A block linear equalizer (BLE) using an approximate Cholesky decomposition is disclosed. The BLE includes channel estimators, a channel monitor unit, a noise power estimator, a parameter selection unit and an approximate Cholesky processor. The channel estimator generates a channel estimate vector from received samples. The channel monitor unit generates a first channel monitor signal for a truncated channel estimate vector and a second channel monitor signal. The noise power estimator estimates a noise power of the received samples. The parameter selection unit selects parameters for approximate Cholesky decomposition based on the first and second channel monitor signals. The approximate Cholesky processor performs block linear equalization on the received samples based on approximate Cholesky decomposition.