ACMA - An Analytical Constant Modulus Algorithm

Iterative constant modulus algorithms such as Godard and CMA have been used to blindly separate a superposition of co-channel constant modulus (CM) signals impinging on an antenna array. These algorithms have certain deficiencies in the context of convergence to local minima and the retrieval of all individual CM signals that are present in the channel.

In the corresponding paper, we show that the underlying constant modulus factorization problem is, in fact, a generalized eigenvalue problem, and may be solved via a simultaneous diagonalization of a set of matrices. With this new, analytical approach, it is possible to detect the number of CM signals present in the channel, and to retrieve all of them exactly, rejecting other, non-CM signals. Only a modest amount of samples are required. The algorithm is robust in the presence of noise, and is tested on measured data, collected from an experimental set-up.

The attached matlab code implements the original 1994 version of the algorithm, including the joint diagonalization required in the final step. Note that, since then, many authors have published improved JD algorithms.

Related publications

1. An Analytical Constant Modulus Algorithm
   A.J. van der Veen; A. Paulraj;
   IEEE Trans. Signal Processing,
   Volume 44, Issue 5, pp. 1136-1155, May 1996.
   document