One-bit sparse array DOA estimation

One-bit quantization has become an important topic in massive MIMO systems, as it offers low cost and low complexity in the implementation. Techniques to achieve high performance in spite of the coarse quantizers have recently been advanced. In the context of array processing and direction-of-arrival (DOA) estimation also, one bit quantizers have been studied in the past, although not as extensively. This paper shows that sparse arrays such as nested and coprime arrays are more robust to the deleterious effects of one-bit quantization, compared to uniform linear arrays (ULAs); in fact, sparse arrays with one-bit quantizers are often found to be as good as ULAs with unquantized data. Nested and coprime arrays without quanitzers are known to be able to resolve more DOAs than the number of sensors, when sources are uncorrelated. It will be demonstrated that this continues to be true even with one-bit quantization.

[1]  P. P. Vaidyanathan,et al.  Cramér-Rao bounds for coprime and other sparse arrays, which find more sources than sensors , 2017, Digit. Signal Process..

[2]  M. Viberg,et al.  Two decades of array signal processing research: the parametric approach , 1996, IEEE Signal Process. Mag..

[3]  P. P. Vaidyanathan,et al.  Remarks on the Spatial Smoothing Step in Coarray MUSIC , 2015, IEEE Signal Processing Letters.

[4]  Alessandro Neri,et al.  Estimation of the autocorrelation function of complex Gaussian stationary processes by amplitude clipped signals , 1994, IEEE Trans. Inf. Theory.

[5]  John Bowman Thomas,et al.  An introduction to statistical communication theory , 1969 .

[6]  Erik G. Larsson,et al.  Massive MIMO with 1-bit ADC , 2014, ArXiv.

[7]  Alessandro Neri,et al.  Methods for estimating the autocorrelation function of complex Gaussian stationary processes , 1987, IEEE Trans. Acoust. Speech Signal Process..

[8]  J. V. Vleck,et al.  The spectrum of clipped noise , 1966 .

[9]  A. Moffet Minimum-redundancy linear arrays , 1968 .

[10]  Harry L. Van Trees,et al.  Optimum Array Processing: Part IV of Detection, Estimation, and Modulation Theory , 2002 .

[11]  Josef A. Nossek,et al.  DOA Parameter Estimation with 1-bit Quantization Bounds, Methods and the Exponential Replacement , 2016, WSA.

[12]  Wei Cui,et al.  Extension of nested arrays with the fourth-order difference co-array enhancement , 2016, 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[13]  P. P. Vaidyanathan,et al.  Nested Arrays: A Novel Approach to Array Processing With Enhanced Degrees of Freedom , 2010, IEEE Transactions on Signal Processing.

[14]  Avinash C. Kak,et al.  Array signal processing , 1985 .

[15]  Erik G. Larsson,et al.  Massive MIMO for next generation wireless systems , 2013, IEEE Communications Magazine.

[16]  Yimin Zhang,et al.  Generalized Coprime Array Configurations for Direction-of-Arrival Estimation , 2015, IEEE Transactions on Signal Processing.

[17]  Paolo Banelli,et al.  Theoretical analysis and performance of OFDM signals in nonlinear AWGN channels , 2000, IEEE Trans. Commun..

[18]  Kristen Rohlfs,et al.  Tools of Radio Astronomy , 1986 .

[19]  P. P. Vaidyanathan,et al.  Sparse Sensing With Co-Prime Samplers and Arrays , 2011, IEEE Transactions on Signal Processing.

[20]  P Kuyper,et al.  Triggered correlation. , 1968, IEEE transactions on bio-medical engineering.

[21]  T. Engin Tuncer,et al.  Classical and Modern Direction-of-Arrival Estimation , 2009 .

[22]  A. Weiss,et al.  DOA estimation using one-bit quantized measurements , 2002 .

[23]  Emil Björnson,et al.  Massive MIMO: ten myths and one critical question , 2015, IEEE Communications Magazine.

[24]  Josef A. Nossek,et al.  1-bit direction of arrival estimation based on Compressed Sensing , 2015, 2015 IEEE 16th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC).

[25]  M. Skolnik,et al.  Introduction to Radar Systems , 2021, Advances in Adaptive Radar Detection and Range Estimation.

[26]  Marcel J. M. Pelgrom,et al.  Analog-to-Digital Conversion , 2016 .

[27]  Julian J. Bussgang,et al.  Crosscorrelation functions of amplitude-distorted gaussian signals , 1952 .

[28]  Geoffrey Ye Li,et al.  An Overview of Massive MIMO: Benefits and Challenges , 2014, IEEE Journal of Selected Topics in Signal Processing.

[29]  P. P. Vaidyanathan,et al.  Super Nested Arrays: Linear Sparse Arrays With Reduced Mutual Coupling—Part I: Fundamentals , 2016, IEEE Transactions on Signal Processing.

[30]  D. Middleton An Introduction to Statistical Communication Theory , 1960 .

[31]  P. Vaidyanathan,et al.  Coprime sampling and the music algorithm , 2011, 2011 Digital Signal Processing and Signal Processing Education Meeting (DSP/SPE).

[32]  Peter Dayan,et al.  Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems , 2001 .