# Difference between single layer and dual layer beamforming in LTE

I'm trying to understand the difference between single and dual layer beamforming in LTE as described in TS 36.101 section B.4.1 and B.4.2 respectively. Also refer to TS 36.211 section 6.3.4.2.3 for selection of precoding matrices.

My questions are as follows,

1. What does the following linear operation(From TS 36.211 section 6.3.4.2.3) of subtracting twice the projection matrix from identity signify and how is it relevant to beamforming? $$\rm W_n=I-2u_n u_n^H/u_n^Hu_n$$

2. What is the difference between single and dual layer beamforming based on their respective precoding transformations given below?

For single layer beamforming (From Section B.4.1 TS 36.101) $$\begin{bmatrix}y_{bf}(i)\\\tilde{y}_{bf}(i)\end{bmatrix}=\frac{1}{\sqrt 2}\left(W_1(i)y^{(7)}(i)+W_2(i)y^{(8)}(i)\right)$$

For dual layer beamforming (From Section B.4.2 TS 36.101) $$\begin{bmatrix}y_{bf}(i)\\\tilde{y}_{bf}(i)\end{bmatrix}=W(i)\begin{bmatrix}y^{(7)}(i)\\y^{(8)}(i)\end{bmatrix}$$

• This document explains how you get those equations: sharetechnote.com/html/… – Behind The Sciences May 19 '16 at 6:14
• @BehindTheSciences The blog page doesn't explain the meaning of the subspace projections of u. – Naveen May 19 '16 at 14:41
• @Naveen the equation of your 1) is not for beamforming, but matrix precoding for transmission mode 3 (open loop mimo) and transmission mode 4(closed loop mimo). By looking at the index (7) and (8) of your beamforming equation, they are antenna port 7 and 8 and they are transmission mode 7(single layer) and 8(dual layer). Your two points are for two totally different stuff. The matrix of point 1 are fixed; whilte the matrix of point 2 are dynamic depending on the estimation of eNB. The link of Behind the Sciences covers the fundamental parts but is not correct in confusing the two matrix types. – AlexTP May 1 '17 at 13:53