The presence of α stable distributed ambient channel noise in wireless systems can degrade the per-formance of existing constamt modulus（CM） equalizers.The problem of blind equalization in noisy communication channels was investigated by addressing the negative effects of heavy-tailed noise to the original constant modulus algorithm based on a stochastic gradient descent（SGD-CMA）.Two modified algorithms were proposed.The first is robust CM algorithm based on SGD（SGD-RCMA） and the second is robust CM based on recursive least square（RLS-RCMA） novel methods are robust under both Gaussian and α stable distributed ambient noise environments.And compared to SGD-RCMA method

the RLS-RCMA method has a significantly faster convergence rate and more powerful ISI impressing ability.