{"references": ["[1] H. Sampath, P. Stoica, and A. Paulraj, \"Generalized linear precoderand decoder design for MIMO channelsusing the weighted MMSE criterion,\" IEEE Trans. Commun., vol. 49, pp. 2198\u20132206, Dec. 2001. [2] A. Scaglione, P. Stoica, S. Barbarossa, G. B. Giannakis, and H. Sampath, \"Optimal designs for space-time linear precoders and decoders,\"IEEE Trans. Signal Process., vol. 50, pp. 1051\u20131064, May 2002. [3] Y. Ding, T. N. Davidson, Z.-Q.Luo, and K.-M. Wong, \"MinimumBER block precoders for zeroforcing equalization,\" IEEE Trans.Signal Process., vol. 51, pp. 2410\u20132423, Sep. 2003.[4] D. P. Palomar, J. M. Cioffi, and M. A. Lagunas, \"Joint Tx-Rx beamforming design for multicarrier MIMO channels: A unified framework for convex optimization,\" IEEE Trans. Signal Process., vol. 51, pp. 2381\u20132401, Sep. 2003. [5] A. J. Goldsmith and S. G. Chua, \"Variable-rate variable-power MQAM for fading channels,\" IEEE Trans. Commun., vol. 45, no. 10, pp. 1218\u20131230, Oct. 1997. [6] S. M. Alouini and A. J. Goldsmith, \"Adaptive modulation over Nakagami fading channels,\" Wireless Pers. Commun., vol. 13, no. 1-2, pp. 119\u2013 143, May 2000. [7] P. F. Xia, S. L. Zhou, and G. B. Giannakis, \"Adaptive MIMO-OFDM based on partial channel state information,\" IEEE Trans. Signal Process., vol. 52, no. 1, pp. 202\u2013213, Jan. 2004. [8] P. Yang, Y. Xiao, L. Li, Q. Tang, Y. Yu, and S. Li, \"Link adaptation for spatial modulation with limited feedback,\" IEEE Trans. Veh. Technol., vol. 61, no. 8, pp. 3808\u20133813, Oct. 2012. [9] C.-C. Li, Y.-P.Lin, S.-H. Tsai, and P. P. Vaidyanathan, \"Optimization of transceivers with bit allocation to maximize bit rate for MIMO transmission,\" IEEE Trans. Commun., vol. 57, no. 11, pp. 3556\u20133560, Dec. 2009. [10] D. J. Love, R. W. Heath Jr., V. K. N. Lau, D. Gesbert, B. D. Rao, and M. Andrews, \"An overview of limited feedback in wireless communication systems,\" IEEE Sel. Area Commun., vol. 26, no. 8, pp. 1341\u20131365, Oct. 2008. [11] D. J. Love and R. W. Heath Jr., \"Limited feedback unitary precoding for spatial multiplexing systems,\" IEEE Trans. Inf. Theory, vol. 51, no. 8, pp. 2967\u2013 2976, Aug.2005."]}

This work considers the combined design of bit loading, precoding and receives filters for a multiple-input-multipleoutput (MIMO) digital communication system. Both the transmitter and the receiver are assumed to know the channel matrix perfectly. It is well known that, for linear MIMO transceivers, orthogonal transmission (i.e., diagonalization of the channel matrix) is optimal for some criteria such as maximum mutual information. It has been shown that if the receiver uses the linear minimum mean squared error (MMSE) detector, the optimal transmission strategy is to perform bit loading on orthogonal sub-channels. The transmission rate of the channel is adapted by assigning bits dynamically to the subchannels of the MIMO system. A variable-rate MIMO system with a decision feedback receiver is considered.The nested sub-matrices are generated that can be updated as time evolves.Predictive quantization is used for the feedback of bit loading to take advantage of the time correlation inherited from the temporally correlated channel. To derive the optimal predictor of the next bit loading for predictive quantization & obtain the statistics of the prediction error using this method.The quantizer is designed to achieve a smaller quantization error.The process of comparing the decoding method is proposed to enhance the design and its methodology. This provides better outcome related to the MMSE and bit rate while comparing with the conventional methods.