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A communication system is always prone to impairments, impairments such as noise, inter symbol interference (ISI) etc. are a major threat in channels but they are always compensated by the receiver in communication system. The compensation is usually done by introducing equalization and its different techniques. Submitted paper starts with equalization methods for doubly selective channel. To recognize the technique like Maximum Likelihood (ML), similarly another technique called Zero Forcing (ZF) and finally this paper will focus on Minimum Mean Square Error (MMSE) techniques and its complexity reduction by using Conjugate Gradient method. In MMSE Serial Linear Equalizer (SLE), different windows from channel are taken and recover the original out of it, whereas MMSE Block Linear Equalizer (BLE) recovers the signal from the whole block. MMSE-BLE gives better performance than MMSE-SLE considering values of BitError Rate (BER). The channel model considered for MMSE was SISO and MIMO. The performance of MMSE-BLE is enhanced by reducing its complexity by using the iterative methods. We use Conjugate Gradient algorithm, which is one of the best among all the iterative methods.