Conjugate gradient based Complex Block LMS employing time-varying optimally derived stepsizes

The complex block least mean square (LMS) algorithm has been widely used in various adaptive filtering applications. However, the main drawback of the complex block LMS is its slow convergence. In this paper, a novel algorithm called complex block conjugate LMS (CBC-LMS) is presented, which incorporates the conjugate gradient principle into the complex block LMS algorithm. The proposed CBC-LMS employs orthogonal search directions in contrast to the steepest descent approach used in the complex block LMS algorithm. In addition, along each conjugate direction an optimal update is generated for the complex adaptive filter coefficients using the Taylor series approximation. Simulation results confirm that in channel estimation applications, the CBC-LMS exhibits faster convergence speed than the complex block LMS and the recently proposed complex optimal block adaptive LMS (Complex OBA-LMS), while maintaining excellent accuracy.