Derivatives of Matrix to Vector/Scalar

$$y=Hx+n$$
$$y=\begin{bmatrix}y_1\\y_2\\...\\y_n\end{bmatrix}=\begin{bmatrix}a_{11}&a_{12}&...&a_{1n}\\a_{21}&a_{22}&...& a_{2n}\\...\\a_{n1}&a_{n2}&...& a_{nn}\end{bmatrix}\begin{bmatrix}x_1\\x_2\\...\\x_n\end{bmatrix}+\begin{bmatrix}n_1\\n_2\\...\\n_n \end{bmatrix}$$
$$\min_x((y-Hx)^2)$$

WHITE NOISE

White noise is defined to be a stationary random process having a constant spectral density function:
$$S_{wn}(j\omega)=\int_{-\infty}^{\infty}R_X(\tau)e^{-j\omega\tau}d(\tau)=A=const$$
where $$R_X(\tau)=\int_{-\infty}^{\infty}x(t)x(t+\tau)$$

CW Interference

This post shows the theory of CW interference and Matlab source codes for validating the theory.
- The received satellite signal can be represented as
$$s(t)=A_sC(t)D(t)cos(2\pi(f_c+f_d)t+\Phi_0)$$

How to determine C/N0 and SNR

In this tutorial we will show a technique to determine CN0 and the behind story
-Suppose that I(m) and Q(m) is the results of tracking phase at mth millisecond
$$I(m)=\sum_{n=0}^{N-1}(s(m,n)+w(m,n))cos(2\pi f_{IF}n)PRN(n)$$
$$Q(m)=\sum_{n=0}^{N-1}(s(m,n)+w(m,n))sin(2\pi f_{IF}n)PRN(n)$$
We have
$$P_s=(\frac{1}{M}\sum_{m=0}^{M-1}I(m))^2$$
$$P_{total}=\frac{1}{M}\sum_{m=0}^{M-1}|I(m)+jQ(m)|^2$$
$$P_n=P_{total}-Ps$$
$$CN_0=10log_{10}(\frac{2P_sF_s}{P_nN})$$