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In this paper we focus on finding a suitable Link Adaptation (LA) algorithm which is implemented as Channel Quality Indicator (CQI) selection technique in the 3GPP Long Term Evolution (LTE) system. The potential of Link Adaptation in the LTE system is not fully exploited. Therefore in our study, we compare the performances from different LA algorithms in the LTE system. The presented LA algorithms are EESM, RawBER and MMIB which utilize the post processing SINRs (Signal-to-Interference-and-Noise power Ratio) to compute the effective SNR (Signal-to-Noise power Ratio), uncoded bit error probability and mutual information as mapping function, respectively. We present our simulation results and show that the EESM algorithm can significantly improve the performance of the whole system both in the SISO case and the MIMO case.