Gaussian White Noise Generation Function with Zero Mean and Specified Variance

Gaussian white noise is a random process widely used in signal processing and communication systems, characterized by zero mean and constant power spectral density (i.e., variance). Generating such noise is highly useful for simulations and algorithm testing.

### Gaussian White Noise with Zero Mean and Given Variance Gaussian white noise can be generated using standard normal distribution random number generators. The implementation involves two key steps: First, generate random numbers from a standard normal distribution (mean=0, variance=1). Then, scale these values by multiplying with the square root of the target variance (since standard deviation equals the square root of variance). In MATLAB, this can be implemented using the randn() function combined with scaling: noise = sqrt(variance) * randn(1,N) where N is the number of samples. The resulting random sequence will have zero mean and the specified variance.

### Complex Gaussian White Noise Complex Gaussian white noise consists of real and imaginary parts that are independent Gaussian random variables, typically with equal variances. The generation method parallels the real-valued case but requires generating two independent Gaussian random sequences. One sequence forms the real part, while the other forms the imaginary part, combined into complex format. In code implementation: real_part = sqrt(variance/2) * randn(1,N); imag_part = sqrt(variance/2) * randn(1,N); complex_noise = real_part + 1i*imag_part. The variance is divided by 2 to maintain proper power distribution between real and imaginary components.

In practical applications, these noise generation functions are essential for channel modeling, signal simulation, filter testing, and other scenarios where ensuring random interference follows Gaussian white noise characteristics is critical for system validation and performance analysis.