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- 1. Topics in Digital CommunicationsFundamentals of MIMOTechnology and SpatialMultiplexing© 2012 Fuyun Lingfling@twinclouds.comFundamentals of MIMOTechnology and SpatialMultiplexingFuyun Ling
- 2. Topics in Digital CommunicationsOutline• Introduction• Efficiency of MIMO Data Transmission with SpatialMultiplexing• Basic Forms of MIMO Transmission and Reception• MIMO Receivers – Complexity Reduction• Examples of MIMO Systems• Additional Discussion and Remarks• Acknowledgement© 2012 Fuyun Lingfling@twinclouds.com• Introduction• Efficiency of MIMO Data Transmission with SpatialMultiplexing• Basic Forms of MIMO Transmission and Reception• MIMO Receivers – Complexity Reduction• Examples of MIMO Systems• Additional Discussion and Remarks• Acknowledgement2
- 3. Topics in Digital CommunicationsIntroduction© 2012 Fuyun Lingfling@twinclouds.com3
- 4. Topics in Digital CommunicationsWhat is MIMO• MIMO: Multiple Input/Multiple Output Systems– Doesn’t have to be wireless• Degenerated forms:SIMO MISO SISO• MIMO can provide multiple independent channels(spatial multiplexing).– SIMO and MISO only provide diversity over a single channel© 2012 Fuyun Lingfling@twinclouds.com• MIMO: Multiple Input/Multiple Output Systems– Doesn’t have to be wireless• Degenerated forms:SIMO MISO SISO• MIMO can provide multiple independent channels(spatial multiplexing).– SIMO and MISO only provide diversity over a single channelRev. 06/2012 4
- 5. Topics in Digital CommunicationsHistory of MIMO• Early Results– A.R. Kaye and D.A. George (1970)• First Description of MIMO Channels– Branderburg and Wyner (1974)• Capacity Analysis– W. van Etten (1975, 1976)• Receiver Structures– Arogyaswami Paulraj and Thomas Kailath (1993, 1994)• Concept of Spatial Multiplexing– Telatar (1995)• MIMO Channel Capacity© 2012 Fuyun Lingfling@twinclouds.com• Early Results– A.R. Kaye and D.A. George (1970)• First Description of MIMO Channels– Branderburg and Wyner (1974)• Capacity Analysis– W. van Etten (1975, 1976)• Receiver Structures– Arogyaswami Paulraj and Thomas Kailath (1993, 1994)• Concept of Spatial Multiplexing– Telatar (1995)• MIMO Channel CapacityRev. 06/2012 5
- 6. Topics in Digital CommunicationsHistory of MIMO (cont.)• Major Re-Introduction of MIMO Concepts and Systems– Greg Raleigh and Gerard J. Foschini (1996)• Described a practical system with “Layered Space-TimeArchitecture” and detailed analysis– Bell Labs announcement on BLAST MIMO technology (1998)• First demonstrated spatial multiplexing in laboratory prototype• Caught industry’s attention on the MIMO technology• Started new development wave• The title is a little vague to cause some misinterpretation– Caused more interest due to the misunderstanding– Nothing was wrong in the text© 2012 Fuyun Lingfling@twinclouds.com• Major Re-Introduction of MIMO Concepts and Systems– Greg Raleigh and Gerard J. Foschini (1996)• Described a practical system with “Layered Space-TimeArchitecture” and detailed analysis– Bell Labs announcement on BLAST MIMO technology (1998)• First demonstrated spatial multiplexing in laboratory prototype• Caught industry’s attention on the MIMO technology• Started new development wave• The title is a little vague to cause some misinterpretation– Caused more interest due to the misunderstanding– Nothing was wrong in the textRev. 06/2012 6
- 7. Topics in Digital CommunicationsHistory of MIMO (cont.)• Practical Development– Iospan Wireless Inc. developed the first commercial system inthat used MIMO with OFDM (2001)– Airgo Networks developed an IEEE 802.11n precursorimplementation based on MIMO-OFDM (2005)– MIMO-OFDM in IEEE 802.11n standard (development from2006)– MIMO-OFDM in IEEE 802.16e (WiMax) standard (developmentfrom 2006)– MIMO-OFDM in 3GPP HSDPA, LTE standards (developmentfrom 2008)© 2012 Fuyun Lingfling@twinclouds.com• Practical Development– Iospan Wireless Inc. developed the first commercial system inthat used MIMO with OFDM (2001)– Airgo Networks developed an IEEE 802.11n precursorimplementation based on MIMO-OFDM (2005)– MIMO-OFDM in IEEE 802.11n standard (development from2006)– MIMO-OFDM in IEEE 802.16e (WiMax) standard (developmentfrom 2006)– MIMO-OFDM in 3GPP HSDPA, LTE standards (developmentfrom 2008)Rev. 06/2012 7
- 8. Topics in Digital CommunicationsKey Features of MIMO• Providing Spatial Diversity– Not unique, SIMO and MISO can also provide spatial diversty• SIMO – Receiver diversity• MISO – Transmitter diversity• Providing Spatial Multiplexing– Unique to MIMO– MIMO system can create N, up to min(Nt, Nr), independentparallel channels– Essential for achieving high spectrum efficiency (capacity >1bit/Hz) at high SNR– Spatial Multiplexing may not be advantageous in low SNRenvironment© 2012 Fuyun Lingfling@twinclouds.com• Providing Spatial Diversity– Not unique, SIMO and MISO can also provide spatial diversty• SIMO – Receiver diversity• MISO – Transmitter diversity• Providing Spatial Multiplexing– Unique to MIMO– MIMO system can create N, up to min(Nt, Nr), independentparallel channels– Essential for achieving high spectrum efficiency (capacity >1bit/Hz) at high SNR– Spatial Multiplexing may not be advantageous in low SNRenvironmentRev. 06/2012 8
- 9. Topics in Digital CommunicationsEfficiency of MIMO DataTransmission with SpatialMultiplexing© 2012 Fuyun Lingfling@twinclouds.comEfficiency of MIMO DataTransmission with SpatialMultiplexingRev. 06/2012 9
- 10. Topics in Digital CommunicationsSpectral Efficiency of Single Channel Transmission• System Capacity from Information Theory– Shannon’s unconstrained, bandwidth-limited channel capacity forthe ideal AWGN channel with arbitrary inputs isC = log2(1 + SNR)• C is in unit of bit/(second*Hz) per use (I.e. per channel)• At low spectral efficiency, i.e., low SNR: C ≈ SNR/ln 2 (linear)• At high spectral efficiency, i.e, C and SNR are large:C ≈ log2(SNR) (~ 3 dB, or double SNR, per bit)• Example:– C = 1 => SNR = 1 (0 dB);– C = 5 => SNR = 31 (14.9 dB);– C = 10 => SNR = 1023 (30.1 dB);– C = 15 => SNR = 32767 (45.2 dB: difficult to achieve!);– Conclusion: difficult to achieve very high spectral efficiencytransmission with a single channel.© 2012 Fuyun Lingfling@twinclouds.com• System Capacity from Information Theory– Shannon’s unconstrained, bandwidth-limited channel capacity forthe ideal AWGN channel with arbitrary inputs isC = log2(1 + SNR)• C is in unit of bit/(second*Hz) per use (I.e. per channel)• At low spectral efficiency, i.e., low SNR: C ≈ SNR/ln 2 (linear)• At high spectral efficiency, i.e, C and SNR are large:C ≈ log2(SNR) (~ 3 dB, or double SNR, per bit)• Example:– C = 1 => SNR = 1 (0 dB);– C = 5 => SNR = 31 (14.9 dB);– C = 10 => SNR = 1023 (30.1 dB);– C = 15 => SNR = 32767 (45.2 dB: difficult to achieve!);– Conclusion: difficult to achieve very high spectral efficiencytransmission with a single channel.Rev. 06/2012 10
- 11. Topics in Digital CommunicationsMIMO for High Spectral Efficiency Transmission• MIMO and Spatial Multiplexing– In proper environments, a MIMO system can create multipleindependent parallel channels from Spatial Multiplexing• The number (N) of such channels is ≤ min(NTx, NRx)– In the ideal case, these channels have the same magnitudesand SNRs• To fairly compare with non-MIMO case, we assume total transmittedpower are the same (the same total interference power to othercells) in both cases, i.e., each channel has an SNRMIMO = SNR/N.– The total Spectral Efficiency is• At low SNRsince© 2012 Fuyun Lingfling@twinclouds.com• MIMO and Spatial Multiplexing– In proper environments, a MIMO system can create multipleindependent parallel channels from Spatial Multiplexing• The number (N) of such channels is ≤ min(NTx, NRx)– In the ideal case, these channels have the same magnitudesand SNRs• To fairly compare with non-MIMO case, we assume total transmittedpower are the same (the same total interference power to othercells) in both cases, i.e., each channel has an SNRMIMO = SNR/N.– The total Spectral Efficiency is• At low SNRsinceRev. 06/2012 1112 20log (1 ) log (1 / )NTotal inC SNR N SNR N /( 0), ln2ln2TotalN SNR NSNR C SNR ln(1 ) 0x x for x
- 12. Topics in Digital CommunicationsSpectral Efficiency with Spatial Multiplexing(N = 1, 2, and 4)-20-100102030405060700.01 0.1 1 10 100SNR(dB)# of bits per HzRequred SNR at different bits/HzN = 1N = 2N = 4© 2012 Fuyun Lingfling@twinclouds.com-20-100102030405060700.01 0.1 1 10 100SNR(dB)# of bits per HzRequred SNR at different bits/HzN = 1N = 2N = 4Rev. 06/2012 12
- 13. Topics in Digital CommunicationsConclusions on Transmission SpectralEfficiency using MIMO• In high spectral efficiency region (high SNR), 3 dB SNRincrease is needed for the increase of each bit per Hz.– It’s difficult to achieve high spectral efficiency if only a singlechannel is used• With spatial multiplexing, MIMO can create multipleparallel channels to achieve high efficiency transmission– It will be most efficient in a rich scattering environment, wherethe magnitudes of these channels have small dispersion• With constant transmitted power (constant interference),MIMO does not improve the efficiency at low SNRcomparing to the single channel case– MIMO is much more effective in high SNR regions© 2012 Fuyun Lingfling@twinclouds.com• In high spectral efficiency region (high SNR), 3 dB SNRincrease is needed for the increase of each bit per Hz.– It’s difficult to achieve high spectral efficiency if only a singlechannel is used• With spatial multiplexing, MIMO can create multipleparallel channels to achieve high efficiency transmission– It will be most efficient in a rich scattering environment, wherethe magnitudes of these channels have small dispersion• With constant transmitted power (constant interference),MIMO does not improve the efficiency at low SNRcomparing to the single channel case– MIMO is much more effective in high SNR regionsRev. 06/2012 13
- 14. Topics in Digital CommunicationsBasic Forms of MIMOTransmission and reception© 2012 Fuyun Lingfling@twinclouds.comBasic Forms of MIMOTransmission and receptionRev. 06/2012 14
- 15. Topics in Digital CommunicationsHigh Level Description of a MIMO System• Block Diagram of a MIMO System• Matrix Representation( ) Mod. Symbolsi k s© 2012 Fuyun Lingfling@twinclouds.com• Block Diagram of a MIMO System• Matrix RepresentationRev. 06/2012 15 0 1( ) ( ) ( ), ( ) ( ) ( )r r t t r t tTN N N N N N Nk k k k k k y H x n x s s( ) Mod. Symbolsi k s
- 16. Topics in Digital CommunicationsChannel Matrix and Its Estimation• To utilize the potential of MIMO, it is essential toaccurately know the channel matrix (or simply H).• The channel matrix is usually estimated using knownsymbols embedded in the transmitted data squence– Called reference symbols or pilots• Here we assume the elements of H are scalars• The estimation is done in the receiver. Thus it is knowthere.• To fully utilize the spatial multiplexing, it is desirable tofeedback the parameters of H to the transmitter– Require to using part of the reverse channelr tN NH© 2012 Fuyun Lingfling@twinclouds.com• To utilize the potential of MIMO, it is essential toaccurately know the channel matrix (or simply H).• The channel matrix is usually estimated using knownsymbols embedded in the transmitted data squence– Called reference symbols or pilots• Here we assume the elements of H are scalars• The estimation is done in the receiver. Thus it is knowthere.• To fully utilize the spatial multiplexing, it is desirable tofeedback the parameters of H to the transmitter– Require to using part of the reverse channelRev. 06/2012 16
- 17. Topics in Digital CommunicationsChannel Known to the Transmitter: Precoding• Using Singular Value Decomposition, the matrix H canbe diagnalized by orthogonal matrices U and V suchthat:li‘s are the singular values of H• Thus,• By transmitting instead ofand pre-multiply the receive signal vector byr t r r r t t tN N N N N N N N H U V1 0 0 00 0 00 0 00 0 0 00 0 0 0r tN N N © 2012 Fuyun Lingfling@twinclouds.com• Using Singular Value Decomposition, the matrix H canbe diagnalized by orthogonal matrices U and V suchthat:li‘s are the singular values of H• Thus,• By transmitting instead ofand pre-multiply the receive signal vector byRev. 06/2012 171 0 0 00 0 00 0 00 0 0 00 0 0 0r tN N N ( ) ( )t t t tHN N N Nk kx V x ( )tN kxr rHN NU( ) ( ) ( )r r r r t t t t rN N N N N N N N Nk k k y U V x n
- 18. Topics in Digital CommunicationsPrecoding (cont.)• The transformed received signal vector becomes:• The i-the elements of : , i.e., Nparallel scalar channels!• V is orthonormal – No change in noise statistics• Water-filling weighting – Achieving channel total capacity• Precoding require the transmitter has the knowledge ofthe channel, which may or may not be easy to achieve– Approximate knowledge of the channel also helps• System capacity can be achieve by water-fillingweighting each channel (associated with li).( ) ( ) ( )( ) ( )r r r r r r t t t t t t r r rr t t rH H HN N N N N N N N N N N N N N NN N N Nk k kk k y U U V V x U nx n( ) ( ) ( )i i i iy k s k n k ( )rN ky© 2012 Fuyun Lingfling@twinclouds.com• The transformed received signal vector becomes:• The i-the elements of : , i.e., Nparallel scalar channels!• V is orthonormal – No change in noise statistics• Water-filling weighting – Achieving channel total capacity• Precoding require the transmitter has the knowledge ofthe channel, which may or may not be easy to achieve– Approximate knowledge of the channel also helps• System capacity can be achieve by water-fillingweighting each channel (associated with li).Rev. 06/2012 18
- 19. Topics in Digital CommunicationsLinear MIMO Receivers• Consider the basic MIMO system equation:• We first consider the zero forcing form– Premultiply y by HH we havewhere is an Nt x Nt square matrix– Premultiply by the (psudo)inverse of R, x is recovered as– When n = 0,• This is the zero forcing solution of Linear MIMO receiver(indices dropped for clarity) y Hx nH y H y Rx n© 2012 Fuyun Lingfling@twinclouds.com• Consider the basic MIMO system equation:• We first consider the zero forcing form– Premultiply y by HH we havewhere is an Nt x Nt square matrix– Premultiply by the (psudo)inverse of R, x is recovered as– When n = 0,• This is the zero forcing solution of Linear MIMO receiverRev. 06/2012 19H y H y Rx nHR H Hy1 1ˆ H x R H y x R nˆ x x
- 20. Topics in Digital CommunicationsLinear MIMO Receivers (cont.)• Derivation of MMSE MIMO receiver– Consider again– To determine coefficient matrix A, such that, the estimate of x,minimize the norm of the error vector, i.e., minimize– A can be determined by taking derivative of ewith respect to Aor using orthogonal principle, i.e.:– Thus A satisfies:where we assume , and the noise is white.– Finally y Hx nˆMMSE x Ay2| | | |HE e E Ay x© 2012 Fuyun Lingfling@twinclouds.com• Derivation of MMSE MIMO receiver– Consider again– To determine coefficient matrix A, such that, the estimate of x,minimize the norm of the error vector, i.e., minimize– A can be determined by taking derivative of ewith respect to Aor using orthogonal principle, i.e.:– Thus A satisfies:where we assume , and the noise is white.– FinallyRev. 06/2012 20 0H H H HE E E E ey Ay x y A yy xy 1 12H H H HE E A xy yy H HH IHE xx I HE nx 0 12 2ˆ , ( ) ~H H H HMMSE r rN N x AH y H HH I y HH I
- 21. Topics in Digital CommunicationsLinear MIMO Receivers (cont.)• Discussions of zero forcing (ZF) and MMSE receivers– ZF receiver generate an unbiased estimate of Tx symbols– It’s main problem is noise enhancement– MMSE receiver provides better SNR at output– The estimate is biased• Not a serious problem for PSK Tx symbols• Need bias removal for QAM signals– It can be show that MMSE receiver converges to as ZF receiverwhen SNR goes to infinity, i.e.,– Linear receivers do not provide as good performance as non-linear receivers© 2012 Fuyun Lingfling@twinclouds.com• Discussions of zero forcing (ZF) and MMSE receivers– ZF receiver generate an unbiased estimate of Tx symbols– It’s main problem is noise enhancement– MMSE receiver provides better SNR at output– The estimate is biased• Not a serious problem for PSK Tx symbols• Need bias removal for QAM signals– It can be show that MMSE receiver converges to as ZF receiverwhen SNR goes to infinity, i.e.,– Linear receivers do not provide as good performance as non-linear receiversRev. 06/2012 21 212 10lim ( )H H H H HH I H H H
- 22. Topics in Digital CommunicationsMaximum Likelihood (ML) Estimator• Recall:• The ML estimator determines , which minimizeswhere , i.e., its elements are Tx symbols• This is a constraint LS estimation problem– It is nonlinear and its complexity is (NP)-hard– In the receivers, , i.e., its elements are complex numbers• The performance of the ML estimator is much better thanthe linear receivers. However, it is also much morecomplex than the linear receivers– Complexity on order of KNt (K – symbol order) y Hx nˆMLy HxˆMLxˆ tNML x s© 2012 Fuyun Lingfling@twinclouds.com• Recall:• The ML estimator determines , which minimizeswhere , i.e., its elements are Tx symbols• This is a constraint LS estimation problem– It is nonlinear and its complexity is (NP)-hard– In the receivers, , i.e., its elements are complex numbers• The performance of the ML estimator is much better thanthe linear receivers. However, it is also much morecomplex than the linear receivers– Complexity on order of KNt (K – symbol order)Rev. 06/2012 22ˆ tNML x
- 23. Topics in Digital CommunicationsQRD ML Estimator• Prerequisite: QR decomposition (often used in MIMO)– Assuming H has a rank of Nt, we have: H = QRwhere Q is an Nr x Nt orthnormal matrix, R is an Nt x Nt uppertriangular matrix.• Solution:– Since Q is orthnormal, we have:– Can be viewed as an Nt layer system© 2012 Fuyun Lingfling@twinclouds.com• Prerequisite: QR decomposition (often used in MIMO)– Assuming H has a rank of Nt, we have: H = QRwhere Q is an Nr x Nt orthnormal matrix, R is an Nt x Nt uppertriangular matrix.• Solution:– Since Q is orthnormal, we have:– Can be viewed as an Nt layer systemRev. 06/2012 232 22 2200 01 0 10 02 1 11 1 1 11 11 1ˆ ˆ ˆ ˆ( )ˆˆ0ˆˆ0 0ttt tt tH HML ML ML MLNNMLN NN Nr r ry sy r r sy sr y Hx y QRx Q Q y Rx Q y Rxy Rx
- 24. Topics in Digital CommunicationsQRD ML Estimator (cont.)– Each layer has a metric function:– The objective of the estimator is to find a sequence of thatminimizes the overall metric– Tree search can be used to find the ML solution2 20 1 1 1 1 1 1 2 1 2 2 2 2 1 2 1ˆ ˆ ˆ ˆ ˆ ˆ( ) , ( , )t t t t t t t t t t t t t tN N N N N N N N N N N N N Ng s y r s g s s y r s r s 21 0 1 1 0 00 0 01 1 0 1 1ˆ ˆ ˆ ˆ ˆ ˆ( , , )t t t tN N N Ng s s s y r s r s r s 0 1 1 2 1 1 0 1 1ˆ ˆ ˆ ˆ ˆ ˆ( ) ( , ) ( , , )t t t t tN N N N Ng s g s s g s s s ˆ{ }is© 2012 Fuyun Lingfling@twinclouds.com– Each layer has a metric function:– The objective of the estimator is to find a sequence of thatminimizes the overall metric– Tree search can be used to find the ML solutionRev. 06/2012 240 1 1 2 1 1 0 1 1ˆ ˆ ˆ ˆ ˆ ˆ( ) ( , ) ( , , )t t t t tN N N N Ng s g s s g s s s
- 25. Topics in Digital CommunicationsQRD ML Estimator (cont.)• QRD Complexity increases exponentially with the lengthof Tx data vector and the Tx data symbol size– e.g. for Nt = 4 and QAM64 (K=64), 64+642+643+644 = 17,043,520metrics need to be computed.– Practically impossible for large alphabet size (K) and long vector• The result is the ML estimate of the Tx data vector.• In a coded system it is necessary to generate soft bitmetrics in order to achieve better system performance– Generating soft bit metrics (LLRs) for decoding:• The values in exp() were calculated above• It’s very computationally intense ~ 2xlog2(K)xKNt© 2012 Fuyun Lingfling@twinclouds.com• QRD Complexity increases exponentially with the lengthof Tx data vector and the Tx data symbol size– e.g. for Nt = 4 and QAM64 (K=64), 64+642+643+644 = 17,043,520metrics need to be computed.– Practically impossible for large alphabet size (K) and long vector• The result is the ML estimate of the Tx data vector.• In a coded system it is necessary to generate soft bitmetrics in order to achieve better system performance– Generating soft bit metrics (LLRs) for decoding:• The values in exp() were calculated above• It’s very computationally intense ~ 2xlog2(K)xKNtRev. 06/2012 25 2 22 21 1: ( ) 1 : ( ) 1ln exp ln expk ks sLLR x x x xy Hx y Hx
- 26. Topics in Digital CommunicationsMIMO Receivers – ComplexityReduction© 2012 Fuyun Lingfling@twinclouds.comMIMO Receivers – ComplexityReductionRev. 06/2012 26
- 27. Topics in Digital CommunicationsGeneral Discussion• MIMO linear receivers (ZF and MMSE) are simple toimplement. However, their performance are relativelypoor comparing to ML receiver• Practical MIMO receivers has been developed to bridgethe gap between these two extremes including:– Zero-Forcing receiver with decision feedback– QRD ML receiver with Sphere Detector (QRD SD)– M-algorithm based QRC ML receiver (QRD-M)– Lattice reduction• There are many variations of these implementations• The simplified QRD methods are direct consequences ofcorresponding results from investigations ofsimplification of MLSE equalizers in 1970-80s© 2012 Fuyun Lingfling@twinclouds.com• MIMO linear receivers (ZF and MMSE) are simple toimplement. However, their performance are relativelypoor comparing to ML receiver• Practical MIMO receivers has been developed to bridgethe gap between these two extremes including:– Zero-Forcing receiver with decision feedback– QRD ML receiver with Sphere Detector (QRD SD)– M-algorithm based QRC ML receiver (QRD-M)– Lattice reduction• There are many variations of these implementations• The simplified QRD methods are direct consequences ofcorresponding results from investigations ofsimplification of MLSE equalizers in 1970-80sRev. 06/2012 27
- 28. Topics in Digital CommunicationsZero-Forcing with Decision Feedback (ZF-DF)• Zero-Forcing receiver can also be expressed in the QRDform, namelyi.e., , to be solved using backward substitution– A decision is made in each step of backward substitution;– The decision is used in next stepH y Hx n QRx n Q y y Rx n1ˆ x R y© 2012 Fuyun Lingfling@twinclouds.com• Zero-Forcing receiver can also be expressed in the QRDform, namelyi.e., , to be solved using backward substitution– A decision is made in each step of backward substitution;– The decision is used in next stepRev. 06/2012 28
- 29. Topics in Digital CommunicationsQRD-M• In the ZF-DF, one decision is made in each stage (onesurvivor path)• The performance can be improved if more than one (M)survivor paths with smallest cumulative metrics aresaved• The M survivors are extended to MK paths (K = symbolorder) to next stage.• The M paths with smallest cumulative metrics are saved• Repeat the above two steps until detection is completed• QRD-M has fixed computational complexity• Performance depends on M– The larger M, the better performance, but the higher complexity© 2012 Fuyun Lingfling@twinclouds.com• In the ZF-DF, one decision is made in each stage (onesurvivor path)• The performance can be improved if more than one (M)survivor paths with smallest cumulative metrics aresaved• The M survivors are extended to MK paths (K = symbolorder) to next stage.• The M paths with smallest cumulative metrics are saved• Repeat the above two steps until detection is completed• QRD-M has fixed computational complexity• Performance depends on M– The larger M, the better performance, but the higher complexityRev. 06/2012 29
- 30. Topics in Digital CommunicationsQRD-SD (Sphere Detector)• In QRD-SD, the paths with cumulative metrics smallerthan a predetermined threshold are saved at each stage• The survivors are extended to PK paths (P – number ofsurvived paths, K – symbol order) to next stage.• Again, the paths with cumulative metrics smaller than apredetermined threshold are saved• Repeat the above two steps until detection is completed(The end nodes of the survived paths are in a spherearound the received signal points)• The computational complexity of QRD-SD is not fixed• The performance and complexity depend on the threshold– The higher threshold, the better performance but also the highercomplexity© 2012 Fuyun Lingfling@twinclouds.com• In QRD-SD, the paths with cumulative metrics smallerthan a predetermined threshold are saved at each stage• The survivors are extended to PK paths (P – number ofsurvived paths, K – symbol order) to next stage.• Again, the paths with cumulative metrics smaller than apredetermined threshold are saved• Repeat the above two steps until detection is completed(The end nodes of the survived paths are in a spherearound the received signal points)• The computational complexity of QRD-SD is not fixed• The performance and complexity depend on the threshold– The higher threshold, the better performance but also the highercomplexityRev. 06/2012 30
- 31. Topics in Digital CommunicationsQRD Estimator Examples• QRD-ML• ZF-DF© 2012 Fuyun Lingfling@twinclouds.com• QRD-ML• ZF-DFRev. 06/2012 31
- 32. Topics in Digital CommunicationsQRD Estimator Examples (cont.)• QRD-M (M = 2)• QRD-SD (T = 5)© 2012 Fuyun Lingfling@twinclouds.com• QRD-M (M = 2)• QRD-SD (T = 5)Rev. 06/2012 32
- 33. Topics in Digital CommunicationsMLD Complexity Reduction for Small Nt• In [LA07] a method to reduce MLD complexity for smallNt was described, it is summarized as follows:(1) Decompose H and x as:(2) We rewrite:(3) Determine MNt-1 that minimize for eachdistinctive as:a)b) Find the closest constellation point to byslicing as the estimate of s1.c) Find the smallest one in the MNt-1 metrics with thecorresponding and– The complexity is proportional to MNt-1 instead of MNt 1,ts H h H x s 221s y Hx y Hs h 1,ˆs s21s y Hs h s© 2012 Fuyun Lingfling@twinclouds.com• In [LA07] a method to reduce MLD complexity for smallNt was described, it is summarized as follows:(1) Decompose H and x as:(2) We rewrite:(3) Determine MNt-1 that minimize for eachdistinctive as:a)b) Find the closest constellation point to byslicing as the estimate of s1.c) Find the smallest one in the MNt-1 metrics with thecorresponding and– The complexity is proportional to MNt-1 instead of MNtRev. 06/2012 3321s y Hs h s 1 11 1( ) ( ) ( )H H H Hs s h h h y Hs h h h h y Hs 1( ) ( )H Hh h h y Hs 1ˆs1ˆs s
- 34. Topics in Digital CommunicationsMLD Complexity Reduction for Small Nt (cont.)• This approach is most effective for small Nt and largeconstellation size, e.g, two antenna with 64QAM• Bit metrics can be computed similar to full MLD• The result is optimal (no approximation)• It was originally proposed in[AL07] Y. Lomnitz and D. Andelman, “Efficient maximumlikelihood detector for MIMO systems with small numberof streams,” Electronics Letters, pp. 1212-1214, Vol. 43,No. 22, Oct. 2007.© 2012 Fuyun Lingfling@twinclouds.com• This approach is most effective for small Nt and largeconstellation size, e.g, two antenna with 64QAM• Bit metrics can be computed similar to full MLD• The result is optimal (no approximation)• It was originally proposed in[AL07] Y. Lomnitz and D. Andelman, “Efficient maximumlikelihood detector for MIMO systems with small numberof streams,” Electronics Letters, pp. 1212-1214, Vol. 43,No. 22, Oct. 2007.Rev. 06/2012 34
- 35. Topics in Digital CommunicationsSoft Decoding Bit Metrics (LLRs)• Generating soft bit metrics (LLRs) for decoding coded data,has the similar form as the QRD-ML case:– where the sk’s are only taking from the survived paths• Further simplification: Dual-Max or Max-Log approximation– Also applicable for the QRD-ML case– Good approximation at high SNR• In both cases, if sk(x) = 1, or sk(x) = −1 does not exist, it willtake the smallest possible value. 2 22 21 1: ( ) 1 : ( ) 1ln exp ln expk ks sLLR x x x xy Hx y Hx© 2012 Fuyun Lingfling@twinclouds.com• Generating soft bit metrics (LLRs) for decoding coded data,has the similar form as the QRD-ML case:– where the sk’s are only taking from the survived paths• Further simplification: Dual-Max or Max-Log approximation– Also applicable for the QRD-ML case– Good approximation at high SNR• In both cases, if sk(x) = 1, or sk(x) = −1 does not exist, it willtake the smallest possible value.Rev. 06/2012 35 2 22 21 1( ) 1 ( ) 1max maxk ks sLLR x xy Hx y Hx
- 36. Topics in Digital CommunicationsExamples of MIMO Systems© 2012 Fuyun Lingfling@twinclouds.comRev. 06/2012 36
- 37. Topics in Digital CommunicationsBLAST and Its Variations• BLAST stands for Bell Labs Layered Space Time• It was first implemented in the lab environmentdemonstrating the advantage of MIMO (1996 – 1998)• Later designs were based the same concept withimprovements• D-BLAST (D is for Diagonal) was first developed before1998• V-BLAST (V is for Vertical) was soon developedafterwards (1998) to simplify implementation– Used in most practical designs• Modified D-BLAST to take advantage of both© 2012 Fuyun Lingfling@twinclouds.com• BLAST stands for Bell Labs Layered Space Time• It was first implemented in the lab environmentdemonstrating the advantage of MIMO (1996 – 1998)• Later designs were based the same concept withimprovements• D-BLAST (D is for Diagonal) was first developed before1998• V-BLAST (V is for Vertical) was soon developedafterwards (1998) to simplify implementation– Used in most practical designs• Modified D-BLAST to take advantage of bothRev. 06/2012 37
- 38. Topics in Digital CommunicationsBLAST (cont.)• D-BLAST– Layered design with the number of layers equal to the number ofantennas– Each layer coded independently– Advantages: Fully utilize spatial and time diversity– Disadvantages: Multiple decoders, increased complexity© 2012 Fuyun Lingfling@twinclouds.com• D-BLAST– Layered design with the number of layers equal to the number ofantennas– Each layer coded independently– Advantages: Fully utilize spatial and time diversity– Disadvantages: Multiple decoders, increased complexityRev. 06/2012 38
- 39. Topics in Digital CommunicationsBLAST (cont.)• V-BLAST– Can be implemented with one encoder per antenna or with only oneencoder and one decoder– Encoded data assigned to multiple antennas and over time– Advantages: Simplified implementation, good performance in AWGN– Disadvantages: Lower time diversity gain– Modified D-BLAST: Assign the encoded data (single encoder)diagonally and interleaved in time© 2012 Fuyun Lingfling@twinclouds.com• V-BLAST– Can be implemented with one encoder per antenna or with only oneencoder and one decoder– Encoded data assigned to multiple antennas and over time– Advantages: Simplified implementation, good performance in AWGN– Disadvantages: Lower time diversity gain– Modified D-BLAST: Assign the encoded data (single encoder)diagonally and interleaved in timeRev. 06/2012 39
- 40. Topics in Digital CommunicationsMIMO in OFDM Based Systems• MIMO is most widely used in OFDM Systems– MIMO is most suitable for single path (flat fading) channels– OFDM can be viewed as a collection of multiple parallel singlepath channels• Each subcarrier is a single path system• Examples of OFDM Systems with MIMO– 802.11n/ac– LTE– WiMax© 2012 Fuyun Lingfling@twinclouds.com• MIMO is most widely used in OFDM Systems– MIMO is most suitable for single path (flat fading) channels– OFDM can be viewed as a collection of multiple parallel singlepath channels• Each subcarrier is a single path system• Examples of OFDM Systems with MIMO– 802.11n/ac– LTE– WiMaxRev. 06/2012 40
- 41. Topics in Digital CommunicationsMIMO in OFDM Systems (cont.)• 802.11n/ac– Spatial multiplexing with 2, 3, or 4 streams• In 802.11, # of streams is the rank of spatial multiplexing• 2x is mandatory, 3x and 4x are optional• 11ac can have up to 8 streams– Modulation: BPSK, QPSK, 16QAM, and 64 QAM– FFT size: 64 (20 MHz), 128 (40MHz)– Transmitter procedure:• Single coded bit sequence mapped into multiple spatial (bit)streams in round-robin fashion• Each bit stream goes through interleaving, mod. symbolmapping, space-time coding and iFFT blocks to yield OFDMsignal for transmission– No special layering processing performed© 2012 Fuyun Lingfling@twinclouds.com• 802.11n/ac– Spatial multiplexing with 2, 3, or 4 streams• In 802.11, # of streams is the rank of spatial multiplexing• 2x is mandatory, 3x and 4x are optional• 11ac can have up to 8 streams– Modulation: BPSK, QPSK, 16QAM, and 64 QAM– FFT size: 64 (20 MHz), 128 (40MHz)– Transmitter procedure:• Single coded bit sequence mapped into multiple spatial (bit)streams in round-robin fashion• Each bit stream goes through interleaving, mod. symbolmapping, space-time coding and iFFT blocks to yield OFDMsignal for transmission– No special layering processing performedRev. 06/2012 41
- 42. Topics in Digital CommunicationsMIMO in OFDM Systems (cont.)• MIMO in LTE Release 8– There are 7 downlink “MIMO” modes in LTE Rel. 8– Only Modes 3 and 4 can support spatial multiplexing– The maximum number of Layers, i.e., the rank of the MIMOspatial multiplexing, is 4– The data is organized as resource blocks, which consist ofmultiple OFDM symbols and multiple subcarriers in each of theOFDM symbols– The block of coded bits of each code word are scrambled andmapped to modulation symbols. These modulation symbols ofone or two codewords are mapped to one or more layers.• The modulation symbols in each layer are mapped to theresource elements – sequentially in frequency bins from oneOFDM symbol to next.© 2012 Fuyun Lingfling@twinclouds.com• MIMO in LTE Release 8– There are 7 downlink “MIMO” modes in LTE Rel. 8– Only Modes 3 and 4 can support spatial multiplexing– The maximum number of Layers, i.e., the rank of the MIMOspatial multiplexing, is 4– The data is organized as resource blocks, which consist ofmultiple OFDM symbols and multiple subcarriers in each of theOFDM symbols– The block of coded bits of each code word are scrambled andmapped to modulation symbols. These modulation symbols ofone or two codewords are mapped to one or more layers.• The modulation symbols in each layer are mapped to theresource elements – sequentially in frequency bins from oneOFDM symbol to next.Rev. 06/2012 42
- 43. Topics in Digital CommunicationsMIMO in OFDM Systems (cont.)• MIMO in LTE Release 8 (cont.)– Precoding in LTE• To save feedback information on reverse link, code-booksare used for close-loop precoding• LTE Codebooks:– TDD-LTE could use optimal precoding due to the link reciprocityCodebookindexNumber of layers 1 20123 -© 2012 Fuyun Lingfling@twinclouds.com• MIMO in LTE Release 8 (cont.)– Precoding in LTE• To save feedback information on reverse link, code-booksare used for close-loop precoding• LTE Codebooks:– TDD-LTE could use optimal precoding due to the link reciprocity© 2012 Fuyun Ling Rev. 06/2012 43CodebookindexNumber of layers1 20 11211001211 11211111212 j121 jj11213 j121-
- 44. Topics in Digital CommunicationsADDITIONAL DISCUSSION ANDREMARKS© 2012 Fuyun Lingfling@twinclouds.comADDITIONAL DISCUSSION ANDREMARKSRev. 06/2012 44
- 45. Topics in Digital CommunicationsFurther Discussion and Remarks• The most important feature of MIMO technology is that itprovides a practical mean to achieve spatial multiplexing,i.e. creates multiple transmission channels.• With multiple transmission channel, the bits per channelis reduced for the same throughput– With fewer bits per channel, the system will keep in the “linear” channelcapacity region– The SNR per channel is reduced when keeping a constant totaltransmission power– The advantage of statistical multiplexing is mainly in the high SNR/highspectral efficiency region– At low SNR region, there’s not much gains• Practical MIMO system efficiency depends on if thechannel is “rich scattering”© 2012 Fuyun Lingfling@twinclouds.com• The most important feature of MIMO technology is that itprovides a practical mean to achieve spatial multiplexing,i.e. creates multiple transmission channels.• With multiple transmission channel, the bits per channelis reduced for the same throughput– With fewer bits per channel, the system will keep in the “linear” channelcapacity region– The SNR per channel is reduced when keeping a constant totaltransmission power– The advantage of statistical multiplexing is mainly in the high SNR/highspectral efficiency region– At low SNR region, there’s not much gains• Practical MIMO system efficiency depends on if thechannel is “rich scattering”Rev. 06/2012 45
- 46. Topics in Digital CommunicationsFurther Discussion and Remarks (cont.)• When the number of transmitter and/or receiver antennais more than the created channel, a MIMO system canalso have diversity gain– Diversity gain can be obtained by different means and notunique to MIMO– MIMO can most effectively utilize the diversity gain together withobtaining statistical multiplexing as shown by Tse et. al.• MIMO can also be used in multiuser communications(Multiuser MIMO) with the same principle– Communication paths are from Tx antenna arrays to antennason multiple receivers– Multiple channels can be created as long as the channels fromthe Tx antennas to multiple Rx antennas are not correlated© 2012 Fuyun Lingfling@twinclouds.com• When the number of transmitter and/or receiver antennais more than the created channel, a MIMO system canalso have diversity gain– Diversity gain can be obtained by different means and notunique to MIMO– MIMO can most effectively utilize the diversity gain together withobtaining statistical multiplexing as shown by Tse et. al.• MIMO can also be used in multiuser communications(Multiuser MIMO) with the same principle– Communication paths are from Tx antenna arrays to antennason multiple receivers– Multiple channels can be created as long as the channels fromthe Tx antennas to multiple Rx antennas are not correlatedRev. 06/2012 46
- 47. Topics in Digital CommunicationsFurther Discussion and Remarks (cont.)• The MIMO transmitter can be implemented by simplydistributing the coded data bits/symbols to multipleantennas– No special Tx data channel “layering” arrangement arenecessary if so desired• Precoding in a MIMO system can achieve channelcapacity– The transmitter will need to know the channel state information(CSI)– The channel at the opposite direction is used to sent the CSIinformation and thus reduce its capacity, unless it is for a TDDsystem© 2012 Fuyun Lingfling@twinclouds.com• The MIMO transmitter can be implemented by simplydistributing the coded data bits/symbols to multipleantennas– No special Tx data channel “layering” arrangement arenecessary if so desired• Precoding in a MIMO system can achieve channelcapacity– The transmitter will need to know the channel state information(CSI)– The channel at the opposite direction is used to sent the CSIinformation and thus reduce its capacity, unless it is for a TDDsystemRev. 06/2012 47
- 48. Topics in Digital CommunicationsFurther Discussion and Remarks (cont.)• Various receiver structures are discussed– Linear receivers are easier to implement but the gaps betweentheir performances and the optimum are relatively large– Maximum Likelihood (ML) receiver can achieve close to optimalperformance• Brute force implementation of ML detector is practicalimpossible in practice except for simple cases• Simplified, mostly suboptimal, algorithms have been adoptedfrom corresponding simplified method previously developedfor maximum likelihood equalization and other types ofreceivers• QRD is most suitable for ML and approximate ML detectors– Lattice reduction methods was developed for improving linearreceiver performance but not widely used today, due to itscomplexity and performance.© 2012 Fuyun Lingfling@twinclouds.com• Various receiver structures are discussed– Linear receivers are easier to implement but the gaps betweentheir performances and the optimum are relatively large– Maximum Likelihood (ML) receiver can achieve close to optimalperformance• Brute force implementation of ML detector is practicalimpossible in practice except for simple cases• Simplified, mostly suboptimal, algorithms have been adoptedfrom corresponding simplified method previously developedfor maximum likelihood equalization and other types ofreceivers• QRD is most suitable for ML and approximate ML detectors– Lattice reduction methods was developed for improving linearreceiver performance but not widely used today, due to itscomplexity and performance.Rev. 06/2012 48
- 49. Topics in Digital CommunicationsAcknowledgement• This presentation is based many references that I havefound. Because there were so many people contributedto the MIMO technology, It would be impossible to list allof the authors who contributed to the each individualparts discussed in the presentation. Any and all of thematerials presented here should be credited torespective authors and I would like to express mysincere thanks to all of the contributors together here.© 2012 Fuyun Lingfling@twinclouds.com• This presentation is based many references that I havefound. Because there were so many people contributedto the MIMO technology, It would be impossible to list allof the authors who contributed to the each individualparts discussed in the presentation. Any and all of thematerials presented here should be credited torespective authors and I would like to express mysincere thanks to all of the contributors together here.Rev. 06/2012 49

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