Decision Circle Based Dual-Mode Constant Modulus Blind Equalization Algorithm

For greatly overcoming defects of multipath underwater acoustic channel and constant modulus error function with asymmetry about zero error, a hyperbolic tangent error function with odd symmetry about zero error is defined, a hyperbolic tangent error function based constant modulus blind equalization algorithm (HCMA) and decision circle based dual-mode constant modulus blind equalization algorithm(DCMA) are proposed. In the DCMA, we propose HSCMA (hyperbolic tangent error function based sign constant modulus blind equalization algorithm) by introducing sign algorithm into the HCMA and determine radius of decision circle by signal-to-noise ratio (SNR). Before the end convergence of DCMA, CMA moves whereas HSCMA stops running to ensure the fast convergence of DCMA. Based on the decision circle, CMA switches automatically to HSCMA. It is demonstrated through computer simulations with underwater acoustic channel that DCMA can smoothly switch iteration process from CMA to HSCMA, converges quickly, and has clear constellation and low added computational complexity. Therefore, it is very suitable for the recovery of the underwater data transmission