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Energy Efficient ACE-SI-based Hybrid Precoding for SWIPT-Enabled Massive MIMO-NOMA Systems
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- 1. Energy Efficient ACE-SI-based Hybrid Precoding for SWIPT-Enabled Massive MIMO-NOMA Systems Deeptanu Datta Roll No. :- 1811EE05 Guided by :- Dr. Sudhir Kumar Department of Electrical Engineering Indian Institute of Technology, Patna June 25, 2020 1 / 52
- 2. Outlines Literature Survey Motivation Contributions Classification of Precoding Hybrid Precoding Structures Model Description SI-operation Optimum A and D ACE Algorithm Updating Formula Simulation Results and Discussions Optimum Precoding Structure Conclusions Future Scope of Work References Publication 2 / 52
- 3. Literature Survey In Beamspace MIMO [1], dominant beams are selected to reduce RF chains. IA-based [2], sparsity masks-based [1], SINR-based [2] methods are commonly used in literature to select beams. RF chains are also reduced by hybrid precoding - can be realized by analog phase shifters or switches [1]. [3, 2, 3, 1, 2] uses APSs to implement hybrid precoding. [1, 3] uses switches and/or inverters in hybrid precoding. 3 / 52
- 4. Literature Survey (contd...) Energy-efficient SIC-based HP is proposed for mmWave massive MIMO systems in [3], where sum-rate problem is splitted into sub-rate problems for each array. Adaptive HP is proposed in [1], where phases of all APSs are jointly optimized to maximize spectral efficiency. In [3], ML-estimated AoDs are used to design precoding vectors in mmWave MIMO systems. PZF-HP is proposed in [2] for MU massive MIMO systems 4 / 52
- 5. Literature Survey (contd...) In [1], analog precoder is designed for MIMO-OMA systems using SIs, whose parameters are updated by ACE algorithm. In [3], switches are used along with APSs to reduce RF chain in mmWave massive MIMO systems. In [2], hybrid precoding is realized by APSs and RF adders in SWIPT-enabled mmWave massive MIMO-NOMA systems. 5 / 52
- 6. Motivation Ordinary MIMO needs large hardwares. High complexity, cost, and power consumption [1]. Hybrid Precoding : simplifies structure : reduces RF chain count : makes it more energy-efficient [2]. Current HP techniques uses APSs - consumes considerable amount of power. APSs needs to be replaced with switches and inverters to guarantee best performance. 6 / 52
- 7. Contributions Novel energy-efficient hybrid precoding is designed for mmWave massive MIMO-NOMA systems with SWIPT. Probability vector is updated by ACE algorithm using smoothed updating procedure to generate both ± 1 √ N randomly [3]. Its performance is validated by extensive simulation study of spectral efficiency and energy efficiency against SNR. 7 / 52
- 8. Classification of Precoding 8 / 52
- 9. Digital Precoding Each antenna is connected to individual RF chains. Full control of amplitude and phase of signals from each individual antennas. Most inefficient for massive MIMO due to high cost and power consumption [1]. Generally used in conventional MIMO. Figure: Digital Precoding 9 / 52
- 10. Analog Precoding RF chains are connected to antenna by phase shifters [2]. Signal phases are adjusted in RF domain to supress interference and increase SINR. Boost in antenna array gain overcomes high pathloss at mmWave frequency [3]. Used in sonar, radar, IEEE 802.11 ad [1]. 10 / 52
- 11. Hybrid Precoding Both analog and digital precoding are combined to extract the advantages of each. 2-stage process : fully-digital precoder is decomposed into high-dimensional analog precoder and low-dimensional digital precoder. Analog Precoding is first applied across all RF paths per RF chain to extract antenna array gain [3]. Digital Precoding is then applied across all RF chains to supress interuser interference [3]. Widely used in mmWave massive MIMO systems. Physically realized by a number of configurations. 11 / 52
- 12. Hybrid Precoding Structures 12 / 52
- 13. Fully-connected architecture Transmitted Signal on each RF chain traverses through N RF paths [3]. Each RF chain extracts full-array gain, so maximum spectral efficiency. NNRF APSs and N RF adders : high complexity, cost, power consumption, so poor energy efficiency [3]. Analog precoding matrix : A = [a1 a2 · · · aNRF ] ai = array steering vector of all N antennas on ith RF chain. 13 / 52
- 14. Sub-connected architecture Transmitted Signal on each RF chain traverses through only M = N NRF RF paths [3]. Array gain per RF chain reduces NRF times. Only N APSs : lower complexity, cost, power consumption, so better energy efficiency [3]. Block diagonal analog precoding matrix A = diag(ai ) ∀ i = 1 : NRF; ai = array steering vector of all M antennas connected to ith RF chain. 14 / 52
- 15. Switch-based architecture Recasting of sub-connected architecture by switches. APSs replaced with switches to enhance energy efficiency [1]. Only NRF switches, so NRF active antennas : array gain reduces drastically [2]. Block diagonal A = diag(ai ) ∀ i = 1 : NRF; all ai has elements from set 1 √ N {0, 1} randomly. 15 / 52
- 16. SI-based architecture Recasting of sub-connected architecture with switches and inverters. One inverter and M switches for each RF chain. All antennas involved to extract full-array gain - most optimum energy-efficient structure [1]. Block diagonal A = diag(ai ) ∀ i = 1 : NRF; all ai has one of two elements ± 1 √ N randomly. 16 / 52
- 17. System Model MU-downlink mmWave massive MIMO-NOMA system is considered with SI-based sub-connected architecture [3]. Users possess power splitting receiver for SWIPT [2]. To extract full multiplexing gain, G = NRF is assumed [2, 1]. NOMA enables each beam to serve multiple users K ≥ G [3]. Ki = number of users accomodated in the ith beam. Signal received by mth user in the gth beam is yg,m = hH g,mA G i=1 di pT i xi + ng,m xi = transmitted signal vector of ith beam, s.t. E(xi xH i ) = IKi 17 / 52
- 18. Desired, Interference, and Noise components Expanding above equation yg,m = hH g,mAdg √ pg,mxg,m + hH g,mAdg pT g[m]xg[m] + hH g,mA G i=1 i=g di pT i xi + ng,m First term - Desired signal component of the mth user in the gth beam. Second term - Interference from users of same beam - Intrabeam Interference. Third term - Interference from users of remaining beams - Interbeam Interference. Fourth term - AWGN Noise introduced by channel. 18 / 52
- 19. SWIPT-Enabled NOMA Effective channel gains are sorted in descending order for all beams i.e., |hH i,j Adi | ≥ |hH i,j+1Adi | ∀ j = 1 : Ki , i = 1 : G User transmit power follows reverse order for all beams i.e., pi,j ≤ pi,j+1 ∀ j = 1 : Ki , i = 1 : G Applying SIC for NOMA at the receiver [3] yg,m = hH g,mAdg √ pg,mxg,m + hH g,mAdg pT g,{1:m−1}xg,{1:m−1} + hH g,mA G i=1 i=g di pT i xi + ng,m Received signal at ID output of mth user in gth beam is ˆyID g,m = yg,m √ γg,m + nPS g,m 19 / 52
- 20. Achievable sum-rate SINR for mth user in gth beam is (SINR)g,m = γg,m|hH g,mAdg |2pg,m (NI)g,m (NI)g,m = γg,m(|hH g,mAdg |2 S pT g,{1 : (m−1)} + G i=1 i=g |hH g,mAdg |2 S(pT i ) + σn 2) + σn 2 PS Achievable rate of mth user in gth beam Rg,m = log2(1 + (SINR)g,m) Spectral efficiency of the system : Rsum = G i = 1 (beam) Ki j = 1 (user) Ri,j 20 / 52
- 21. Channel Model Due to channel sparsity [1] and low SINR, Saleh-Valenzuela geometric channel model is used [2, 1, 1, 2]. hg,m = N Lg,m Lg,m l=1 (paths) αl g,ma(ϕl g,m, θl g,m) Net array steering vector a(ϕl , θl ) = aaz(ϕl ) ⊗ ael(θl ) ∀ l aaz(ϕ) = 1 √ Naz ej2πnaz daz λ sin(ϕ) T is array steering vector in azimuthal direction. Equi-spaced antennas at mmWave freq. daz = del = λ 2 [3]. 21 / 52
- 22. SI-operation For SI-operation, each element in a(ϕ, θ) must be ± 1 √ N . Net ASV for equi-spaced antennas daz = del = λ 2 [3] is given by a(ϕ, θ) = 1 √ N ejπ(naz sin(ϕ)+nel sin(θ)) T [2]. {sin(ϕ) , sin(θ)} ∈ {0, ±1} {ϕ , θ} ∈ 0, ± π 2 , ±π 22 / 52
- 23. Problem Formulation max A,D Rsum s.t. C1 : pi,j ≥ 0, ∀ i, j C2 : pi,j ≤ pi,j+1, ∀ i, j C3 : G i = 1 (beam) Ki j = 1 (user) pi,j ≤ Ptr C4 : Ri,j ≥ Rmin i,j , ∀ i, j C5 : PEH i,j ≥ Pmin i,j , ∀ i, j C6 : ai{j} = ± 1 √ N , ∀ i, j 23 / 52
- 24. Optimum A and D Probabilistic model-based ACE algorithm is used [3]. For SI-operation, N non-zero elements obey constraint C6 in block-diagonal A of sub-connected architecture. Initialization : = [aT aT 2 . . . aT G ]T f = [f1 f2 . . . fN]T ∀ j = 1 : N, j is a Bernoulli random variable, such that fj = Pr j = 1 √ N Initially, f(itr = 0) = 1 2 × 1N×1 24 / 52
- 25. ACE Algorithm Generate E random data samples and reshape them as matrices A. Calculate achievable sum-rate Rsum for each sample. Rearrange the achievable sum-rates in descending order. Rsum(A[1] ) ≥ Rsum(A[2] ) ≥ · · · ≥ Rsum(A[E] ) Select the elites as {A[1] , A[2] , A[3] , · · · , A[Eelite] }. Calculate weight we of each elite ∀ e = 1 : Eelite. Update f for next iteration using smoothed procedure. Repeat all the above steps till f becomes binary vector [3]. 25 / 52
- 26. Updating formula Each elite is allocated a weight based on spectral efficiency achieved by it. Weight alloted to eth elite is we = EeliteRsum(A[e]) Eelite e=1 (Rsum(A[e] )) These weights are used to update f in next iteration using smoothed updating procedure as [3] f(itr+1) = ξ √ N Eelite Eelite e=1 we e(itr) + (1 − ξ)f(itr) 0 ≤ ξ ≤ 1 is smoothing parameter; e(itr) is vectored A of eth elite at itrth iteration. 26 / 52
- 27. Simulation Results Table: Simulation Setup Parameter Value N 64 NRF 4 K 6, 10, and 12 Lg,m 3 α1 g,m (LoS) CN(0, 1) αl g,m ∀l = 1 (NLoS) CN(0, 0.1) ϕl i,j , θl i,j 0, ±π 2 , ±π Ptr 30 mW [2] SNR Ptr σ2 n [1] E 100 [1] Eelite 20 [1] 27 / 52
- 28. Spectral Efficiency Figure: Spectral Efficiency against SNR for K = 6 28 / 52
- 29. Spectral Efficiency (contd...) Figure: Spectral Efficiency against SNR for K = 10 29 / 52
- 30. Spectral Efficiency (contd...) Figure: Spectral Efficiency against SNR for K = 12 30 / 52
- 31. Trends in Spectral Efficiency MIMO-NOMA systems has higher spectral efficiency than MIMO-OMA systems due to higher spectral efficiency of NOMA [3]. Fully digital system has highest spectral efficiency as all N RF chains are used to serve K users concurrently to extract full multiplexing gain [1]. Fully-connected architecture achieves higher spectral efficiency than sub-connected architecture since each RF chain extracts full-array gain. The proposed ACE-SI-based sub-connected HP-NOMA architecture has almost similar trend as APS-based sub-connected HP-NOMA as spectral efficiency depends only on number of users using the same resources concurrently. 31 / 52
- 32. Energy Efficiency Figure: Energy Efficiency against SNR for K = 6 32 / 52
- 33. Energy Efficiency (contd...) Figure: Energy Efficiency against SNR for K = 10 33 / 52
- 34. Energy Efficiency (contd...) Figure: Energy Efficiency against SNR for K = 12 34 / 52
- 35. Trends in Energy Efficiency The proposed ACE-SI-based sub-connected HP-NOMA architecture has highest energy efficiency due to use of only energy-efficient switches and inverters in analog precoder [1]. Fully digital system has the least energy efficiency due to its tremendous cost energy consumption [1]. Sub-connected architecture is more energy-efficient than fully connected architecture due to fewer number of APSs. MIMO-NOMA systems has also higher energy efficiency than MIMO-OMA systems with the same total power consumption due to higher spectral efficiency of NOMA [3]. EE = Rsum Pcons 35 / 52
- 36. Power Consumption Analysis Total power consumed by a precoding structure is Pcons = Ptr + PDP + Px Px = power consumed by internal components of structure, which can be calculated by Table 2. Px relies on internal circuitry of a particular architecture. Inverters are designed by chip with similar power rating as switches, so PINV ≈ PSW [2]. Table: Power Consumption of different precoder components [1] Component Notation Power Consumed (in mW) RF chain PRF 250 Phase Shifter PPS 40 Digital precoder PDP 200 Switch PSW 5 Inverter PINV 5 36 / 52
- 37. Power Consumption Comparison Table: Power Consumption of different precoding schemes Architecture Px Pcons (in Watts) Fully Digital NPRF 16.23 Fully-connected NRFPRF + NNRFPPS 11.47 Sub-connected NRFPRF + NPPS 3.79 Switch-based NRFPRF + NRFPSW 1.25 ACE-SI-based NRFPRF + NPSW + NRFPINV 1.57 (Proposed) 37 / 52
- 38. Optimum Precoding Design As per Table 3, switch-based architecture consumes least power to yield highest energy efficiency. But, it can not extract full-array gain as only NRF antennas are active [2]. The next structure consuming least power is SI-based architecture, which extracts full-array gain [1]. So, the optimum precoding architecture is SI-based architecture. 38 / 52
- 39. Conclusions Energy-efficient ACE-SI-based hybrid precoding scheme is proposed for SWIPT-Enabled massive MIMO-NOMA systems. ACE algorithm is leveraged to update probability parameter vector at each iterations to obtain better performance. Proposed ACE-SI-based HP scheme attains near-optimal sum-rate performance, but highest energy efficiency than existing schemes. 39 / 52
- 40. Future Scope of Work Variation of spectral and energy efficiencies against number of RF chains can be investigated. Variation of spectral and energy efficiencies against number of multipath components can also be studied. T-R separation can be optimized to design more energy-efficient system. 40 / 52
- 41. Publication Deeptanu Datta and Sudhir Kumar, ”Energy Efficient ACE-SI-based Hybrid Precoding for SWIPT-Enabled Massive MIMO-NOMA Systems,” IEEE Communication Letters, 2020. (Current Status : Reject and Resubmitted) 41 / 52
- 42. References Akhil Gupta and Rakesh Kumar Jha, ”A Survey of 5G Network : Architecture and Emerging Technologies,” IEEE Access, vol. 3, pp. 1206-1232, August 2015. A. L. Swindlehurst, E. Ayanoglu, P. Heydari, and F. Capolino, “Millimeter-wave massive MIMO: The next wireless revolution?,” IEEE Communication Magazine, vol. 52, no. 9, pp. 56–62, September 2014. Z. Pi and F. Khan, “An Introduction to Millimeter-Wave Mobile Broadband Systems,” IEEE Communication Magazine, vol. 49, no. 6, pp. 101–107, June 2011. Lu Lu, Geoffrey Ye Li, A. Lee Swindlehurst, Alexei Ashikhmin, and Rui Zhang, ”An Overview of Massive MIMO : Benefits and Challenges,” IEEE Journal on Selected Topics in Signal Processing, vol. 8, no. 5, pp. 742-758, October 2014. 42 / 52
- 43. References (contd...) T. S. Rappaport, Shu Sun, Rimma Mayzus, Hang Zhao, Yaniv Azar, Kevin Wang, G.N. Wong, J.K. Schulz, Mathew Samimi, and Felix Gutierraz, “Millimeter wave mobile communications for 5G cellular: It will work!,” IEEE Access, vol. 1, pp. 335–349, May 2013. T. L. Marzetta, “Noncooperative cellular wireless with unlimited numbers of base station antennas,” IEEE Transactions on Wireless Communications, vol. 9, no. 11, pp. 3590–3600, November 2010. Linglong Dai, Bichai Wang, Zhiguo Ding, Zhaocheng Wang, Sheng Chen, and Lajos Hanzo, ”A Survey of Non-Orthogonal Multiple Access for 5G,” IEEE Communications Surveys and Tutorials, vol.20, no. 3, 3rd Quarter 2018. 43 / 52
- 44. References (contd...) Lav R. Varshney, ”Transporting Information and Energy Simultaneously,” IEEE International Symposium on Information Theory (ISIT), Toronto, Canada, pp. 1612-1616, July 2008. TDP Perera, DNK Jayakody, SK Sharma, S. Chatzinotas, and Jun Li, ”Simultaneous Wireless Information and Power Transfer (SWIPT) : Recent Advances and Future Challenges,” IEEE Communications Surveys and Tutorials, vol. 20, no. 1, pp. 264-302, 1st Quarter 2018. Ali A. Nazir, Xiangyun Zhou, Salman Durrani, and Rodney A. Kennedy Kennedy, ”Throughput and Ergodic Capacity of Wireless Energy Harvesting based DF Relaying Network,” IEEE ICC 2014 - Selected Areas in Communications Symposium. 44 / 52
- 45. References (contd...) R. Mendez-Rial, C. Rusu, A. Alkhateeb, N. Gonzalez-Prelcic, and R. W. Heath, “Channel Estimation and Hybrid Combining for mmWave : Phase shifters or switches?” in Proc. ITA Workshops, pp. 90–97, February 2015. A.F. Molisch, V.V. Ratnam, S Han, S.L.H. Nguyen, L. Li, and K. Haneda, ”Hybrid Beamforming for Massive MIMO : A Survey,” IEEE Communications Magazine, vol. 55, no. 9, pp. 134-141, September 2017. R. Rubinstein and D. Kroese, ”The Cross-Entropy Method : A Unified Approach to Combinatorial Optimization, Monte-Carlo Simulation, and Machine Learning,” Springer Science and Business Media, 2004. 45 / 52
- 46. References (contd...) Fredrik Rusek, Daniel Persson, Buon Kiong Lau, Erik G. Larsson, Thomas L. Marzetta, Ove Edfors, and Fredrik Tufvesson, ”Scaling up MIMO : Opportunities and Challenges with very large arrays, ” IEEE Signal Processing Magazine, vol. 30, no. 1, pp. 40-60, January 2013. X. Gao, L. Dai, Z. Chen, Z. Wang, and Z. Zhang, “Near-optimal beam selection for beamspace mmWave massive MIMO systems,” IEEE Commun. Lett., vol. 20, no. 5, pp. 1054–1057, May 2016. X. Gao, L. Dai, S. Han, I. Chih-Lin, and R. W. Heath, “Energy-Efficient Hybrid Analog and Digital Precoding for mmWave MIMO Systems with Large Antenna Arrays,” IEEE Journal on Selected Areas in Communications, vol. 34, no. 4, pp. 998–1009, April 2016. 46 / 52
- 47. References (contd...) Robert W. Heath Jr, Nuria Gonz´alez-Prelcic, Sundeep Rangan, Wonil Roh, and Akbar M. Sayeed, ”An Overview of Signal Processing Techniques for Millimeter Wave MIMO Systems,” IEEE Journal of Selected Topics in Signal Processing, vol.10, no. 3, pp. 436-453, April 2016. R.M. Rial, C. Rusu, N.G. Prelcic, Ahmed A., and R.W. Heath, ”Hybrid MIMO Architectures for mmWave Communications: Phase Shifters or Switches?,” IEEE Access, vol. 4, pp. 247-267, March 2016. Shuangfeng Han, Chih-Lin I, Zhikun Xu, and Corbett Rowell, “Large-Scale Antenna Systems with Hybrid Precoding Analog and Digital Beamforming for Millimeter Wave 5G,” IEEE Communication Magazine, vol. 53, no. 1, pp. 186–194, January 2015. 47 / 52
- 48. References (contd...) Gao, Dai, Han, and Chih-Lin, ”Machine Learning Inspired Energy-Efficient Hybrid Precoding for MmWave MIMO Systems,” IEEE ICC 2017 Wireless Communications Symposium. Linglong Dai, Bichai Wang, Mugen Peng, and Shanzhi Chen, ”Hybrid Precoding-Based Millimeter-Wave Massive MIMO-NOMA with Simultaneous Wireless Information and Power Transfer,” IEEE Journal on selected areas in Communication, vol. 37, no-1, January 2019, pp. 131-141. L. Dai, B. Wang, Y Yuan, S. Han, C.-L.. I, and Z. Wang, ”Non-orthogonal multiple access for 5G : Solutions, challenges, oportunities, and future research trends,” IEEE Communications Magazine, vol. 53, no. 9, pp. 74-81, September 2015. 48 / 52
- 49. References (contd...) A. Sayeed and J. Brady, “Beamspace MIMO for high-dimensional multiuser communication at millimeter-wave frequencies,” in Proc. IEEE Global Communication Conference (GLOBECOM), pp. 3679–3684, December 2013. Pierluigi V. Amadori and Christos Masouros, “Low RF-Complexity Millimeter-Wave Beamspace-MIMO Systems by Beam Selection,” IEEE Transactions on Communications, vol. 63, no. 6, pp. 2212-2223, June 2015. Isa H. Altoobaji and M.A. Mangoud, ”Hybrid Precoding Design with AoD Estimation for mmWave MIMO Systems,” IEEE MENACOMM 2018, Jounieh, pp. 1-4. 49 / 52
- 50. References (contd...) B. Wang, Dai, Z. Wang, Ge, and Zhou, ”Spectrum and Energy-Efficient Beamspace MIMO-NOMA for Millimeter-Wave Communications Using Lens Antenna Array,” IEEE Journal on Selected Areas in Communications, vol. 35, no. 10, October 2017. Rubinstein, R.Y. (1999). The simulated entropy method for combinatorial and continuous optimization. Methodology and Computing in Applied Probability, 2, pp. 127-190. J.G. Proakis and Masoud Salehi, Digital Communications, 5th Edition, McGraw Hill Publshers. ISBN-13 : 978-93-392-0479-2, ISBN-10 : 978-93-392-0479-4, Indian Edition. Source : https://www.wikipedia.org 50 / 52
- 51. References (contd...) Xudong Zhu, Zhaocheng Wang, Linglong Dai, and Qi Wang, ”Adaptive Hybrid Precoding for Multiuser Massive MIMO,” IEEE Communication Letters, vol. 20, no. 4, April 2016. Le Liang, Wei Xu, and Xudong Zhu, ”Low-Complexity Hybrid Precoding in Massive Multiuser MIMO Systems,” IEEE Wireless Communication Letters, vol. 3, no. 6, December 2014. A. Alkhateeb, Y-H Nam, J. Zhang, and R.W. Heath, ”Massive MIMO combining with Switches,” IEEE Wireless Communications Letters, vol. 5, no. 3, June 2016. 51 / 52
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You’ve spent years preparing for your master’s degree or PhD. You’ve read, studied and spent hours of time and energy writing papers. Now you’ve arrived at the culmination of all this effort: writing your thesis.
A good thesis statement is a single sentence contained in the introduction of a paper that provides the reader with some idea of what the writer is trying to convey in the body of the paper. The thesis statement is a condensed summary of th...
Statistical treatment in a thesis is a way of removing researcher bias by interpreting the data statistically rather than subjectively. Giving a thesis statistical treatment also ensures that all necessary data has been collected.
This video is my Mtech thesis viva submitted to RGPV viva presentation given to RGPV Ragistrar RS Rajput. My thesis work is on SOLAR
This video define/shows the M.tech Thesis presentation:Title of Thesis:-MODEL OF 'MOBILE APP. AND WIRELESS SENSORS FOR NEXT GENERATION
M.tech (Production and Industrial Engineering) Thesis Presentation. Oct. 04, 2018. • 2 likes • 953 views.
M.Tech Thesis Defense Presentation · 1. Energy Efficient ACE-SI-based Hybrid Precoding for SWIPT-Enabled Massive MIMO-NOMA Systems Deeptanu Datta
M.Tech Thesis Presentation. M.Tech Thesis Presentation WLAN Watch: A Step Towards The Study Of 802.11b Wireless LANs. Supervisor: Dr. Pravin Bhagwat.
E2MATRIX deals with Thesis guidance and research work for M.Tech, PhD Students. – A free PowerPoint PPT presentation (displayed as an HTML5 slide show) on
E2MATRIX provides thesis assistance in and thesis guidance with full thesis help and readymade m tech thesis and full documentation.
Presentation needs to be not more than 12-15 slides for a 20 min
Download Slides - M.Tech dissertation ppt | Rajiv Gandhi Proudyogiki Vishwavidyalaya | The main objective of this dissertation is to focus a
[3] V. K. Pandey, “Suppression of artifacts in impedance cardiography,” Ph.D. Thesis, Biomedical Engineering, Indian Institute of Technology Bombay, Mumbai
M.Tech. (Department of Mechanical Engineering). Head Of the Department. Prof. S.K. Dwivedi. M.Tech. (Department of Mechanical Engineering).