Bell Laboratories Layered Space-Time

V-BLAST

V-BLAST (Vertical-Bell Laboratories Layered Space-Time) is a detection algorithm to the receipt of multi-antenna MIMO systems. Available for the first time in 1996 at Bell Laboratories in New Jersey in the United States by Gerard J. Foschini. He proceeded simply to eliminate interference caused successively issuers.

Its principle is quite simple: to make a first detection of the most powerful signal. It regenerates the received signal from this user from this decision. Then, the signal is regenerated subtracted from the received signal and, with this new signal, it proceeds to the detection of the second user's most powerful, since it has already cleared the first and so forth. What gives a vector containing received less interference.

The complete detection algorithm can be summarized as recursive as follows:

Initialize:

${\displaystyle \begin{array}{cc}i& \leftarrow 1\\ r_1& =r\\ G_1& =(H^{H}H+{\sigma }^2{I}_{N_t}{)}^{-1}{H}^H\\ k_1& =\arg min{\Vert (G_1{)}_j\Vert }^2\end{array}}$

Recursive:

${\displaystyle \begin{array}{cc}{w}_k& =(G_i{)}_{ki}\\ y_k& =w_k^T\times r_i\\ {\hat{s}}_k& =sign(y_k)\\ r_{i+1}& =r_i-{\hat{s}}_k(H{)}_{ki}\\ G_{i+1}& =((H_i^H{H}_i)+{\sigma }^2{I}_{Nt}{)}^{-1}{H}_i^H\\ k_{i+1}& =\arg min{\Vert (G_{i+1}{)}_j\Vert }^2\\ i& \leftarrow i+1\end{array}}$