An Approach to Maximize the Admitted Device-to-Device Pairs in MU-MIMO Cellular Networks

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper proposed the user-pairing method to enhance the sum rate. This is a very attractive research topic and important for future mobile networks. This paper needs to answer some concerns as follows:

1) The authors need to evaluate the proposed algorithm. For example, the proposed searching algorithm can be convergence or not. 

Comments on the Quality of English Language

N/A

Author Response

Q1: The authors need to evaluate the proposed algorithm. For example, the proposed searching algorithm can be convergence or not. 

A1: The proposed algorithm is evaluated by adjusting the setting of parameters and comparing the performance with other algorithms under the same conditions, as detailed in the simulation analysis in Section V. The searching algorithm proposed in this paper makes the results more realistic by increasing the simulation times of different scenarios and the random distribution of cellular users and D2D users, and requirements to meet the constraints, Therefore, we think the proposed algorithm is convergence.

Reviewer 2 Report

Comments and Suggestions for Authors

In this paper, the authors proposed join power allocation and channel gain selection algorithm for admitting D2D in MU-MIMO cellular networks, however I have the following comments on the current paper:

1-      In the system model, why D2D users are located far from the CU users?

2-      In equation (1), the large-scale fading is oversimplified by only considering the distance effect without other issues like the operating frequency. Also, the reference of this equation should be given.

3-      In Table 1, why the index column is needed?

4-      In Fig. 5, why the sum rate of the proposed approach is decreasing when the number of admitted D2D pairs is set to 2?

5-      There are many typos in the paper, to name a few:

·         Some mathematical symbols are written italic and non-italic in the text.

·         P.4, l. 136, the word “minimizing” is written wrongly

·         P.5, l 166, I_C-D is repeated.

·         P.5, l. 186, The (7)-----> (7)

·         P.6, l. 200, The (8)-----> (8)

Comments on the Quality of English Language

The paper needs extensive revisions regarding language including typos and grammatical errors

Author Response

We have revised the whole paper regarding language including typos and grammatical errors.

Q1:In the system model, why D2D users are located far from the CU users?

A1: As mentioned in the article, D2D user share the same spectrum with CU will introduce the in-frequency interference to CU at the uplink receiver and the D2D receiver also is interfered by the signal transmitted from CUs. The interference value is dependent on the large-scale fading which is the function of the distance. In the system model, we assume the D2D users are located far from CUs, which can reduce the interference between CU and D2D users. In this assumed scenario, the frequency sharing is more reasonable in order to improve the system capacity and spectral efficiency.

Q2:  In equation (1), the large-scale fading is oversimplified by only considering the distance effect without other issues like the operating frequency. Also, the reference of this equation should be given.

A2: In generally, the large-scale fading is the function of distance and frequency. However, for a given frequency in the same system model, the large-scale fading can be thought only dependent on the distance, the effect by frequency can be deleted in computation. Many researches have the similar assumption about the large-scale fading, we give the reference of equation(1) in the revised manuscript in Page 3. Line 122 .

Q3:  In Table 1, why the index column is needed?

A3: We delete the index column of Table 1 in the revised manuscript, please check it, Thanks!

Q4:  In Fig. 5, why the sum rate of the proposed approach is decreasing when the number of admitted D2D pairs is set to 2?

A4: The detailed analysis is given in Page 12 and Page 13, from line 376 to 409 in the revised manuscript. Please check it, Thanks!

Q5: There are many typos in the paper, to name a few:

• Some mathematical symbols are written italic and non-italic in the text.
• P.4, l. 136, the word “minimizing” is written wrongly
• P.5, l 166, I_C-Dis repeated.
• P.5, l. 186, The (7)-----> (7)
• P.6, l. 200, The (8)-----> (8)

A5: We have revised above mentioned errors in the revised manuscript as shown in corresponding parts as following.

•  The italic and non-italic mathematical symbols in the article are checked and proofread in the revised manuscript.
• P.4, l. 136, the word “minimizing” is corrected
• P.5, l. 172, the second I_C-D is changed into I_D-C .
• P.5, l. 187, The (7)-----> (7)
• P.6, l. 209, The (8)-----> (8)

 

Reviewer 3 Report

Comments and Suggestions for Authors

In this paper, authors present an interesting study related to multi-user MIMO (MU-MIMO) cellular system in which it's users share resources with multiple device-to-device (D2D) pairs. The joint power allocation and channel gain selection algorithm (JPACG) is proposed in order to maximize the number of admitted D2D pairs.

The paper is well organized and written. However, the following suggestions for further improvement of the paper can be given:

- The authors give relatively superficial overview of the existing solutions in the area, of  which some have the similar aims and rationale as the proposed method. More detailed overview should be given with the higlighted approaches, limitations and strengths of the reviewed existing solutions, and with the following discussion related to the differencies, similarities and improvements that proposed method offers in terms of novel approach or introduced modifications/improvements in relation to the previous ones.

- The choice of referent solutions used for the performance comparison must be elaborated which should provide support that adequate referent state-of-the-art methods are observed. Why these particular solutions are choosen? Also, the sequential admitted algorithm (SAA) is first time mentioned in section 5. Simulation Analysis without referencing and formal description.

- The computational complexity seems to be very important feature of the observed methods. This aspect is not properly covered in the manuscript which should be corrected.

 

Comments on the Quality of English Language

The Quality of English Language is acceptable, but some language errors as well as relatively numerous typo errors are detected that should be corrected.

Author Response

Q1: The authors give relatively superficial overview of the existing solutions in the area, of which some have the similar aims and rationale as the proposed method. More detailed overview should be given with the higlighted approaches, limitations and strengths of the reviewed existing solutions, and with the following discussion related to the differencies, similarities and improvements that proposed method offers in terms of novel approach or introduced modifications/improvements in relation to the previous ones.

A1: The modifications to this question can be found in the revised manuscript in Page 9 from line 298 to 329. Please check it, thanks!

Q2: The choice of referent solutions used for the performance comparison must be elaborated which should provide support that adequate referent state-of-the-art methods are observed. Why these particular solutions are choosen? Also, the sequential admitted algorithm (SAA) is first time mentioned in section 5. Simulation Analysis without referencing and formal description.

A2: The chosen referred algorithms are the most related algorithm with our proposed algorithm in resource sharing aspects for cellular system underlaying D2D users. In the revised manuscript, we strengthen the formal description about the simulation analysis to compare the proposed algorithm with other three algorithms including the SAA, ALLSCI and JPDS, and also the exhaustive searching algorithm in section V. Please see the Page.9 from line 298 to line 329 in the revised manuscript. We also mentioned the sequential admitted algorithm (SAA) in the Page 2,line 57 and give the description of this algorithm in the revised manuscript.

Q3: The computational complexity seems to be very important feature of the observed methods. This aspect is not properly covered in the manuscript which should be corrected.

A3: The original text compared the computational complexity of the JPACG algorithm with the exhaustive searching algorithm, and now supplements the complexity analysis of all algorithms, The computational complexity is analyzed in Page.14 from line 435 to line 447, please check it. Thanks!

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors need to improve some points as follows:

1) The authors need to evaluate the proposed algorithm. For example, the proposed searching algorithm can be convergence or not. 

2) The authors need to provide more results in Fig. 5. As can be seen when the number of admitted D2D pairs seems to be a convex pattern (Rsum-JPACG(Proposed)). However, some other methods do not have a convex pattern when the number of high D2D paired. Thus, the authors need to check this point.

Comments on the Quality of English Language

N/A

Author Response

The authors need to improve some points as follows:

1) The authors need to evaluate the proposed algorithm. For example, the proposed searching algorithm can be convergence or not. 

2) The authors need to provide more results in Fig. 5. As can be seen when the number of admitted D2D pairs seems to be a convex pattern (Rsum-JPACG(Proposed)). However, some other methods do not have a convex pattern when the number of high D2D paired. Thus, the authors need to check this point.

 

Answer 1)

Thanks for your comments and our answer is shown in the following:

The objective of this paper is to maximize the number of shared D2D user pairs when the cellular users are the main communication users, and at the same time, each of the uplink MU-MIMO cellular users and shared D2D user pairs must meet the minimum QoS constraints. Because the smaller the co-frequency interference between users, the users working on the same spectrum resources will have a higher communication quality tolerance, allowing more users to communicate with the same frequency at the same time. Therefore, the optimization goal can be equivalent to the minimum total interference of the system. This optimization problem is non-convex because the transmission power of CUs and D2D user pair are intertwined. And then it is transformed into two sub-problems to solve. First is the power allocation for CUs to maximize the sum-rate of CUs when the D2D user pairs are not admitted with QoS requirements, which is still a non-convex problem, the first-order Taylor function is used to transform the non-convex to convex to achieve the power allocation. After determining the power allocation, it can be observed that the interference of D2D user pairs to CUs is mainly affected by the product of the transmission power and the gain of the jamming channel. Therefore, we consider transforming the problem of minimizing the admitted D2D pairs interference with CUs into the choice of admitted order of D2D pairs to minimize the product sum. Since the product sum is a linear function of the transmitted power, the condition for convex optimization is satisfied. Then, the transmission power of D2D user pairs is rationally allocated by convex optimization to reduce the same frequency interference, so as to maximize the number of shared D2D users in the whole system. A pair of D2D users with the least total interference is selected and shared in the system for spectrum resource sharing until all D2D user pairs in the system complete resource sharing or there are no remaining D2D user pairs satisfying all constraints.

According to the process of problem formulation and solution method, the optimization problems of power allocation are transformed to convex problem to solve and the D2D user selection method satisfies the constraints of QoS for cellular users and D2D user pairs. Thus the proposed algorithm should be convergence when the results of power allocation and user selection exist and the simulation results also verify this.

Answer 2)

Thanks for your comments and our answer is shown in the following:

Fig. 5 simulates the trend of the total achievable rate of the system as the number of D2D users increases. The proposed algorithm can be seen as a convex pattern, because as the number of D2D user pairs sharing the same spectrum resource increases, the overall achievable sum rate also continues to increase. However, as the number of D2D user pairs increases to a certain extent, the same frequency interference between different users will affect the sum rate, but still meet the constraint conditions. Therefore, the number of D2D user pairs continues to increase, but the sum rate has already decreased, resulting in a decrease to achieve convex mode. However, due to the limitations of the admit principle, the number of D2D pairs of other methods has not yet reached the level of interference, and they cannot be accessed to the system again because they cannot meet the constraint conditions. For example, the exhaustive method aims to maximize the system sum rate to achieve the access of D2D user pairs. Therefore, the sum rate of the exhaustive method is the highest among all algorithms. When the sum rate decreases, new D2D user pairs are no longer admitted, resulting in a convex pattern that keeps rising. The SAA and ALLCSI algorithms allocate D2D power with the minimum transmission power satisfying the constraint conditions, so the rates of all D2D pairs just meet the minimum rate constraint. Although JPDS algorithm does not allocate at the minimum transmission power, it takes little account of the interference of CUs and pays more. Therefore, it is not that other algorithms do not have convex patterns, but rather that other algorithms are unable to admit more D2D pairs before displaying the trend of convex patterns due to not meeting the constraint conditions. And the variable in Fig. 5 is the number of admitted D2D pairs, so the graph lines of other algorithms cannot be displayed.

Reviewer 2 Report

Comments and Suggestions for Authors

The authors did the required modifications 

Comments on the Quality of English Language

The English writing is adequate

Author Response

Thanks reviewer for the comment!  No further modification comments to our first-round revised manuscript.

Reviewer 3 Report

Comments and Suggestions for Authors

In this paper, authors present an interesting study related to multi-user MIMO (MU-MIMO) cellular system in which it's users share resources with multiple device-to-device (D2D) pairs. The joint power allocation and channel gain selection algorithm (JPACG) is proposed in order to maximize the number of admitted D2D pairs.

The paper is well organized and written. In the revised paper authors managed to resolve the most of the issues reported by the reviewers or have adequatelly answered the raised questions.

In lines 290-322 at page 9, authors elaborated choice of referent methods and gave more in depth comparison of approaches and working principles of the existing and here proposed method thus highlighting the main rationale and idea for the proposed soultion. This greatly improves clarity for the reader as well as the presentation quality. Exactly this was refered in the first comment  (Q1) on the previous version of the paper, i.e. that the state-of-the-art overview is a bit superficial and thus do not properly and clearly higlight approaches, limitations and strengths of existing solutions, and also lacks discussion related to the differencies, similarities and improvements that proposed method offer. This overview in introduction section can be further improved in similar manner as done in lines 290-322 at page 9.

Comments on the Quality of English Language

The Quality of English Language is acceptable, but authors should perform the final  check and correct remaining typo errors and further refine some formulations.

Author Response

Comments and Suggestions for Authors

In this paper, authors present an interesting study related to multi-user MIMO (MU-MIMO) cellular system in which it's users share resources with multiple device-to-device (D2D) pairs. The joint power allocation and channel gain selection algorithm (JPACG) is proposed in order to maximize the number of admitted D2D pairs.

The paper is well organized and written. In the revised paper authors managed to resolve the most of the issues reported by the reviewers or have adequatelly answered the raised questions.

In lines 290-322 at page 9, authors elaborated choice of referent methods and gave more in depth comparison of approaches and working principles of the existing and here proposed method thus highlighting the main rationale and idea for the proposed soultion. This greatly improves clarity for the reader as well as the presentation quality. Exactly this was refered in the first comment  (Q1) on the previous version of the paper, i.e. that the state-of-the-art overview is a bit superficial and thus do not properly and clearly higlight approaches, limitations and strengths of existing solutions, and also lacks discussion related to the differencies, similarities and improvements that proposed method offer. This overview in introduction section can be further improved in similar manner as done in lines 290-322 at page 9.

Answer: Thanks for above comments! According to the comments, we modify the content in the introduction section to give the detailed descript and discussion of related works shown in the page 2 and page 3 for line45- 95, and line 103-109 in the second-round revised manuscript with yellow mark. Please check it, Thanks!

Comments on the Quality of English Language

The Quality of English Language is acceptable, but authors should perform the final check and correct remaining typo errors and further refine some formulations.

Answer: Thanks for above comments! According to the comments, we further check the whole manuscript for typo errors and modified some expression, especially for Algorithm1 in page 9.

Round 3

Reviewer 1 Report

Comments and Suggestions for Authors

The authors fully answered the last round's comments. 

Comments on the Quality of English Language

N/A