Saddle Point Approximation of Mutual Information for Finite-Alphabet Inputs over Doubly Correlated MIMO Rayleigh Fading Channels

Round 1

Reviewer 1 Report

The paper derives saddle point approximations for mutual information for finite constellation inputs through a doubly correlated MIMO Rayleigh fading channels. In general, I think the paper can be improved with more careful editing.

1) line 48: "are applying" should be "are applied"

2) The notation is somewhat nontraditional, using \hat for every variable. Typically, the \hat is reserved for estimates.

3) line 73: I'm confused by the inclusion of reference [17] here. The model in that work is convolutive for multipath fading, which is different from the model here. Perhaps the authors meant another work?

4) line 80: "AMGN" should be "AWGN"

5) line 109: p_m(w_0) is undefined here.

6) line 111: "The proof of Theorem 1 sees Appendix A" should be "The proof of Theorem 1 is shown in Appendix A" (Similarly, for line 116 and line 135.)
line 119: "the exactly accurate express of" should be "the exact expresion of"

7) As mentioned in lines 121-123, I(x;y|H) is approximated using BPSK. Will this hold for 16-QAM then?

8) line 128: "Consequently, (15) remains unsuitable for theoretical applications." Equation (15) has yet to be mentioned yet.

9) line 249: "Because log_2 (x ) is convex function" - The logarithm is a concave function. The inequality in (c-2) is correct because the expectation/function order is the reverse of what it is for convex functions, g(E(h))<=E(g(h)).

10) The second lines of equations (14) and (15) should be indented to improve readability. The same for equations (a-6), (a-9), (b-3), (c-1), (c-5), (c-7), (c-10). For many of these, it makes sense to align the "=" or "\le" or "\ge" symbol. For long equations, such as (c-1), the next line should be indented more.

11) Figures 1 and 2 require more discussion and clarification. For example, state more explictly what "2*2" and "[BPSK,BPSK]" mean. Also, describe the trends in the figures as well. This includes Figures 3 and 4. In Figure 3, the estimates are incorrectly described as "saddle point approximation of upper and lower bounds of \alpha".

12) The authors should consider expanding Table 1, perhaps including the total time (time complexity) for the calculations on their particular system.

 

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

This is an interesting and insightful work but lacks more contents to make it more appealing to potential readers. Authors may need to conduct more comprehensive reading of the state-of-the-art works in 5G and beyond research progress otherwise the work might not look trendy or lack proper background foundation to support it as a timely work. Some following literature works are suggested for authors to consider. 

[1] A. Yadav, M. Juntti and J. Lilleberg, "Linear Precoder Design for Doubly Correlated Partially Coherent Fading MIMO Channels," in IEEE Transactions on Wireless Communications, vol. 13, no. 7, pp. 3621-3635, July 2014, doi: 10.1109/TWC.2014.2317490.

[2] Y. Zhang, Y. Huo, D. Wang, X. Dong and X. You, "Channel Estimation and Hybrid Precoding for Distributed Phased Arrays Based MIMO Wireless Communications," in IEEE Transactions on Vehicular Technology, vol. 69, no. 11, pp. 12921-12937, Nov. 2020, doi: 10.1109/TVT.2020.3015815.

[3] Shi Jin and Xiqi Gao, "Statistical antenna selection for MIMO systems in double-sided correlated rayleigh fading channels," IEEE Wireless Communications and Networking Conference, 2006. WCNC 2006., 2006, pp. 729-733, doi: 10.1109/WCNC.2006.1683558.

Author Response

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Reviewer 3 Report

The interest of this work is a little bit limited since it only computes numerically the mutual information of a correlated MIMO channel (assuming finite alphabet). The main reviewer’s concerns include,

 

• The SoA and mainly the contribution part should be improved. It is not clear what is the main novelty of this work regarding the SoA.

 

• Was not already the mutual information for correlated MIMO channels studied?

 

• It is not clear why saddle point method is considered instead other ones? What is the motivation? This should be discussed in the paper.

 

• The formatting is not appropriated since it seem that some math symbols are scanned. Please separate the notation followed in the paper and system model.

 

• It is strange that the lower bound of saddle point method perfect match the simulation.

Author Response

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Reviewer 4 Report

In the paper a theoretical study of numerical calculation of mutual information for finite-alphabet based transmissions over doubly correlated MIMO fading channels was presented. The main objective was to examine the appropriateness of saddle point method. The proposed solution gives considerable accuracy in estimating the average mutual information, with reduced complexity, that may facilitate practical application of mutual information.

The presented simulations for different scenarios prove efficiency of the proposed method.

The paper provides suitable introduction, convincing description of the proposed method, and discussion on the results followed by the conclusions.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

The authors have satisfactory addresses most the reviewer concerns and therefore the reviewer has no further comments.