Simulate the received signal at an array, and use the data to estimate the arrival directions.

Create an 8-element uniform linear array whose elements are spaced half a wavelength apart.

Simulate 100 snapshots of the received signal at the array. Assume there are two signals, coming from azimuth 30 and 60 degrees, respectively. The noise is white across all array elements, and the SNR is 10 dB.

Use a beamscan spatial spectrum estimator to estimate the arrival directions, based on the simulated data.

Plot the spatial spectrum resulting from the estimation process.

The plot shows peaks at 30 and 60 degrees.

Simulate receiving two uncorrelated incoming signals that have different power levels. A vector named `scov`

stores the power levels.

Create an 8-element uniform linear array whose elements are spaced half a wavelength apart.

Simulate 100 snapshots of the received signal at the array. Assume that one incoming signal originates from 30 degrees azimuth and has a power of 3 W. A second incoming signal originates from 60 degrees azimuth and has a power of 1 W. The two signals are not correlated with each other. The noise is white across all array elements, and the SNR is 10 dB.

Use a beamscan spatial spectrum estimator to estimate the arrival directions, based on the simulated data.

Plot the spatial spectrum resulting from the estimation process.

The plot shows a high peak at 30 degrees and a lower peak at 60 degrees.

Simulate the reception of three signals, two
of which are correlated. A matrix named `scov`

stores
the signal covariance matrix.

Create a signal covariance matrix in which the first and
third of three signals are correlated with each other.

Simulate receiving 100 snapshots of three incoming signals
from 30, 40, and 60 degrees azimuth, respectively. The array that
receives the signals is an 8-element uniform linear array whose elements
are spaced half a wavelength apart. The noise is white across all
array elements, and the SNR is 10 dB.

Simulate receiving a signal at a URA. Compare
the signal's theoretical covariance, `rt`

,
with its sample covariance, `r`

.

Create a 2-by-2 uniform rectangular array whose elements
are spaced 1/4 of a wavelength apart.

Define the noise power independently for each of the four
array elements. Each entry in `ncov`

is the noise
power of an array element. This element's position is the corresponding
column in `pos`

. Assume the noise is uncorrelated
across elements.

Simulate 100 snapshots of the received signal at the array,
and store the theoretical and empirical covariance matrices. Assume
that one incoming signal originates from 30 degrees azimuth and 10
degrees elevation. A second incoming signal originates from 50 degrees
azimuth and 0 degrees elevation. The signals have a power of 1 W and
are not correlated with each other.

View the magnitudes of the theoretical covariance and
sample covariance.

ans =
2.1259 1.8181 1.9261 1.9754
1.8181 2.1000 1.5263 1.9261
1.9261 1.5263 2.1000 1.8181
1.9754 1.9261 1.8181 2.0794
ans =
2.2107 1.7961 2.0205 1.9813
1.7961 1.9858 1.5163 1.8384
2.0205 1.5163 2.1762 1.8072
1.9813 1.8384 1.8072 2.0000

Simulate receiving a signal at a ULA, where
the noise among different sensors is correlated.

Create a 4-element uniform linear array whose elements
are spaced half a wavelength apart.

Define the noise covariance matrix. The value in the (*k*, *j*)
position in the `ncov`

matrix is the covariance between
the *k*^{th} and *j*^{th} array
elements listed in `pos`

.

Simulate 100 snapshots of the received signal at the array.
Assume that one incoming signal originates from 60 degrees azimuth.

View the theoretical and sample covariance matrices for
the received signal.

rt =
1.1000 -0.9027 - 0.4086i 0.6661 + 0.7458i -0.3033 - 0.9529i
-0.9027 + 0.4086i 1.1000 -0.9027 - 0.4086i 0.6661 + 0.7458i
0.6661 - 0.7458i -0.9027 + 0.4086i 1.1000 -0.9027 - 0.4086i
-0.3033 + 0.9529i 0.6661 - 0.7458i -0.9027 + 0.4086i 1.1000
r =
1.1059 -0.8681 - 0.4116i 0.6550 + 0.7017i -0.3151 - 0.9363i
-0.8681 + 0.4116i 1.0037 -0.8458 - 0.3456i 0.6578 + 0.6750i
0.6550 - 0.7017i -0.8458 + 0.3456i 1.0260 -0.8775 - 0.3753i
-0.3151 + 0.9363i 0.6578 - 0.6750i -0.8775 + 0.3753i 1.0606