Hello, everyone I am studying the MUSIC algorithm on the Internet for finding the Angle of Arrival. I have read some paper about MUSIC but I still have some confused points. The MUSIC algorithm I understand is below : At the very beginning, we need to build the data model X=AS+N -- X is the output of antennas [M*1] A is the array manifold vector (there are M antennas) [M*N] S is the vector of N signals amplitude [N*1] N is the vector of M noise sample [M*1] -- I am confused when I want to implement MUSIC to find AOA in reality. I saw some simulation but I did not understand still. What the S exactly is when using SDRs and antennas to receive signals? I consider that S is the sqrt( I^2+Q^2). I and Q is the data from SDRs output. I know A is difference from the shape of array (ULA, UPA, UCA). N is nothing when I implement the MUSIC in reality. Am I right? or something wrong??? I really need someone to help me to understand the MUSIC algorithm. please, thanks a lot!! --------------------------------------- Posted through http://www.DSPRelated.com
Implementing MUSIC algorithm for finding Angle of Arrival
Started by ●April 10, 2015
Reply by ●April 13, 20152015-04-13
On Friday, April 10, 2015 at 11:10:31 AM UTC-4, wiiwiiya wrote:> Hello, everyone > I am studying the MUSIC algorithm on the Internet for finding the Angle > of Arrival. I have read some paper about MUSIC but I still have some > confused points. > The MUSIC algorithm I understand is below : > At the very beginning, we need to build the data model > X=AS+N > -- > X is the output of antennas [M*1] > A is the array manifold vector (there are M antennas) [M*N] > S is the vector of N signals amplitude [N*1] > N is the vector of M noise sample [M*1] > -- > I am confused when I want to implement MUSIC to find AOA in reality. I > saw some simulation but I did not understand still. > What the S exactly is when using SDRs and antennas to receive signals? > I consider that S is the sqrt( I^2+Q^2). I and Q is the data from SDRs > output. > I know A is difference from the shape of array (ULA, UPA, UCA). > N is nothing when I implement the MUSIC in reality. > > Am I right? or something wrong??? > > I really need someone to help me to understand the MUSIC algorithm. > please, > thanks a lot!! > > > --------------------------------------- > Posted through http://www.DSPRelated.comX is what you observe. S is amplitude, not magnitude. This is a fixed, unknown parameter. A represents the AoA, modeled as exp(j someconstant angle_n). This is also a fixed, unknown parameter. N is never observed directly. This is important for analysis and modeling, but in practice most simple algorithms you use to solve AoA problems do not scale with the variance of N, so you ignore it. MuSIC is done in two steps. Step 1 solves for angle_n. Then, you construct an estimate of A based on the estimate for angle_n. Step 2 fits for S based on X and estimated A, typically using least squares. It will help a lot if you actually post the document from which you are trying to learn this stuff.
