In this paper, we propose a solution to find the angle of arrival (AOA), delay, and the complex propagation factor for the monostatic multiple-input multiple-output (MIMO) radar system. In contrast to conventional iterative computationally demanding estimation schemes, we propose a closed form solution for most of the previous parameters. The solution is based on forming an approximate correlation matrix of the received signals at the MIMO radar receiver end. Then, an eigenvalue decomposition (EVD) is performed on the formed approximate correlation matrix. The AOAs of the received signals are deduced from the corresponding eigenvectors. Then, the delays are estimated from the received signal matrix properties. This is followed by forming structured matrices which will be used to find the complex propagation factors. These estimates can be used as initializations for other MIMO radar methods, such as the maximum likelihood algorithm. Simulation results show significantly low root mean square error (RMSE) for AOAs and complex propagation factors. On the other hand, our proposed method achieves zero RMSE in estimating the delays for relatively low signal-to-noise ratios (SNRs).

Multiple-input multiple-output (MIMO) radar is becoming increasingly popular due to its ability to overcome the fluctuation in the received power caused by varying radar cross section [

Several articles in the literature proposed direction finding methods for the bistatic MIMO radar system where the transmitter and receiver are located in different positions such as in [

The rest of the paper is organized as follows: Section

In this section, we present the system model for the monostatic MIMO radar which is similar to the one used in [

For

Neglecting the clutter effect, the radar signal is reflected off the targets, hence experiencing different propagation factors and delays. Therefore, the received signal vector

Monostatic radar system model.

Recall that the transmitted pulse has a total duration of

Now, the received signal can be represented in a compact matrix form by stacking the discretized vectors as

Equation (

Our proposed method localizes the targets without using computationally demanding methods such as the ML. This is done by estimating the parameters of the first target, then subtracting its formed signal from the received signal in (

Estimating the AOAs starts by forming the following approximate correlation matrix:

From the definition of

Next, let us denote

Now, from the assumption in (

It is clear that

We will call matrices satisfying the condition in (

The next step will be taking the EVD of

By comparing (

So, it can be deduced that

It is already proven in [

Algorithm

1:

2:

3:

4:

5:

6:

7:

Notice that

In order to estimate the delays (

1:

2:

3:

4:

5:

6:

7:

8:

9:

Note that

Next, we can compute

Now, that we have the means to find all the required parameters

As stated earlier, the estimated signals are subtracted from

1:

2:

3:

4:

5:

6:

7:

8:

9:

10:

11:

12:

Simulations are performed to assess the performance of the proposed method. Two targets are assumed, i.e.,

The number of iterations of the outer loop in Algorithm

Figures

Root mean square error for the AOA in degrees vs. SNR in dB for

Root mean square error for the delay in chip time

Root mean square error for the complex propagation factor magnitude vs. SNR in dB for

In this paper, we propose a computationally inexpensive algorithm to find the AOAs, delays, and complex propagation factors for monostatic MIMO radar systems. Most of the parameters are found in a closed-form manner. The algorithm starts by computing an approximate correlation matrix, then applying EVD to find the AOAs from the corresponding eigenvectors. The delay is estimated from the zero submatrix in the received signal stack. Then, we utilize the structured matrices from the estimated AOAs and delays to find the complex propagation factors for each target. These estimates can be used as initializations for other iterative MIMO radar methods. Simulation results, on one hand, show relatively low RMSE for the AOAs and complex propagation factors. And on the other hand, simulation results show virtually zero RMSE for the delay estimation.

In this section, we will prove the equation in (

Now, take the derivative of (

Now, dividing both sides by

But,

Dividing both sides of (

Next, rearranging (

So, (

The data is available through simulation of the derived equations in the paper.

The authors declare that there is no conflict of interest regarding the publication of this paper.