposed approaches. Furthermore, we extend the calibration strategies to general nonuniform linear arrays. Numerical examples are provided to verify the effectiveness of the proposed strategies.

In the underwater sonar signal processing technology, linear sonar array should conform to Nyquist sampling theorem, otherwise the problem of azimuth ambiguity will occur in the underwater Direction of Arrival (DOA) estimation. To solve this problem, a kind of nonuniform linear array random spacing array is studied, and the application of this array structure in DOA estimation of underwater targets is studied. In addition, after different transmitted signals of underwater active sonar detection target are scattered and refracted through underwater acoustic channel, the echo signal will appear coherent, which seriously affects the detection accuracy of underwater target. To solve this problem, this paper proposes Compressed Sensing Basic Pursuit De-Noising (CS-BPDN) algorithm based on random array. In this paper, CS-BPDN algorithm and Multiple signal classification (MUSIC) algorithm are combined with random spacing array to estimate the DOA of underwater targets by using the acoustic ray propagation simulation in BELLHOP model. The simulation results show that the CS-BPDN algorithm based on random spacing array can effectively deal with the problem of mixed coherent signals caused by underwater multipath effects.

Channel estimation for massive MIMO with 2-D nested array deployment

Intelligent reflecting surface (IRS) has emerged as a promising technique to enhance wireless communication performance cost-effectively. The existing literature has mainly considered IRS being deployed near user terminals to improve their performance. However, this approach may incur a high cost if IRSs need to be densely deployed in the network to cater to random user locations. To avoid such high deployment cost, in this paper we consider a new IRS aided wireless network architecture, where IRSs are deployed in the vicinity of each base station (BS) to assist in its communications with distributed users regardless of their locations. Besides significantly enhancing IRSs’ signal coverage, this scheme helps reduce the IRS-associated channel estimation overhead as compared to conventional user-side IRSs, by exploiting the nearly static BS-IRS channels over short distance. For this scheme, we propose a new two-stage transmission protocol to achieve IRS channel estimation and reflection optimization for uplink data transmission efficiently. In addition, we propose effective methods for solving the user-IRS association problem based on long-term/statistical channel knowledge and the selected user-IRS-BS cascaded channel estimation problem. Finally, all IRSs’ passive reflections are jointly optimized with the BS’s multi-antenna receive combining to maximize the minimum achievable rate among all users for data transmission. Numerical results show that the proposed co-site-IRS empowered BS scheme can achieve significant performance gains over the conventional BS without co-site IRS and existing schemes for IRS channel estimation and reflection optimization, thus enabling an appealing low-cost and high-performance BS design for future wireless networks.

The massive multiple-input-multiple-output (MIMO) technology relies on many antennas at base stations to offer high throughput to meet 5G network requirements. However, each base station requires accurate channel state information during channel estimation. Pilot contamination is one of the significant challenges that limit higher order MIMO deployment because it causes channel estimation error. In this paper, a Wiener predictor (WP) using the temporal-based prediction technique was first proposed and then extended as the coordinated WP (CoWP). The WP method is based on prediction using information that has been stored and processed at the base station from a modified subframe, whereas the extended CoWP method requires neighboring base station coordination to assign collection and prediction with other base stations. Results showed a reduction in channel estimation error due to pilot contamination after the Wiener-based prediction and coordinated base station techniques were used. The proposed CoWP technique can increase the performance of channel estimation error by up to 25 and 30 dB relative to the performance of other research technique and conventional MMSE channel estimation. This paper indicates that the pilot contamination effect can be minimized by exploiting the temporal dimension, and this approach increases the number of MIMO order for future 5G base stations, which currently limited due to pilot contamination.