Method of processing waveforms at a multiple-input-multiple-output (MIMO) radar for an unknown target

1. A method of processing waveforms related to an unknown random target at a multiple-input multiple-output (MIMO) radar, comprising:

initiating a finite signal, at a waveform generator, to be transmitted towards an unknown target from a multiple-input multiple-output (MIMO) radar, wherein the waveform generator is electronically connected to the MIMO radar, wherein the MIMO radar comprises a set of transmitting antenna elements, a set of receiving antenna elements, a digital to analog (D/A) filter, a modulation section, a demodulation section, an analog to digital (A/D) filter, and a receiver filter;

transmitting a plurality of incident waveforms from the set of transmitting antenna elements, wherein the plurality of incident waveforms is associated with the finite signal transferred to the set of transmitting antenna elements through the D/A filter and the modulation section;

receiving a plurality of reflected waveforms at the set of receiving antenna elements of the MIMO radar, wherein the plurality of incident waveforms is transformed into the plurality of reflected waveforms by a transfer function of the unknown target and a transfer function of a volume of surrounding clutter,

transferring the plurality of reflected waveforms through the demodulation section and the A/D filter towards the receiver filter, wherein a plurality of target related information is extracted at the receiver filter, wherein the plurality of target related information comprises a target impulse response and a clutter impulse response, wherein the receiver filter is communicably coupled with a processing unit, wherein the processing unit includes circuitry with program instructions to:

derive an expression for the plurality of reflected waveforms as a function of the target impulse response, the clutter impulse response, and a sequence of white noise, wherein the sequence of white noise is from the set of receiving antenna elements;

formulate a received signal from the expression for the plurality of reflected waveforms, wherein the received signal is a function of the target impulse response, the clutter impulse response, and the sequence of white noise;

determine an output of the receiver filter as a function of the received signal, the clutter impulse response, and the sequence of white noise;

determine a signal-to-interference-plus-noise ratio (SINR) from the output of the receiver filter and derive a quadratic form of the SINR;

characterize an outage probability for the MIMO radar by determining a closed-form expression of a cumulative density function (CDF) of the quadratic form of the SINR; and

derive at least one calculation module for the outage probability, wherein the at least one calculation module is solved to reduce the outage probability of the MIMO radar.

2. The method of processing waveforms related to an unknown random target at a multiple-input multiple-output (MIMO) radar of claim 1 , wherein the at least one calculation module is derived such that a value of the outage probability in a subsequent increment is less than a scaled value of the outage probability in a preceding increment.

3. The method of processing waveforms related to an unknown random target at a multiple-input multiple-output (MIMO) radar of claim 1 , wherein the at least one calculation module is derived by constraining allocated power.

4. The method of processing waveforms related to an unknown random target at a multiple-input multiple-output (MIMO) radar of claim 1 , wherein the at least one calculation module is a non-convex function.

5. The method of processing waveforms related to an unknown random target at a multiple-input multiple-output (MIMO) radar of claim 1 , wherein the at least one calculation module is solved using an interior-point method.

6. The method of processing waveforms related to an unknown random target at a multiple-input multiple-output (MIMO) radar of claim 1 , wherein the at least one calculation module is solved using a sequential quadratic programming (SQP) iterative method.

7. The method of processing waveforms related to an unknown random target at a multiple-input multiple-output (MIMO) radar of claim 1 , wherein the set of transmitting antenna elements comprises N T antenna elements, wherein a dimension of the plurality of incident waveforms is N T ×1.

8. The method of processing waveforms related to an unknown random target at a multiple-input multiple-output (MIMO) radar of claim 1 , wherein the set of receiving antenna elements comprises N R antenna elements, wherein a dimension of the plurality of reflected waveforms is N R ×1.

9. The method of processing waveforms related to an unknown random target at a multiple-input multiple-output (MIMO) radar of claim 1 , wherein the MIMO radar is a collocated MIMO radar.

10. The method of processing waveforms related to an unknown random target at a multiple-input multiple-output (MIMO) radar of claim 1 , wherein the MIMO radar is a distributed MIMO radar.

11. The method of processing waveforms related to an unknown random target at a multiple-input multiple-output (MIMO) radar of claim 1 , wherein an output of the at least one calculation module is validated through Monte Carlo simulation.

12. The method of processing waveforms related to an unknown random target at a multiple-input multiple-output (MIMO) radar of claim 1 , wherein the target impulse response and the clutter impulse response of the received signal are Toeplitz block matrices.

13. The method of processing waveforms related to an unknown random target at a multiple-input multiple-output (MIMO) radar of claim 1 , wherein the at least one calculation module is a function of a scaling parameter, wherein the scaling parameter ranges from 0 to 1.