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System object: phased.ULA
Namespace: phased

Simulate received plane waves


Y = collectPlaneWave(H,X,ANG)
Y = collectPlaneWave(H,X,ANG,FREQ)
Y = collectPlaneWave(H,X,ANG,FREQ,C)


Y = collectPlaneWave(H,X,ANG) returns the received signals at the sensor array, H, when the input signals indicated by X arrive at the array from the directions specified in ANG.

Y = collectPlaneWave(H,X,ANG,FREQ), in addition, specifies the incoming signal carrier frequency in FREQ.

Y = collectPlaneWave(H,X,ANG,FREQ,C), in addition, specifies the signal propagation speed in C.

Input Arguments


Array object.


Incoming signals, specified as an M-column matrix. Each column of X represents an individual incoming signal.


Directions from which incoming signals arrive, in degrees. ANG can be either a 2-by-M matrix or a row vector of length M.

If ANG is a 2-by-M matrix, each column specifies the direction of arrival of the corresponding signal in X. Each column of ANG is in the form [azimuth; elevation]. The azimuth angle must be between –180° and 180°, inclusive. The elevation angle must be between –90° and 90°, inclusive.

If ANG is a row vector of length M, each entry in ANG specifies the azimuth angle. In this case, the corresponding elevation angle is assumed to be 0°.


Carrier frequency of signal in hertz. FREQ must be a scalar.

Default: 3e8


Propagation speed of signal in meters per second.

Default: Speed of light

Output Arguments


Received signals. Y is an N-column matrix, where N is the number of elements in the array H. Each column of Y is the received signal at the corresponding array element, with all incoming signals combined.


expand all

Simulate two received plane-wave random signals at a 4-element ULA. The signals arrive from 10° and 30° azimuth. Both signals have an elevation angle of 0°. Assume the propagation speed is the speed of light and the carrier frequency of the signal is 100 MHz.

array = phased.ULA(4);
y = collectPlaneWave(array,randn(4,2),[10 30],100e6,physconst('LightSpeed'))
y = 4×4 complex

   0.7430 - 0.3705i   0.8433 - 0.1314i   0.8433 + 0.1314i   0.7430 + 0.3705i
   0.8418 + 0.4308i   0.5632 + 0.1721i   0.5632 - 0.1721i   0.8418 - 0.4308i
  -2.4817 + 0.9157i  -2.6683 + 0.3175i  -2.6683 - 0.3175i  -2.4817 - 0.9157i
   1.0724 - 0.4748i   1.1895 - 0.1671i   1.1895 + 0.1671i   1.0724 + 0.4748i


collectPlaneWave modulates the input signal with a phase corresponding to the delay caused by the direction of arrival. The method does not account for the response of individual elements in the array.

For further details, see [1].


[1] Van Trees, H. Optimum Array Processing. New York: Wiley-Interscience, 2002.