On the Performance of LDPC-Coded MIMO Schemes for Underwater Communications Using 5G-like Processing

Round 1

Reviewer 1 Report

This paper includes simulation results of MIMI underwater acoustic communications that are potentially useful to future researchers. The following points could be considered when revising the paper.

1. The bit error rates are around 5% to 10% even after employing LDPC codes. The paper should clearly discuss such high BERs and state if these are acceptable for underwater applications. The paper states that the BER obtained with 0.7 correlation is too high and are almost unacceptable. This implies that other results are acceptable, although the resulting BERs are nearly so high. With appropriate citation of references, acceptable maximum value of BER (for a realistic range of Eb/No) should be stated.
2. The paper reviews relevant past work by dozens of researchers, but the results are not compared with any other. At least the results with ideal channel estimation (Figures 3, 4 and 5) should be compared with other published results. This is especially important because of the high BERs (earlier point) reported here. Such comparisons would bring about a degree of validation for the simulation reports reported in this paper. It could be argued that the thrust of the paper is to compare different scenarios with the baseline (ideal channel estimation) case(s), and so absolute results are not important. Notwithstanding this argument, the results are likely to appear sound when comparisons are included.
3. Details of the background AWGN applied should be provided.
4. Details of how Rayleigh fading is implemented should be provided.
5. The paper mentions (in two places) that the impulse noise introduced by sea life activity could be as high as 40 dB above the background AWGN. However, the variance of the impulse noise is selected as 10 times that of the AWGN. Even so, the resulting BER deterioration is so high that the BER, after using LDPC codes, is still around 5% to 10%. This point should be discussed in detail.
6. A marked-up copy of the paper is included. This contains many corrections (grammatical or typographical), suggestions and queries.

Comments for author File: Comments.pdf

Author Response

Dear Sir,

This is a revised version of the Manuscript applsci-1654040 entitled ”On the Performance of LDPC-Coded MIMO Schemes for Underwater Communications using 5G-Like Processing”, by M. Marques da Silva, Rui Dinis, José Aleixo, and Luís M. L. Oliveira.

We would like to thank the reviewer for the helpful comments. We believe we addressed all issues raised by the reviewer in the revised version of the manuscript. We include a detailed answer to the reviewer’s comments.

 

Kindest regards,

Mario Marques da Silva

José Aleixo

Luís M. L. Oliveira

Rui Dinis

 

 

 

Referees' Comments to Author with Responses

 

Reviewer Comments to the Author

Comment: The bit error rates are around 5% to 10% even after employing LDPC codes. The paper should clearly discuss such high BERs and state if these are acceptable for underwater applications. The paper states that the BER obtained with 0.7 correlation is too high and are almost unacceptable. This implies that other results are acceptable, although the resulting BERs are nearly so high. With appropriate citation of references, acceptable maximum value of BER (for a realistic range of Eb/No) should be stated.

Authors’ Reply: The graphics were remade to make the BER limits more visible. It is known that for voice the BER required is of the order of 10^(-3), while 10^(-6) is typically required for data[1] [ref_1]. As can be seen from figure 3 (baseline 1), such performance is obtained, even without LDPC codes. Computing the graphics below 10^(-3) is extremely time demanding using the Monte Carlo simulation. This is the reason why the other graphics limits the ordinate results between 0 and 10^(-3). The statement that refers that 0.7 correlation is unacceptable was removed from the article.

Comment: The paper reviews relevant past work by dozens of researchers, but the results are not compared with any other. At least the results with ideal channel estimation (Figures 3, 4 and 5) should be compared with other published results. This is especially important because of the high BERs (earlier point) reported here. Such comparisons would bring about a degree of validation for the simulation reports reported in this paper. It could be argued that the thrust of the paper is to compare different scenarios with the baseline (ideal channel estimation) case(s), and so absolute results are not important. Notwithstanding this argument, the results are likely to appear sound when comparisons are included.

Authors’ Reply: The results without impulsive noise were obtained from [15]. The inclusion of impulsive noise is a novelty of this manuscript. We could not find references with such scenario, possible to be compared with.

Comment: Details of the background AWGN applied should be provided.

Authors’ Reply: The standard variation of the Additive White Gaussian Noise (AWGN) noise is computed for each level of Eb/N0. Then, the noise to be added to the signal of each receiving antenna and each symbol of the block of symbols is generated randomly using Gaussian function, for both real component and imaginary component using the function: Nk=(randn(R,N)+1j*randn(R,N))*sigma(nEN), where Nk is the noise, R is the number of receiving antennas, N is the number of symbols of the block of symbols, and sigma is the standard deviation of noise.

 

Comment: Details of how Rayleigh fading is implemented should be provided.

Authors’ Reply: A severe Rayleigh fading channel was considered with 20 uncorrelated equal power paths. This corresponds to a highly demanding channel, which can be viewed as a worst-case scenario for underwater propagation. The high number of multipath and having all of them the same average power makes this channel very destructive, in terms of the creation of intersymbol interference, which can be viewed as the most disruptive cause that limits underwater acoustic communications. A different channel is generated, using Matlab simulation, for each pair transmitting-receiving antenna. The values “alpha” correspond to the multipath gain, being generated using a Gaussian function (randn), independently for the inphase and quadrature components, as alpha=alpha_med.*(randn(NRay,1)+1j*randn(NRay,1))/sqrt(2). It is worth noting the alpha_med and sqrt(2) components aim to assure that the channel has unitary gain, such that the level of noise added is correct. Similarly, a frequency baseline is generated as f=[-N/2:N/2-1]'/Ts, where N corresponds to the number of symbols in the block of symbols, and Ts to the symbol period. Then, the frequency domain channel function is generated of each multipath as: Hk(:,r,t)=Hk(:,r,t)+alpha(nRay)*exp(-1j*2*pi*f*tau(nRay)), where r corresponds to each receiving antenna, t represents each transmitting antenna, nRay stands for each channel multipath.

Comment: The paper mentions (in two places) that the impulse noise introduced by sea life activity could be as high as 40 dB above the background AWGN. However, the variance of the impulse noise is selected as 10 times that of the AWGN. Even so, the resulting BER deterioration is so high that the BER, after using LDPC codes, is still around 5% to 10%. This point should be discussed in detail.

Authors’ Reply: The reference about the impulsive noise that could be as high as 40 dB above the background AWGN noise was removed. In fact, for the marine environment, 10 dB is a more acceptable value. Nevertheless, an analysis of the performance with different levels of impulsive noise can be viewed as a future work.

Comment: A marked-up copy of the paper is included. This contains many corrections (grammatical or typographical), suggestions and queries.

Authors’ Reply: We thank the reviewer for this relevant contribution. These suggestions were incorporated in the revised manuscript, as well as several other changes.

 

• [1] [ref_1] Marques da Silva, “Cable and Wireless Networks: Theory & Practice” CRC Press, 1st edition, ISBN: 9781498746816, FL, USA, January 2016 (https://www.crcpress.com/Cable-and-Wireless-Networks-Theory-and-Practice/Silva/9781498746816)

 

Reviewer 2 Report

The Authors present the work titles “On the Performance of LDPC-Coded MIMO Schemes for Underwater Communications using 5G-Like Processing”. The article discusses the use of LDPC coding and MIMO architecture for under water acoustic communications.

The paper, that follow a series from the same authors on this topic, lacks of several details required for an accurate understanding and to enable the reader to reproduce the same data.

 

• The paper lacks most of the information regarding the simulation parameters (please add in the paper all the meaningful parameters).
  1. Multipath statistical characteristics, beside number of paths and power what multipath model was chosen? What’s the multipath coherence bandwidth.
  2. What are the characteristics of the impulse noise (beside average power)?
  3. It is not clear from the article but, from the Markov chain model in figure 2, it looks like the noise is modeled with a discrete time Markov chain. If that is the case, what time interval is considered?
  4. How the transition rates for the Markov chain were chosen.

 

• Looking at the simulation results, the bit error rates are in the order of 10^-1. Such error rate would make any channel practically useless.
  1. How realistic are the simulation parameters?
  2. How much of the error rate is related to inter-symbol-interference and how much is related to inter-channel-interference? Potentially, plotting separately the different contributions would be useful for a better understanding.

 

• Given the formalization of equation 2, the H matrix should be RxT, rather than TxR as stated.

 

• The different BER plots have different axis scale, I would suggest, for ease of comparison, to use the same scale for all the plots.

Author Response

Dear Sir,

This is a revised version of the Manuscript applsci-1654040 entitled ”On the Performance of LDPC-Coded MIMO Schemes for Underwater Communications using 5G-Like Processing”, by M. Marques da Silva, Rui Dinis, José Aleixo, and Luís M. L. Oliveira.

We would like to thank the reviewer for the helpful comments. We believe we addressed all issues raised by the reviewer in the revised version of the manuscript. We include a detailed answer to the reviewer’s comments.

 

Kindest regards,

Mario Marques da Silva

José Aleixo

Luís M. L. Oliveira

Rui Dinis

 

Referees' Comments to Author with Responses

 

Reviewer Comments to the Author

 The paper lacks most of the information regarding the simulation parameters (please add in the paper all the meaningful parameters).

1. Multipath statistical characteristics, beside number of paths and power what multipath model was chosen?

Authors’ Reply: More information was added to the manuscript to clarify the issues raised by the reviewer. A severe Rayleigh fading channel was considered with 20 uncorrelated equal power paths. This corresponds to a highly demanding channel, which can be viewed as a worst-case scenario for underwater propagation. The high number of multipath and having all of them the same average power makes this channel very destructive, in terms of the creation of intersymbol interference, which can be viewed as the most disruptive cause that limits underwater acoustic communications. A different channel is generated, using Matlab simulation, for each pair transmitting-receiving antenna. The values “alpha” correspond to the multipath gain, being generated using a Gaussian function (randn), independently for the inphase and quadrature components, as alpha=alpha_med.*(randn(NRay,1)+1j*randn(NRay,1))/sqrt(2). It is worth noting the alpha_med and sqrt(2) components aim to assure that the channel has unitary gain, such that the level of noise added is correct. Similarly, a frequency baseline is generated as f=[-N/2:N/2-1]'/Ts, where N corresponds to the number of symbols in the block of symbols, and Ts to the symbol period. Then, the frequency domain channel function is generated of each multipath as: Hk(:,r,t)=Hk(:,r,t)+alpha(nRay)*exp(-1j*2*pi*f*tau(nRay)), where r corresponds to each receiving antenna, t represents each transmitting antenna, nRay stands for each channel multipath.

1. What are the characteristics of the impulse noise (beside average power)? It is not clear from the article but, from the Markov chain model in figure 2, it looks like the noise is modeled with a discrete time Markov chain. If that is the case, what time interval is considered?

Authors’ Reply: The impulsive noise is modelled with a discrete time Markov chain (Markov chain, Binary State Model). The time interval corresponds to the symbol period. Each symbol is randomly subject to a different impulsive noise. In other words, impulsive noise may vary from symbol to symbol. Such impulsive noise characterization was added to the manuscript.

1. How the transition rates for the Markov chain were chosen.

Authors’ Reply: We have defined the following probabilities: Prob(Good->Bad)=0.1; Prob(Good->Good)=0.9; Prob(Bad->Bad)=0.2; Prob(Bad->Good)=0.8. Note that Prob(Good->Bad) stands for the probability of transition from Good to Bad state. Naturally that other parameters could have been chosen. These parameters were chosen because it was considered that they could better translate a real scenario. Nevertheless, a study with different parameters will be studied in future work. Such impulsive noise characterization was added to the manuscript.

Looking at the simulation results, the bit error rates are in the order of 10^-1. Such error rate would make any channel practically useless.

1. How realistic are the simulation parameters?

Authors’ Reply: The graphics were remade to make the BER limits more visible. It is known that for voice the BER required is of the order of 10^(-3), while 10^(-6) is typically required for data[1] [ref_1]. As can be seen from figure 3 (baseline 1), such performance is obtained, even without LDPC codes. Computing the graphics below 10^(-3) is extremely time demanding using the Monte Carlo simulation. This is the reason why the other graphics limits the ordinate results between 0 and 10^(-3).

1. How much of the error rate is related to inter-symbol-interference and how much is related to inter-channel-interference? Potentially, plotting separately the different contributions would be useful for a better understanding.

Authors’ Reply: We assume that the channels have guard bands such that adjacent channel interference does not occur, and that reuse factor 7 is utilized to assure the absence of co-channel interference. Therefore, the results focus on intersymbol interference.

1.  Given the formalization of equation 2, the H matrix should be RxT, rather than TxR as stated.

 Authors’ Reply: We thank the reviewer for having detected this typo. The revised version of the manuscript has corrected this typo.

1. The different BER plots have different axis scale, I would suggest, for ease of comparison, to use the same scale for all the plots.

Authors’ Reply: We thank the reviewer for this important comment. The graphics were remade to make the BER limits more visible.

• [1] [ref_1] Marques da Silva, “Cable and Wireless Networks: Theory & Practice” CRC Press, 1st edition, ISBN: 9781498746816, FL, USA, January 2016 (https://www.crcpress.com/Cable-and-Wireless-Networks-Theory-and-Practice/Silva/9781498746816)

 

Reviewer 3 Report

In this work, the authors studied the performance of UWA communications by using the MIMO communication scheme. Some simulations have been performed to verify its performance. There are some issues should be solved before this work can be accepted.

1. Some references are cited incorrectly, for example,  on page 2, paragraph 5, Ref. 13 should be Ref. 14.
2. The authors should provide more discussions on the simulation time for different MIMO scenarios in Figs. 3-9.
3. The manuscript needs a careful editing since there are some grammatical errors.

Author Response

Dear Sir,

This is a revised version of the Manuscript applsci-1654040 entitled ”On the Performance of LDPC-Coded MIMO Schemes for Underwater Communications using 5G-Like Processing”, by M. Marques da Silva, Rui Dinis, José Aleixo, and Luís M. L. Oliveira.

We would like to thank the reviewer for the helpful comments. We believe we addressed all issues raised by the reviewer in the revised version of the manuscript. We include a detailed answer to the reviewer’s comments.

 Kindest regards,

Mario Marques da Silva

José Aleixo

Luís M. L. Oliveira

Rui Dinis

Reviewer Comments to the Author

Comment: In this work, the authors studied the performance of UWA communications by using the MIMO communication scheme. Some simulations have been performed to verify its performance. There are some issues should be solved before this work can be accepted.

1. Some references are cited incorrectly, for example,  on page 2, paragraph 5, Ref. 13 should be Ref. 14.
2. The authors should provide more discussions on the simulation time for different MIMO scenarios in Figs. 3-9.
3. The manuscript needs a careful editing since there are some grammatical errors.

Authors’ Reply: As recommended, the referred items were taken into account in the revised manuscript.

Round 2

Reviewer 1 Report

A couple of major concerns remain unaddressed in the modified version.

1. The main thrust of the paper is to investigate the performance under impulsive noise. None of the results of simulations with impulse noise, with or without employment of LDPC codes, -- shown in Figures 4 to 8 -- show an acceptable BER performance for the entire Eb/N0 range. BER obtained for all these cases is poorer than 10^-3. As stated in the authors' rebuttal, only the baseline case in Figure 3, which does NOT include impulsive noise, shows acceptable BER values. Simulation trials producing BER values of less than 10P^-3 are certainly possible (as reported in numerous papers) albeit computationally intensive. That said, the main issue is that even for Eb/N0 of over 15, the BER obtained is unacceptably high when impulsive noise is present -- even when LDPC codes are used.
2. Removal of statements (which had been appropriately cited) that the impulsive noise could be 40 dB higher than the background AWGN would not eliminate the concern that the results (which are not stellar, as stated in the earlier point) are shown for conditions that are far milder than that would be expected.
3. The power levels (i.e. variance and other values used) Guassian and fading noise should be provided -- not just the method to generate them.
4. A few papers do report techniques to mitigate impulsive noise. The authors are encouraged do cite some of these papers and also provide comparison of results.

Impulsive noise and carrier frequency offset cancellation for underwater acoustic OFDM communications, Y. Zhou et al.,  WUWNet'21: The 15th International Conference on Underwater Networks & SystemsNovember 2021 Article No.: 19Pages 1–5https://doi.org/10.1145/3491315.3491325 Impulsive noise mitigation in underwater acoustic communication systems: experimental studies, R. Barazideh et al., arXiv: 1901.00464v1, 2 Jan 2019

Author Response

Dear Sir,

 

This is a revised version of the Manuscript applsci-1654040 entitled ”On the Performance of LDPC-Coded MIMO Schemes for Underwater Communications using 5G-Like Processing”, by M. Marques da Silva, Rui Dinis, José Aleixo, and Luís M. L. Oliveira.

We would like to thank the reviewer for the helpful comments. We believe we addressed all issues raised by the reviewer in the revised version of the manuscript. We include a detailed answer to the reviewer’s comments.

 

Kindest regards,

Mario Marques da Silva

José Aleixo

Luís M. L. Oliveira

Rui Dinis

 

Referees' Comments to Author with Responses

 

Reviewer Comments to the Author

Comment: The main thrust of the paper is to investigate the performance under impulsive noise. None of the results of simulations with impulse noise, with or without employment of LDPC codes, -- shown in Figures 4 to 8 -- show an acceptable BER performance for the entire Eb/N0 range. BER obtained for all these cases is poorer than 10^-3. As stated in the authors' rebuttal, only the baseline case in Figure 3, which does NOT include impulsive noise, shows acceptable BER values. Simulation trials producing BER values of less than 10P^-3 are certainly possible (as reported in numerous papers) albeit computationally intensive. That said, the main issue is that even for Eb/N0 of over 15, the BER obtained is unacceptably high when impulsive noise is present -- even when LDPC codes are used.

Authors’ Reply: The graphics were remade, and new simulations were done with performances as low as 10^-6. The new plots show that such performance can be achieved, albeit at the cost of a higher Eb/N0. Note that the reference (Impulsive noise and carrier frequency offset cancellation for underwater acoustic OFDM communications, Y. Zhou et al.,  WUWNet'21: The 15th International Conference on Underwater Networks & Systems November 2021 Article No.: 19Pages 1–5https://doi.org/10.1145/3491315.3491325) considers SNR values up to 30 dB.

 

Comment: Removal of statements (which had been appropriately cited) that the impulsive noise could be 40 dB higher than the background AWGN would not eliminate the concern that the results (which are not stellar, as stated in the earlier point) are shown for conditions that are far milder than that would be expected.

Authors’ Reply:  Simulations have been remade for impulsive noise of 20 dB, instead of 10 dB. It is agreed that, in some extreme cases of radiocommunications, impulsive noise can be as high as 40 dB above the background AWGN. Nevertheless, it is understood that 20 dB is already an extreme level in UWA scenarios. Moreover, simulations carried out (not plotted) lead to very pessimistic results for 40 dB, although all signal processing that is being employed, such as block transmission technique (SC-FDE), MIMO system, error correction code, etc.

 

Comment: The power levels (i.e. variance and other values used) Gaussian and fading noise should be provided -- not just the method to generate them.

Authors’ Reply: The variance of the Gaussian noise corresponds to the power of noise. Therefore, having an Eb/N0 of 10 dB, means that the variance of the AWGN noise is 10 dB above the power of the signal. Since the signal has unitary power, the power of AWGN noise, i.e., its variance is 10 dB below. A severe Rayleigh fading channel was considered with 20 uncorrelated equal power paths. The channel gain was normalized such that it does not introduce any gain or attenuation to the transmitted signal. Therefore, one can state that the variance of the channel is unitary. Such a channel with 20 uncorrelated equal power paths corresponds to a highly demanding channel, which can be viewed as a worst-case scenario for underwater propagation. The high number of multipath and having all of them the same average power makes this channel very destructive, in terms of the creation of intersymbol interference, which can be viewed as the most disruptive cause that limits UWA communications.

 

Comment: A few papers do report techniques to mitigate impulsive noise. The authors are encouraged to cite some of these papers and also provide comparison of results.

Authors’ Reply: These references were added to the article, as recommended. Moreover, the probability of impulsive noise under consideration in this article is higher than that considered in reference [24], making this a more pessimistic scenario. We considered p1,0=0.1 and p0,1=0.8. Moreover, we have defined the following probabilities: Prob(Good->Bad)=0.1; Prob(Good->Good)=0.9; Prob(Bad->Bad)=0.2; Prob(Bad->Good)=0.8, while in [24] a probability of p1,0=0,0098 was assumed (i.e., Prob(Good->Bad). Note that Prob(Good->Bad) stands for the probability of transition from Good to Bad state.

 

Reviewer 2 Report

Although some improvements have been made with respect to the first submission, however important detail (requested during the first revision round) are still missing.

Following are few points:

• Regarding the number of multipath paths, where the number 20 comes from? From what propagation model does it come from?
• What about the Markov chain parameters, are the transition probabilities picked randomly or are associated with a specific model?
• Where the channel correlation values come from?
• For each of the parameters please refer to specific models.
• The Authors mention that the wildlife can generate impulsive noise 40dB above background but, in the simulation, they apply impulsive noise 10 times (10dB) higher that AWGN. This choice looks inconsistent with what stated. How the Authors choose just 10dB?
• It looks like ZF results are missing in many of the plots (if they are overlapped with some other trace, a different maker should be used).

Author Response

Dear Sir,

This is a revised version of the Manuscript applsci-1654040 entitled ”On the Performance of LDPC-Coded MIMO Schemes for Underwater Communications using 5G-Like Processing”, by M. Marques da Silva, Rui Dinis, José Aleixo, and Luís M. L. Oliveira.

We would like to thank the reviewer for the helpful comments. We believe we addressed all issues raised by the reviewer in the revised version of the manuscript. We include a detailed answer to the reviewer’s comments.

 

Kindest regards,

Mario Marques da Silva

José Aleixo

Luís M. L. Oliveira

Rui Dinis

 

Referees' Comments to Author with Responses

 

Comment: Regarding the number of multipath paths, where the number 20 comes from? From what propagation model does it come from?

Authors’ Reply: 20 uncorrelated equal power paths corresponds to an extreme case of Rayleigh fading channel. This corresponds to a highly demanding channel, which can be viewed as a worst-case scenario for underwater propagation. The high number of multipath and having all of them the same average power makes this channel very destructive, in terms of the creation of intersymbol interference, which can be viewed as the most disruptive cause that limits UWA communications. It is worth noting that the channel gain was normalized such that it does not introduce any gain or attenuation to the transmitted signal, and therefore, the level of noise added keeps synchronized.

Comment: What about the Markov chain parameters, are the transition probabilities picked randomly or are associated with a specific model?

Authors’ Reply: The probability of impulsive noise under consideration in this article is higher than that considered in reference [24], making this a more pessimistic scenario. We considered p1,0=0.1 and p0,1=0.8. Moreover, we have defined the following probabilities: Prob(Good->Bad)=0.1; Prob(Good->Good)=0.9; Prob(Bad->Bad)=0.2; Prob(Bad->Good)=0.8, while in [24] a probability of p1,0=0,0098 was assumed (i.e., Prob(Good->Bad). Note that Prob(Good->Bad) stands for the probability of transition from Good to Bad state.

Comment: Where the channel correlation values come from?

Authors’ Reply: The channel correlation is a result of a reduced separation between antenna elements. An uncorrelated channel requires a typical separation of 3 to 5 wavelengths. In UWA communications, where carrier frequencies of the order of 15 kHz are employed, such separation is difficult to achieve. Therefore, studying the performance with different values of channel correlation is important to evaluate the different receivers. Naturally that the channel correlation depends on the carrier frequency and distance, being worth studying the performance as a function of different channel correlation values, rather than of the distance.

 

Comment: The Authors mention that the wildlife can generate impulsive noise 40dB above background but, in the simulation, they apply impulsive noise 10 times (10dB) higher that AWGN. This choice looks inconsistent with what stated. How the Authors choose just 10dB?

Authors’ Reply: Simulations have been remade for impulsive noise of 20 dB, instead of 10 dB. It is agreed that, in some extreme cases of radiocommunications, impulsive noise can be as high as 40 dB above the background AWGN. Nevertheless, it is understood that 20 dB is already an extreme level in UWA scenarios. Moreover, simulations carried out (not plotted) lead to very pessimistic results for 40 dB, although all signal processing that is being employed, such as block transmission technique (SC-FDE), MIMO system, error correction code, etc.

Comment: It looks like ZF results are missing in many of the plots (if they are overlapped with some other trace, a different maker should be used).

Authors’ Reply: The ZF and IB-DFE present the same results (these curves are superimposed, with and without Impulsive Noise). It is worth noting that such superposition of the IB-DFE over the ZF curves occurs in all graphics of the article. All graphics were remade, and different marks were applied to the curves, as recommended.

Round 3

Reviewer 1 Report

The revised paper addresses most of the suggestions and concerns raised by the reviewer. Two relevant and recent papers have now been cited, as suggested, but only in a fleeting manner -- as one of them assumes less stringent noise conditions.

Author Response

Dear Sir,

 This is a revised version of the Manuscript applsci-1654040 entitled ”On the Performance of LDPC-Coded MIMO Schemes for Underwater Communications using 5G-Like Processing”, by M. Marques da Silva, Rui Dinis, José Aleixo, and Luís M. L. Oliveira.

We would like to thank the reviewer for the helpful comments. We believe we addressed all issues raised by the reviewer in the revised version of the manuscript. We include a detailed answer to the reviewer’s comments.

 Kindest regards,

Mario Marques da Silva

José Aleixo

Luís M. L. Oliveira

Rui Dinis

 

 Reviewer Comments to the Author

Comment: The revised paper addresses most of the suggestions and concerns raised by the reviewer. Two relevant and recent papers have now been cited, as suggested, but only in a fleeting manner -- as one of them assumes less stringent noise conditions.

Authors’ Reply: As recommended, the two added references were better introduced in the revised version of the manuscript. It is agreed that the study aimed to be published in this article comprises a more stringent noise condition than the reference [11]. Future work will study the performance under different impulsive noise conditions, namely with different power levels, different probabilities, etc.

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

The article deals with a topic of great interest, given that underwater environments present very adverse conditions for acoustic wave communications. They are difficult to characterize due to their anisotropy and non-homogeneity. In addition, the background noise also depends on the place and time of the measurements. It is not the same to characterize the noise in the Strait of Gibraltar or in the Azores Islands, or during the passage of migrating cetaceans. The authors propose a simulation where they compare different technologies and communication techniques, applying the Monte Carlo method. Their descriptions of the different communication systems under comparison are numerous and of high level, but they do not explain much about the physical layer that they are going to use, this being the most critical and unknown part of the system. They make use of Rayleigh-type channels with 20 uncorrelated paths of equal power. Why 20 and why of equal power? This is not explained. They use the Markov chain as an impulsive noise model with p1,0 = 0.1 and p0,1 = 0.8. Why do they choose these values and not others? They choose an impulse noise variance which is 10 times larger than the AWGN variance. Why 10, specifically? In my opinion, the results they obtain are too theoretical and, therefore, of doubtful utility for their application in such a highly variable scenario such as the underwater environment. An interesting contribution to this topic would have been to carry out preliminary tests in several underwater locations whose environment had previously been characterized – spatially and temporally – to then test the different technologies and techniques that are mentioned in the article.

Reviewer 2 Report

This paper shows the performance of several well-known receivers: ZF, MRC, EGC, and IB-DFE, with MIMO and SC-FDE technique, on LDPC-coded UWA communications and concludes that the MRC performed better than other receivers.

The ZF, MRC, EGC, and IB-DFE are all classical methods in wireless communications, including UWA communications. It has become a consensus that the MRC has achieved the best performance compared to other receivers, which has been proven in theory. So there are almost no new findings from the simulation results. For example, the conclusion that the diversity gains of MIMO space increase with the number of receivers has been theoretically proven, which is shown in Fig.10. Similarly, Fig.4 gives the conclusion that the LDPC codes are well suited for UWA communications. However, the LDPC has been widely used in UWA communications. Please clarify the necessity of the simulation corresponding to Fig.4. Overall, the innovation of this paper is insufficient and the authors should further clarify the novelty compared with the existing work.

Besides, I have some comments as follows.

There is no definition on  in Eq. (8).

In line 208, the author has not given the definition of the world “MFB”.

 

Reviewer 3 Report

1. In the page 5, a severe Rayleigh fading channel was considered with 20 uncorrelated equal power paths. In the table 1, the MIMO diversities are 4x32. The underwater 4x32 MIMO channel model should be demonstrated in detail.
2. In the page 5, the LDPC codes of length 32400 were adopted, with a code rate ½ . The LDPC codes of length 32400 should be demonstrated in detail.
3. Please revise and enhance the English writing to improve the manuscript’s readability.