List of Symbols

xn

N × 1 data vector at time index n

n

Discrete time index

N

Dimension of data vector xn

r

Number of signals present in the linear data model of xn

Rxx

Autocorrelation matrix associated with xn

Rxx(n)

Estimate of Rxx at time n

In × k

The n × k identity matrix

In

The n × n identity matrix

A

N × r matrix whose columns are steering vectors of incoming signals

σ 2

Variance of the white, Gaussian noise

QDQH

The eigendecomposition of Rxx, where QQH = I, and Q can be partitioned as [Qs Qn],

2

2

2

where Qs is N × r and Qn is N × (N − r). D = diag{σ 0,

σ 1, …, σ N - 1}, where

σ 02 ≥ σ 21 ≥ … ≥ σ 2r − 1 > σ 2r = σ 2r + 1 = … = σ 2N − 1

Qs(n)

Qs(n) is the estimate of Qs at time index n

X(n)

n × N data matrix whose ith row is xHi

USVH

Singular value decomposition of the data matrix X(n), with S = diag{σ 0, σ 1, …, σ N - 1}.

The columns of U are the left singular vectors of X and the columns of V are the right

singular vectors. The matrix V can be partitioned as V = [Vs

Vn] with Vs = Qs and

Vn = Qn

zn

zn = Qs(n)xn, r × 1 compressed data vector

c

Speed of light

D

Distance between elements of uniform linear array in meters

d

Distance between elements of a uniform linear array in wavelengths

wn

N × 1 vector of complex beamformer weights

List of Acronyms

DOA

Direction of arrival

ESPRIT

Estimation of signal parameters via rotational invariance techniques

EVD

Eigenvalue decomposition

MIL

Matrix inversion lemma

MUSIC

Multiple signal classification

SVD

Singular value decomposition

SW

Sliding window

ULA

Uniform linear array

URA

Uniform rectangular array

DFT

Discrete Fourier transform