Abstract: In this paper we describe the Levenvberg-Marquardt
(LM) algorithm for identification and equalization of CDMA
signals received by an antenna array in communication channels.
The synthesis explains the digital separation and equalization of
signals after propagation through multipath generating intersymbol
interference (ISI). Exploiting discrete data transmitted and three
diversities induced at the reception, the problem can be composed
by the Block Component Decomposition (BCD) of a tensor of
order 3 which is a new tensor decomposition generalizing the
PARAFAC decomposition. We optimize the BCD decomposition by
Levenvberg-Marquardt method gives encouraging results compared to
classical alternating least squares algorithm (ALS). In the equalization
part, we use the Minimum Mean Square Error (MMSE) to perform
the presented method. The simulation results using the LM algorithm
are important.