A Training-Based Mutual Information Lower Bound for Large-Scale Systems

We provide a mutual information lower bound that can be used to analyze the effect of training in models with unknown parameters. For large-scale systems, we show that this bound can be calculated using the difference between two derivatives of a conditional entropy function. The bound does not require explicit estimation of the unknown parameters. We provide a step-by-step process for computing the bound, and provide an example application. A comparison with known classical mutual information bounds is provided.

[1]  Shlomo Shamai,et al.  The impact of frequency-flat fading on the spectral efficiency of CDMA , 2001, IEEE Trans. Inf. Theory.

[2]  Shlomo Shamai,et al.  Mutual information and minimum mean-square error in Gaussian channels , 2004, IEEE Transactions on Information Theory.

[3]  Michael L. Honig,et al.  Advances in Multiuser Detection , 2009 .

[4]  Shi Jin,et al.  Joint cHANNEL-AND-dATA estimation for large-MIMO systems with low-precision ADCs , 2015, 2015 IEEE International Symposium on Information Theory (ISIT).

[5]  Sergio Verdú,et al.  Randomly spread CDMA: asymptotics via statistical physics , 2005, IEEE Transactions on Information Theory.

[6]  Manfred Opper,et al.  Statistical mechanics of generalization , 1998 .

[7]  Chih-Chun Wang,et al.  Multiuser Detection of Sparsely Spread CDMA , 2008, IEEE Journal on Selected Areas in Communications.

[8]  Ralf R. Müller,et al.  An achievable rate of large block-fading MIMO systems with no CSI via successive decoding , 2010, 2010 International Symposium On Information Theory & Its Applications.

[9]  강국진,et al.  시그모이드 트랜스퍼함수를 가진 퍼셉트론의 일반화 ( Generalization in a Perceptron with a Sigmoid Transfer Function ) , 1993 .

[10]  Babak Hassibi,et al.  How much training is needed in multiple-antenna wireless links? , 2003, IEEE Trans. Inf. Theory.

[11]  Y. Kabashima,et al.  Learning from correlated patterns by simple perceptrons , 2008, 0809.1978.

[12]  Ha H. Nguyen,et al.  Optimal Training Sequences for Large-Scale MIMO-OFDM Systems , 2017, IEEE Transactions on Signal Processing.

[13]  Julian J. Bussgang,et al.  Crosscorrelation functions of amplitude-distorted gaussian signals , 1952 .

[14]  Ralf R. Müller,et al.  Large-System Analysis of Joint Channel and Data Estimation for MIMO DS-CDMA Systems , 2010, IEEE Transactions on Information Theory.

[15]  Cheng Tao,et al.  How Much Training Is Needed in One-Bit Massive MIMO Systems at Low SNR? , 2016, 2016 IEEE Global Communications Conference (GLOBECOM).

[16]  Ralf R. Müller,et al.  On an Achievable Rate of Large Rayleigh Block-Fading MIMO Channels With No CSI , 2011, IEEE Transactions on Information Theory.

[17]  Robert Schober,et al.  Performance limits of massive MIMO systems based on Bayes-optimal inference , 2015, 2015 IEEE International Conference on Communications (ICC).

[18]  Rusdha Muharar.  Optimal Power Allocation and Training Duration for Uplink Multiuser Massive MIMO Systems With MMSE Receivers , 2020, IEEE Access.

[19]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[20]  S. Kak.  Information, physics, and computation , 1996 .

[21]  A. Cavagna,et al.  Spin-glass theory for pedestrians , 2005, cond-mat/0505032.

[22]  Raymond W. Yeung,et al.  Information Theory and Network Coding , 2008 .

[23]  Theodoros A. Tsiftsis,et al.  On the Joint Impact of Hardware Impairments and Imperfect CSI on Successive Decoding , 2016, IEEE Transactions on Vehicular Technology.

[24]  Shi Jin,et al.  Bayes-Optimal Joint Channel-and-Data Estimation for Massive MIMO With Low-Precision ADCs , 2015, IEEE Transactions on Signal Processing.

[25]  Cheng Tao,et al.  Channel Estimation and Performance Analysis of One-Bit Massive MIMO Systems , 2016, IEEE Transactions on Signal Processing.

[26]  Andrea J. Goldsmith,et al.  Generalizing Capacity: New Definitions and Capacity Theorems for Composite Channels , 2010, IEEE Transactions on Information Theory.