# dopsteeringvec

Doppler steering vector

## Syntax

DSTV = dopsteeringvec(dopplerfreq,numpulses)
DSTV = dopsteeringvec(dopplerfreq,numpulses,PRF)

## Description

DSTV = dopsteeringvec(dopplerfreq,numpulses) returns the N-by-1 temporal (time-domain) Doppler steering vector for a target at a normalized Doppler frequency of dopplerfreq in hertz. The pulse repetition frequency is assumed to be 1 Hz.

DSTV = dopsteeringvec(dopplerfreq,numpulses,PRF) specifies the pulse repetition frequency, PRF.

## Input Arguments

 dopplerfreq The Doppler frequency in hertz. The normalized Doppler frequency is the Doppler frequency divided by the pulse repetition frequency. This argument supports single and double precision. numpulses The number of pulses. The time-domain Doppler steering vector consists of numpulses samples taken at intervals of 1/PRF (slow-time samples). This argument supports single and double precision. PRF Pulse repetition frequency in hertz. The time-domain Doppler steering vector consists of numpulses samples taken at intervals of 1/PRF (slow-time samples). The normalized Doppler frequency is the Doppler frequency divided by the pulse repetition frequency. This argument supports single and double precision.

## Output Arguments

 DSTV Temporal (time-domain) Doppler steering vector. DSTV is an N-by-1 column vector where N is the number of pulses, numpulses.

## Examples

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Calculate the steering vector corresponding to a Doppler frequency of 200 Hz. Assume there are 10 pulses and the PRF is 1 kHz.

dstv = dopsteeringvec(200,10,1000)
dstv = 10×1 complex

1.0000 + 0.0000i
0.3090 + 0.9511i
-0.8090 + 0.5878i
-0.8090 - 0.5878i
0.3090 - 0.9511i
1.0000 - 0.0000i
0.3090 + 0.9511i
-0.8090 + 0.5878i
-0.8090 - 0.5878i
0.3090 - 0.9511i

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### Temporal Doppler Steering Vector

The temporal (time-domain) steering vector corresponding to a point scatterer is:

${e}^{j2\pi {f}_{d}{T}_{p}n}$

where n=0,1,2, ..., N-1 are slow-time samples (one sample from each pulse), fd is the Doppler frequency, and Tp is the pulse repetition interval. The product of the Doppler frequency and the pulse repetition interval is the normalized Doppler frequency.

## Algorithms

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### Single Precision

This functions supports single and double precision for input arguments. If the input arguments are single precision, the output is single precision. If the input arguments are double precision, the output is double precision.

## References

[1] Melvin, W. L. “A STAP Overview,” IEEE® Aerospace and Electronic Systems Magazine, Vol. 19, Number 1, 2004, pp. 19–35.

[2] Richards, M. A. Fundamentals of Radar Signal Processing. New York: McGraw-Hill, 2005.