An automatic pairing joint direction-of-arrival (DOA) and frequency estimation is presented to overcome the unsatisfactory performances of estimation of signal parameter via rotational invariance techniques- (ESPRIT-) like algorithm of Wang (2010), which requires an additional pairing. By using multiple-delay output of a uniform linear antenna arrays (ULA), the proposed algorithm can estimate joint angles and frequencies with an improved ESPRIT. Compared with Wang’s ESPRIT algorithm, the angle estimation performance of the proposed algorithm is greatly improved. The frequency estimation performance of the proposed algorithm is same with that of Wang’s ESPRIT algorithm. Furthermore, the proposed algorithm can obtain automatic pairing DOA and frequency parameters, and it has a comparative computational complexity in contrast to Wang’s ESPRIT algorithm. By the way, this proposed algorithm can also work well for nonuniform linear arrays. The useful behavior of this proposed algorithm is verified by simulations.

Uniform linear antenna (ULA) arrays have been used in radar, sonar, electron reconnaissance, seismic data processing, and so on [

The authors in [

Angle-frequency scatter of the Wang’s ESPRIT algorithm at SNR = 0 dB.

An improved ESPRIT for joint direction-of-arrival (DOA) and frequency estimation is presented in this paper. Compared with Wang’s ESPRIT algorithm, the algorithm has the improved performance of DOA estimation. Moreover, the proposed algorithm can obtain automatically paired DOA and frequency estimation, while Wang’s ESPRIT algorithm requires the additional pairing. The proposed algorithm has a comparative computational complexity in contrast to Wang’s ESPRIT algorithm. Moreover, this proposed algorithm can also work well for nonuniform linear arrays.

We consider a uniform linear array with spacing

The outputs of the uniform linear antenna arrays (ULA) is

Based on this available samples, the problem is to estimate the angles and the frequencies of all sources from the

In order to joint estimate DOA and frequency, we add

The delayed signal for (

The delayed signal for (

The delayed signal for (

According to (

We can use received signal to attain the direction matrix

According to (

Let

Because

There exists a transformation matrix

The following summarizes the major steps of this proposed algorithm.

Compute the covariance matrix from the received signal via

Get the signal subspace

Employ EVD on

Compute

Compute the matrix

The proposed algorithm can obtain automatically parameter estimation

Note that

In contrast to Wang’s ESPRIT algorithm, the proposed algorithm has a comparative computational load. For the proposed algorithm, the covariance matrix estimation costs

The performance of this proposed algorithm with nonuniform linear array will be discussed in this section. The distance between the

There is an array of

Replacing matrix

For a nonuniform linear array, (

We define

The proposed algorithm has the following advantages.

The proposed algorithm has a better angle estimation performance than Wang’s ESPRIT algorithm.

The proposed algorithm can obtain automatically paired parameter estimation, while Wang’s ESPRIT algorithm requires additional pairing.

The proposed algorithm has a comparative computational complexity in contrast to Wang’s ESPRIT algorithm.

This proposed algorithm also suit for nonuniform linear arrays.

We present Monte Carlo simulations that are used to assess the angle and frequency estimation performance of this algorithm. The number of Monte Carlo trials is 1000. Note that

Define

The performance of Wang’s ESPRIT algorithm and this proposed algorithm is investigated.

Angle-frequency scatter of proposed method, SNR = 0 dB.

We compare this proposed algorithm with Wang’s ESPRIT algorithm and CRB. From Figures

Angle estimation performance comparison at

Frequency estimation performance comparison at

Angle estimation performance comparison at

Angle estimation performance comparison at

Angle estimation performance comparison at

This proposed algorithm performance under different snapshots

Angle-frequency estimation with different snapshot

Angle estimation

Frequency estimation

The performance of this algorithm under different source number

Angle-frequency estimation with different sources.

Angle estimation

Frequency estimation

The performance of this algorithm under different antenna number

Angle-frequency estimation with different antennas.

Angle estimation

Frequency estimation

The performance of this algorithm under different delay number

Angle-frequency estimation with different delay number.

Angle estimation

Frequency estimation

The performance of this proposed algorithm with nonuniform linear arrays is investigated.

Angle-frequency scatter for nonuniform linear arrays, SNR = 10 dB.

This paper has presented an improved joint angle-frequency estimation method, which has better angle estimation performance than Wang’s ESPRIT algorithm and has the same frequency estimation accuracy. The computational complexity of this proposed algorithm is comparative in contrast to Wang’s ESPRIT algorithm. Since the DOA and frequency estimations suffer from the same permutation ambiguity, this novel method can obtain automatically paired DOA and frequency. This advantage is more obvious when the input SNR is below 0 dB. Furthermore, the proposed algorithm can also work well in the case of nonuniform linear arrays.

This paper is supported by China NSF Grant (61201208), Aeronautical Science Foundation of China (2009ZC52036), Nanjing University of Aeronautics and Astronautics Research Funding (NN2012068), and the Fundamental Research Funds for the Central Universities (NZ2012010, kfjj120115, kfjj20110215).