Hybrid and Full-Digital Beamforming in mmWave Massive MIMO Systems: A Comparison Considering Low-Resolution ADCs
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摘要
In a millimeter-wave(mmWave) Massive multiple-input multiple-output(MIMO) systems, full-digital beamforming(i.e., connecting each antenna with a specific radio-frequency(RF) chain) becomes inefficient due to the hardware cost and power consumption. Therefore, hybrid analog and digital transceiver where the number of RF chains are much smaller than that of the antennas has drawn great research interest. In this work, we investigate the use of low-resolution analog-to-digital converters(ADCs) in the uplink of multi-user hybrid and full-digital mmWave Massive MIMO systems. To be specific, we compare the performance of full-digital minimum mean square error(MMSE) and hybrid MMSE beamforming in both sum rates and energy efficiency. Accurate approximations of sum rates and energy efficiency are provided for both schemes, which captures the dominant factors. The analytical results show that full-digital beamforming outperforms hybrid beamforming in terms of sum rates and requires only a small portion(γ) of antennas used by hybrid beamforming to achieve the same sum rates. We given sufficient condition for full-digital beamforming to outperform hybrid beamforming in terms of energy efficiency. Moreover, an algorithm is proposed to search for the optimal ADC resolution bits. Numerical results demonstrate the correctness of the analysis.
In a millimeter-wave(mmWave) Massive multiple-input multiple-output(MIMO) systems, full-digital beamforming(i.e., connecting each antenna with a specific radio-frequency(RF) chain) becomes inefficient due to the hardware cost and power consumption. Therefore, hybrid analog and digital transceiver where the number of RF chains are much smaller than that of the antennas has drawn great research interest. In this work, we investigate the use of low-resolution analog-to-digital converters(ADCs) in the uplink of multi-user hybrid and full-digital mmWave Massive MIMO systems. To be specific, we compare the performance of full-digital minimum mean square error(MMSE) and hybrid MMSE beamforming in both sum rates and energy efficiency. Accurate approximations of sum rates and energy efficiency are provided for both schemes, which captures the dominant factors. The analytical results show that full-digital beamforming outperforms hybrid beamforming in terms of sum rates and requires only a small portion(γ) of antennas used by hybrid beamforming to achieve the same sum rates. We given sufficient condition for full-digital beamforming to outperform hybrid beamforming in terms of energy efficiency. Moreover, an algorithm is proposed to search for the optimal ADC resolution bits. Numerical results demonstrate the correctness of the analysis.
In a millimeter-wave(mmWave) Massive multiple-input multiple-output(MIMO) systems, full-digital beamforming(i.e., connecting each antenna with a specific radio-frequency(RF) chain) becomes inefficient due to the hardware cost and power consumption. Therefore, hybrid analog and digital transceiver where the number of RF chains are much smaller than that of the antennas has drawn great research interest. In this work, we investigate the use of low-resolution analog-to-digital converters(ADCs) in the uplink of multi-user hybrid and full-digital mmWave Massive MIMO systems. To be specific, we compare the performance of full-digital minimum mean square error(MMSE) and hybrid MMSE beamforming in both sum rates and energy efficiency. Accurate approximations of sum rates and energy efficiency are provided for both schemes, which captures the dominant factors. The analytical results show that full-digital beamforming outperforms hybrid beamforming in terms of sum rates and requires only a small portion(γ) of antennas used by hybrid beamforming to achieve the same sum rates. We given sufficient condition for full-digital beamforming to outperform hybrid beamforming in terms of energy efficiency. Moreover, an algorithm is proposed to search for the optimal ADC resolution bits. Numerical results demonstrate the correctness of the analysis.
引文
[1]L.Wei,R.Q.Hu,Y.Qian,and G.Wu,“Key elements to enable millimeter wave communications for 5g wireless systems,”IEEE Wireless Communications,vol.21,no.6,December 2014,pp.136-143.
[2]C.H.Doan,S.Emami,D.A.Sobel,A.M.Niknejad,and R.W.Brodersen,“Design considerations for 60 ghz cmos radios,”IEEE Communications Magazine,vol.42,no.12,Dec 2004,pp.132-140.
[3]F.Rusek,D.Persson,E.G.Larsson,T.L.Marzetta,and F.Tufvesson,“Scaling Up MIMO:Opportunities and Challenges with Very Large Ar-rays,”IEEE Signal Processing Magazine,vol.30,no.1,jan 2013,pp.40-60.
[4]H.Yin,D.Gesbert,M.Filippou,and Y.Liu,“ACoordinated Approach to Channel Estimation in Large-Scale Multiple-Antenna Systems,”IEEEJournal on Selected Areas in Communications,vol.31,no.2,feb 2013,pp.264-273.
[5]C.Zhang,Y.Huang,Y.Jing,S.Jin,and L.Yang,“Sum-Rate Analysis for Massive MIMO Downlink with Joint Statistical Beamforming and User Scheduling,”IEEE Transactions on Wireless Communications,vol.16,no.4,2017,pp.2181-2194.
[6]W.Zhang,H.Ren,C.Pan,M.Chen,R.C.De Lamare,B.Du,and J.Dai,“Large-scale antenna systems with UL/DL hardware mismatch:Achievable rates analysis and calibration,”IEEETransactions on Communications,vol.63,no.4,2015,pp.1216-1229.
[7]W.Zhang,R.C.De Lamare,C.Pan,M.Chen,J.Dai,B.Wu,and X.Bao,“Widely linear precoding for large-scale MIMO with IQI:Algorithms and performance analysis,”IEEE Transactions on Wireless Communications,vol.16,no.5,2017,pp.3298-3312.
[8]X.Zhang,A.F.Molisch,and S.-Y.Kung,“Variable-phase-shift-based rf-baseband codesign for mimo antenna selection,”IEEE Transactions on Signal Processing,vol.53,no.11,Nov 2005,pp.4091-4103.
[9]L.Liang,W.Xu,and X.Dong,“Low-complexity hybrid precoding in massive multiuser mimo systems,”IEEE Wireless Communications Letters,vol.3,no.6,Dec 2014,pp.653-656.
[10]T.E.Bogale,L.B.Le,A.Haghighat,and L.Vandendorpe,“On the number of rf chains and phase shifters,and scheduling design with hybrid analog-digital beamforming,”IEEE Transactions on Wireless Communications,vol.15,no.5,May 2016,pp.3311-3326.
[11]Q.Yu,X.Zhai,and M.Zhao,“An energy-efficient hybrid precoding algorithm for multiuser mmwave massive mimo systems,”in 2017 IEEE86th Vehicular Technology Conference(VTC-Fall),Sept 2017,pp.1-5.
[12]A.Li and C.Masouros,“Hybrid analog-digital millimeter-wave mu-mimo transmission with virtual path selection,”IEEE Communications Letters,vol.21,no.2,Feb 2017,pp.438-441.
[13]J.Zhang,L.Dai,X.Li,Y.Liu,and L.Hanzo,“On Low-Resolution ADCs in Practical 5G Millimeter-Wave Massive MIMO Systems,”IEEE Communications Magazine,2018,pp.2-8.
[14]M.Sarajlic,L.Liu,and O.Edfors,“When Are Low Resolution ADCs Energy Efficient in Massive MIMO?”IEEE Access,vol.5,2017,pp.14837-14 853.
[15]L.Fan,S.Jin,C.K.Wen,and H.Zhang,“Uplink achievable rate for massive MIMO systems with low-resolution ADC,”IEEE Communications Letters,vol.19,no.12,2015,pp.2186-2189.
[16]W.B.Abbas,F.Gomez-Cuba,and M.Zorzi,“Millimeter Wave Receiver Efficiency:A Comprehensive Comparison of Beamforming Schemes with Low Resolution ADCs,”IEEE Transactions on Wireless Communications,vol.16,no.12,2017,pp.8131-8146.
[17]K.Roth and J.A.Nossek,“Achievable Rate and Energy Efficiency of Hybrid and Digital Beamforming Receivers With Low Resolution ADC,”Ieee Journal on Selected Areas In Communications,vol.35,no.9,2017,pp.2056-2068.
[18]K.Roth,H.Pirzadeh,A.Lee Swindlehurst,and J.A.Nossek,“A Comparison of Hybrid Beamforming and Digital Beamforming With Low-Resolution ADCs for Multiple Users and Imperfect CSI,”IEEE Journal on Selected Topics in Signal Processing,vol.12,no.3,2018,pp.484-498.
[19]J.Mo,A.Alkhateeb,S.Abu-Surra,and R.W.Heath,“Hybrid architectures with few-bit adc receivers:Achievable rates and energy-rate tradeoffs,”IEEE Transactions on Wireless Communications,vol.16,no.4,April 2017,pp.2274-2287.
[20]J.Singh,O.Dabeer,and U.Madhow,“Communication limits with low precision analog-to-digital conversion at the receiver,”in 2007 IEEEInternational Conference on Communications,June 2007,pp.6269-6274.
[21]J.Mo and R.W.Heath,“Capacity analysis of one-bit quantized mimo systems with transmitter channel state information,”IEEE Transactions on Signal Processing,vol.63,no.20,Oct 2015,pp.5498-5512.
[22]J.H.Mo,A.Alkhateeb,S.Abu-Surra,and R.W.Heath,“Hybrid Archi-tectures With Few-Bit ADC Receivers:Achievable Rates and Energy-Rate Tradeoffs,”IEEE Transactions on Wireless Communications,vol.16,no.4,2017,pp.2274-2287.
[23]J.Y.Zhang,L.L.Dai,Z.Y.He,S.Jin,and X.Li,“Performance Analysis of Mixed-ADC Massive MIMO Systems Over Rician Fading Channels,”Ieee Journal on Selected Areas In Communications,vol.35,no.6,2017,pp.1327-1338.
[24]P.Dong,H.Zhang,W.Xu,G.Y.Li,and X.You,“Performance Analysis of Multiuser Massive MIMO With Spatially Correlated Channels Using Low-Precision ADC,”IEEE Communications Letters,vol.22,no.1,jan 2018,pp.205-208.
[25]T.E.Bogale and L.B.Le,“Beamforming for multiuser massive mimo systems:Digital versus hybrid analog-digital,”in 2014 IEEE Global Communications Conference,Dec 2014,pp.4066-4071.
[26]L.Fan,S.Jin,C.K.Wen,and H.Zhang,“Uplink achievable rate for massive mimo systems with low-resolution adc,”IEEE Communications Letters,vol.19,no.12,Dec 2015,pp.2186-2189.
[27]M.Kraemer,D.Dragomirescu,and R.Plana,“Design of a very low-power,low-cost 60 ghz receiver front-end implemented in 65 nm cmos technology,”International Journal of Microwave&Wireless Technologies,vol.3,no.2,2011,pp.131-138.
[28]L.Long,“Energy-efficient 60 ghz phased-array design for multi-gb/s communication systems,”Ph.D.dissertation,Dept.Elect.Eng.Comput.Sci.,Univ.California,Berkeley,Berkeley,2014.
[29]R.Mendez-Rial,C.Rusu,N.Gonzalez-Prelcic,A.Alkhateeb,and R.W.Heath,“Hybrid MIMOArchitectures for Millimeter Wave Communications:Phase Shifters or Switches?”IEEE Access,vol.4,2016,pp.247-267.
[2]C.H.Doan,S.Emami,D.A.Sobel,A.M.Niknejad,and R.W.Brodersen,“Design considerations for 60 ghz cmos radios,”IEEE Communications Magazine,vol.42,no.12,Dec 2004,pp.132-140.
[3]F.Rusek,D.Persson,E.G.Larsson,T.L.Marzetta,and F.Tufvesson,“Scaling Up MIMO:Opportunities and Challenges with Very Large Ar-rays,”IEEE Signal Processing Magazine,vol.30,no.1,jan 2013,pp.40-60.
[4]H.Yin,D.Gesbert,M.Filippou,and Y.Liu,“ACoordinated Approach to Channel Estimation in Large-Scale Multiple-Antenna Systems,”IEEEJournal on Selected Areas in Communications,vol.31,no.2,feb 2013,pp.264-273.
[5]C.Zhang,Y.Huang,Y.Jing,S.Jin,and L.Yang,“Sum-Rate Analysis for Massive MIMO Downlink with Joint Statistical Beamforming and User Scheduling,”IEEE Transactions on Wireless Communications,vol.16,no.4,2017,pp.2181-2194.
[6]W.Zhang,H.Ren,C.Pan,M.Chen,R.C.De Lamare,B.Du,and J.Dai,“Large-scale antenna systems with UL/DL hardware mismatch:Achievable rates analysis and calibration,”IEEETransactions on Communications,vol.63,no.4,2015,pp.1216-1229.
[7]W.Zhang,R.C.De Lamare,C.Pan,M.Chen,J.Dai,B.Wu,and X.Bao,“Widely linear precoding for large-scale MIMO with IQI:Algorithms and performance analysis,”IEEE Transactions on Wireless Communications,vol.16,no.5,2017,pp.3298-3312.
[8]X.Zhang,A.F.Molisch,and S.-Y.Kung,“Variable-phase-shift-based rf-baseband codesign for mimo antenna selection,”IEEE Transactions on Signal Processing,vol.53,no.11,Nov 2005,pp.4091-4103.
[9]L.Liang,W.Xu,and X.Dong,“Low-complexity hybrid precoding in massive multiuser mimo systems,”IEEE Wireless Communications Letters,vol.3,no.6,Dec 2014,pp.653-656.
[10]T.E.Bogale,L.B.Le,A.Haghighat,and L.Vandendorpe,“On the number of rf chains and phase shifters,and scheduling design with hybrid analog-digital beamforming,”IEEE Transactions on Wireless Communications,vol.15,no.5,May 2016,pp.3311-3326.
[11]Q.Yu,X.Zhai,and M.Zhao,“An energy-efficient hybrid precoding algorithm for multiuser mmwave massive mimo systems,”in 2017 IEEE86th Vehicular Technology Conference(VTC-Fall),Sept 2017,pp.1-5.
[12]A.Li and C.Masouros,“Hybrid analog-digital millimeter-wave mu-mimo transmission with virtual path selection,”IEEE Communications Letters,vol.21,no.2,Feb 2017,pp.438-441.
[13]J.Zhang,L.Dai,X.Li,Y.Liu,and L.Hanzo,“On Low-Resolution ADCs in Practical 5G Millimeter-Wave Massive MIMO Systems,”IEEE Communications Magazine,2018,pp.2-8.
[14]M.Sarajlic,L.Liu,and O.Edfors,“When Are Low Resolution ADCs Energy Efficient in Massive MIMO?”IEEE Access,vol.5,2017,pp.14837-14 853.
[15]L.Fan,S.Jin,C.K.Wen,and H.Zhang,“Uplink achievable rate for massive MIMO systems with low-resolution ADC,”IEEE Communications Letters,vol.19,no.12,2015,pp.2186-2189.
[16]W.B.Abbas,F.Gomez-Cuba,and M.Zorzi,“Millimeter Wave Receiver Efficiency:A Comprehensive Comparison of Beamforming Schemes with Low Resolution ADCs,”IEEE Transactions on Wireless Communications,vol.16,no.12,2017,pp.8131-8146.
[17]K.Roth and J.A.Nossek,“Achievable Rate and Energy Efficiency of Hybrid and Digital Beamforming Receivers With Low Resolution ADC,”Ieee Journal on Selected Areas In Communications,vol.35,no.9,2017,pp.2056-2068.
[18]K.Roth,H.Pirzadeh,A.Lee Swindlehurst,and J.A.Nossek,“A Comparison of Hybrid Beamforming and Digital Beamforming With Low-Resolution ADCs for Multiple Users and Imperfect CSI,”IEEE Journal on Selected Topics in Signal Processing,vol.12,no.3,2018,pp.484-498.
[19]J.Mo,A.Alkhateeb,S.Abu-Surra,and R.W.Heath,“Hybrid architectures with few-bit adc receivers:Achievable rates and energy-rate tradeoffs,”IEEE Transactions on Wireless Communications,vol.16,no.4,April 2017,pp.2274-2287.
[20]J.Singh,O.Dabeer,and U.Madhow,“Communication limits with low precision analog-to-digital conversion at the receiver,”in 2007 IEEEInternational Conference on Communications,June 2007,pp.6269-6274.
[21]J.Mo and R.W.Heath,“Capacity analysis of one-bit quantized mimo systems with transmitter channel state information,”IEEE Transactions on Signal Processing,vol.63,no.20,Oct 2015,pp.5498-5512.
[22]J.H.Mo,A.Alkhateeb,S.Abu-Surra,and R.W.Heath,“Hybrid Archi-tectures With Few-Bit ADC Receivers:Achievable Rates and Energy-Rate Tradeoffs,”IEEE Transactions on Wireless Communications,vol.16,no.4,2017,pp.2274-2287.
[23]J.Y.Zhang,L.L.Dai,Z.Y.He,S.Jin,and X.Li,“Performance Analysis of Mixed-ADC Massive MIMO Systems Over Rician Fading Channels,”Ieee Journal on Selected Areas In Communications,vol.35,no.6,2017,pp.1327-1338.
[24]P.Dong,H.Zhang,W.Xu,G.Y.Li,and X.You,“Performance Analysis of Multiuser Massive MIMO With Spatially Correlated Channels Using Low-Precision ADC,”IEEE Communications Letters,vol.22,no.1,jan 2018,pp.205-208.
[25]T.E.Bogale and L.B.Le,“Beamforming for multiuser massive mimo systems:Digital versus hybrid analog-digital,”in 2014 IEEE Global Communications Conference,Dec 2014,pp.4066-4071.
[26]L.Fan,S.Jin,C.K.Wen,and H.Zhang,“Uplink achievable rate for massive mimo systems with low-resolution adc,”IEEE Communications Letters,vol.19,no.12,Dec 2015,pp.2186-2189.
[27]M.Kraemer,D.Dragomirescu,and R.Plana,“Design of a very low-power,low-cost 60 ghz receiver front-end implemented in 65 nm cmos technology,”International Journal of Microwave&Wireless Technologies,vol.3,no.2,2011,pp.131-138.
[28]L.Long,“Energy-efficient 60 ghz phased-array design for multi-gb/s communication systems,”Ph.D.dissertation,Dept.Elect.Eng.Comput.Sci.,Univ.California,Berkeley,Berkeley,2014.
[29]R.Mendez-Rial,C.Rusu,N.Gonzalez-Prelcic,A.Alkhateeb,and R.W.Heath,“Hybrid MIMOArchitectures for Millimeter Wave Communications:Phase Shifters or Switches?”IEEE Access,vol.4,2016,pp.247-267.