Numerical properties of the DCD-RLS algorithm for stereo acoustic echo cancellation

Efficient FPGA implementation of the DCD-RLS algorithm for stereo acoustic echo cancellation

“…The method is presented in Table I [4], [7] and is comprised of five steps. The first stage consists of the update performed for the autocorrelation matrix estimate ), ( n x R based on the L most recent input complex samples and the forgetting factor λ   .…”

“…By operating on the auxiliary system of equations in stage 4, the solution vector ) ( n h  is computed using a limited (or maximum allowed) number of updates, denoted in [4], [5], [6], [7] as N u . The overall complexity of the DCD-RLS algorithm is proportional to 2LN u (N u <10), making it attractive for hardware implementations.…”

“…The filter length is 2L=1024, corresponding to a standard setup with four adaptive filters comprised of L=512 coefficients. The corresponding complex valued coefficients are represented with 2xM b =32 bits/coefficient [4], [7]. They are stored in a Random Access Memory (RAM) with 2L locations.…”

“…They are performed in groups of 2L=1024 successive operations. We chose for the forgetting factor the value λ=1-1/(16L) [7]. Thus, the multiplications with λ are replaced by bit-shifts and subtractions [7] in steps 1 and 3, where…”

“…The DCD-RLS has similar performance with fewer computational resources and is attractive for practical applications. Considering the numerical analysis that we performed in [7] for the variables comprising the algorithm in different scenarios, this paper proposes an efficient finite precision implementation for the DCD-RLS method.…”