Horizontal alignment of equality signs written on different position of multiple equations

Question

I want to align these subequations which have two equality signs occuring at different postions. I want equations with equality sign occuring at middlle to be aligned same and the equations with equality sign occuring at end to be aligned same. My code is:

\begin{subequations}
\begin{align}
\E\left[2 \cdot (a_R(n)^2-R_{R1}) \cdot 2 \cdot a_R(n)\cdot x^*(n) \right]&=0
\intertext{Assuming the symbols in different symbol periods are uncorrelated, we get}
\E\left[a_R(n) \cdot x^*(n)\right] = k \cdot \E\left[a_R(n)^2\right]\\
k \cdot \E\left[2 \cdot (a_R(n)^2-R_{R1}) \cdot 2 \cdot a_R(n)^2\right] &=0
\end{align}
\begin{align}
\E\left[a_R(n)^4\right] &= R_{R1}\E\left[a_R(n)^2\right]
\intertext{So, the value for $R_{R1}$ can be calculated as:}
R_{R1}&=\frac{\E\left[|a_R(n)^4|\right]}{\E\left[|a_R(n)^2|\right]}
\end{align}
\end{subequations}

Output:

The equation 4.12a,4.12c should have same alignment and 4.12b,4.12d,4.12e should have same alignment without changing of their positions.

Answer 1

Here is a solution with mathtools (needless to load amsmath in this case), based on the alignat environment:

\documentclass{article}
\usepackage[utf8]{inputenc}%
\usepackage{mathtools}
\DeclareMathOperator{\E}{E}

\begin{document}

\begin{subequations}
\begin{alignat}{2}
& &\mathllap{\E\left[2 \cdot (a_R(n)^2-R_{R1}) \cdot 2 \cdot a_R(n)\cdot x^*(n) \right]}&=0
\intertext{Assuming the symbols in different symbol periods are uncorrelated, we get}
 \E\left[a_R(n) \cdot x^*(n)\right] & = k \cdot \E\left[a_R(n)^2\right]\\[1ex]
& & \mathllap{k \cdot \E\left[2 \cdot (a_R(n)^2-R_{R1}) \cdot 2 \cdot a_R(n)^2\right]} &=0 \\[1ex]
  \E\left[a_R(n)^4\right] &= R_{R1}\E\left[a_R(n)^2\right]
\intertext{So, the value for $R_{R1}$ can be calculated as:}
  R_{R1}&=\frac{\E\left[|a_R(n)^4|\right]}{\E\left[|a_R(n)^2|\right]}
\end{alignat}
\end{subequations}

\end{document}