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Karhunen-Loeve transformation (KLT) is a very powerful technique used in data compression, when the data elements are highly correlate. In a 2D rake receiver, the data are delayed by a tapped-delay-line, the time delay between them are very short, and hence the signal are highly correlated. By using KLT, the dimension of the correlation matrix can be reduced dramatically with little or no reduction in the performance. This new algorithm is called as "beamspace-KLT" method. It is demonstrated that beamspace-KLT has a better performance than beamspace-frequency method introduced by Y.F. Chen when they have the same dimension correlation matrix. To achieve the same performance, beamspace-KLT method need a lower dimension correlation matrix than beamspace-frequency method. Another very important benefit of this beamspace-KLT algorithm is that, when using a dynamic adaptive algorithm to solve the generalize eigenvalue (GE) problem, this algorithm can converge faster.