To realize rapid data transmission, the broadband transmission technique is being extensively explored and applied in existing wireless communication systems. The multi-path channel in broadband wireless communication systems is sparse and this sparsity can be used as prior knowledge to estimate the channel. To make use of sparsity, this paper recommends a switching norm-based least mean square/fourth (SN-LMS/F) adaptive approach for sparse channel estimation and echo cancellation. The suggested SN-LMS/F is implemented by adding a soft parameter adjustment function (SPF) into the conventional LMS/F adaptive method's cost function and utilizes both the l0 and l1 norm to exploit system sparsity with reduced complexity. The simulated output indicates that the suggested SN-LMS/F adaptive technique provides a more desirable performance for sparse channel estimation and echo cancellation with reduced execution time.