How to make a random circularly-symmetric gaussian distributed additive noise component with mean 0 and variance (sigma^2)/2?

Question

Himanshi 2023-10-3

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2028705-how-to-make-a-random-circularly-symmetric-gaussian-distributed-additive-noise-component-with-mean-0

评论： Jon 2023-10-4

采纳的回答： Jon

circular gaussian.fig

在 MATLAB Online 中打开

yBob(t) = xAlice(t) hab(t) + nb(t)

where t denotes the time, denotes the convolution operator, hab(t) denotes the circularly-symmetric Gaussian-distributed channel response with mean 0 and variance σ2 h /2 in each dimension, and nb(t) denotes the circularly-symmetric Gaussian-distributed additive noise component with mean 0 and variance σ2 n /2 in each dimension.

hab(t) and nb(t) should be different, but how?

If I write this code then I get same hab(t) and nb(t):

N=16;
t = linspace(0, 2*pi, N);
j = sqrt(-1);
hab = cos(t) + j*sin (t);
plot(x, y, 'bo-', 'LineWidth', 2);
grid on;
title('hab');
xlabel('Real Component');
ylabel('Imaginary Component');
nb = cos(t) + j*sin(t);
plot(x, y, 'bo-', 'LineWidth', 2);
grid on;
title('nab');
xlabel('Real Component');
ylabel('Imaginary Component');

But I want different hab and nb. hab and nb should be circularly symmetric gaussian-distributed with 0 mean.

Using below code I didn't get circular symmetric gaussian but only gaussian with mean 0. But I want both.

hab = (1/sqrt(2))*(randn(N, 1) +1i*randn(N,1));  
plot(hab, 'bo-', 'LineWidth', 2);
grid on;
title('hab');
xlabel('Real Component');
ylabel('Imaginary Component');
nb = (1/sqrt(2))*(randn(N, 1) +1i*randn(N,1));
plot(nb, 'bo-', 'LineWidth', 2);
grid on;
title('nb');
xlabel('Real Component');
ylabel('Imaginary Component');

Through this I got the different value of hab and nb, but it is not circularly-symmetric gaussian.

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Jon 2023-10-3

Why do you say that it is not circularly symmetric gaussian? How are you checking this and deciding it is not circularly symmetric gaussian?

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Answer 1

Jon 2023-10-3

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2028705-how-to-make-a-random-circularly-symmetric-gaussian-distributed-additive-noise-component-with-mean-0#answer_1324650

编辑：Jon 2023-10-3

在 MATLAB Online 中打开

Using your code and plotting results, qualitatively it looks like you are getting two circularly symmetric distriuted sets of data, what is it that you think isn't working?

N = 1000;

hab = (1/sqrt(2))*(randn(N, 1) +1i*randn(N,1)); %circularly-symmetric Gaussian-distributed and channel coefficient

nb = (1/sqrt(2))*(randn(N, 1) +1i*randn(N,1));

plot(hab,'o'),

xlim([-3,3])

ylim([-3,3])

axis equal

title('hab')

plot(nb,'o')

xlim([-3,3])

ylim([-3,3])

axis equal