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CAPITALS
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On Minimizing the Mean Squared Error In the Presence Of Channel State Information Errors
Gabor Fodor Ericsson Research Royal Institute of Technology (Dept. of Automatic Control)
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Characters for Embedded font: !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~¡¢£¤¥¦§¨©ª«¬®¯°±²³´¶·¸¹º»¼½ÀÁÂÃÄÅÆÇÈËÌÍÎÏÐÑÒÓÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷øùúûüýþÿĀāĂăąĆćĊċČĎďĐđĒĖėĘęĚěĞğĠġĢģĪīĮįİıĶķĹĺĻļĽľŁłŃńŅņŇňŌŐőŒœŔŕŖŗŘřŚśŞşŠšŢţŤťŪūŮůŰűŲųŴŵŶŷŸŹźŻżŽžƒȘșˆˇ˘˙˚˛˜˝ẀẁẃẄẅỲỳ–—‘’‚“”„†‡•…‰‹›⁄€™ĀĀĂĂĄĄĆĆĊĊČČĎĎĐĐĒĒĖĖĘĘĚĚĞĞĠĠĢĢĪĪĮĮİĶĶĹĹĻĻĽĽŃŃŅŅŇŇŌŌŐŐŔŔŖŖŘŘŚŚŞŞŢŢŤŤŪŪŮŮŰŰŲŲŴŴŶŶŹŹŻŻȘș−≤≥fifl
ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰαβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ
ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐəǽẀẁẂẃẄẅỲỳ№
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Minimizing the MSE with CSI Errors | KTH Seminar | 2018-04-25 | Page 2
Mimo evolution
MU-MIMO SU-MIMO
Massive MU-MIMO Massive SU-MIMO Massive multi-layer
MU-MIMO
Multi-layer MU-MIMO
Mor
e an
tenn
as
LTE: Long Term Evolution SU MIMO: Single User Multiple Input Multiple Output MU MIMO: Multiuser Multiple Input Multiple Output
G.Fodor,N.Rajatheva,W.Zirwas,L.Thiele,M.Kurras,K.Guo,A.Tolli,J.H.Sorensen,E.deCarvalho,"AnOverviewofMassiveMIMOTechnologyComponentsinMETIS",IEEECommunicaLonsMagazine,Vol.55,Issue6,pp.155-161,June2017.
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Characters for Embedded font: !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~¡¢£¤¥¦§¨©ª«¬®¯°±²³´¶·¸¹º»¼½ÀÁÂÃÄÅÆÇÈËÌÍÎÏÐÑÒÓÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷øùúûüýþÿĀāĂăąĆćĊċČĎďĐđĒĖėĘęĚěĞğĠġĢģĪīĮįİıĶķĹĺĻļĽľŁłŃńŅņŇňŌŐőŒœŔŕŖŗŘřŚśŞşŠšŢţŤťŪūŮůŰűŲųŴŵŶŷŸŹźŻżŽžƒȘșˆˇ˘˙˚˛˜˝ẀẁẃẄẅỲỳ–—‘’‚“”„†‡•…‰‹›⁄€™ĀĀĂĂĄĄĆĆĊĊČČĎĎĐĐĒĒĖĖĘĘĚĚĞĞĠĠĢĢĪĪĮĮİĶĶĹĹĻĻĽĽŃŃŅŅŇŇŌŌŐŐŔŔŖŖŘŘŚŚŞŞŢŢŤŤŪŪŮŮŰŰŲŲŴŴŶŶŹŹŻŻȘș−≤≥fifl
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ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐəǽẀẁẂẃẄẅỲỳ№
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Related Works (Pilot-to-Data Power Ratio)
› T. Kim and J. G. Andrews, “Optimal Pilot-to-Data Power Ratio for MIMO-OFDM,” IEEE Globecom, St. Louis, MO, USA, Dec. 2005, pp. 1481–1485.
› T. Marzetta, “How Much Training is Needed for Multiuser MIMO ?” IEEE Asilomar Conference on Signals, Systems and Computers (ACSSC) ,pp. 359–363, Jun. 2006.
› C. P. Sukumar and R. M. M. Eltawil, “Joint Power Loading of Data and Pilots in OFDM Using Imperfect Channel State Information at the Transmitter,” in IEEE Global Communications Conference, Nov. 2008, pp. 1–5.
› N. Jindal and A. Lozano, “A Unified Treatment of Optimum Pilot Overhead in Multipath Fading Channels,” IEEE Trans. on Communications, vol. 58, no. 10, pp. 2939–2948, October 2010.
› K. Min, M. Jung, T. Kim, Y. Kim, J. Lee, and S. Choi, “Pilot Power Ratio for Uplink Sum-Rate Maximization in Zero-Forcing Based MU-MIMO Systems with Large Number of Antennas,” in IEEE Vehicular Technology Conference (VTC-Fall), Sep. 2013, pp. 1–5.
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Characters for Embedded font: !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~¡¢£¤¥¦§¨©ª«¬®¯°±²³´¶·¸¹º»¼½ÀÁÂÃÄÅÆÇÈËÌÍÎÏÐÑÒÓÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷øùúûüýþÿĀāĂăąĆćĊċČĎďĐđĒĖėĘęĚěĞğĠġĢģĪīĮįİıĶķĹĺĻļĽľŁłŃńŅņŇňŌŐőŒœŔŕŖŗŘřŚśŞşŠšŢţŤťŪūŮůŰűŲųŴŵŶŷŸŹźŻżŽžƒȘșˆˇ˘˙˚˛˜˝ẀẁẃẄẅỲỳ–—‘’‚“”„†‡•…‰‹›⁄€™ĀĀĂĂĄĄĆĆĊĊČČĎĎĐĐĒĒĖĖĘĘĚĚĞĞĠĠĢĢĪĪĮĮİĶĶĹĹĻĻĽĽŃŃŅŅŇŇŌŌŐŐŔŔŖŖŘŘŚŚŞŞŢŢŤŤŪŪŮŮŰŰŲŲŴŴŶŶŹŹŻŻȘș−≤≥fifl
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ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐəǽẀẁẂẃẄẅỲỳ№
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Related Works (MMSE Receiver)
› M. Wrulich, C. Mehlfuhrer, and M. Rupp, “Managing the interference structure of MIMO HSDPA: A multi-user interference aware MMSE receiver with moderate complexity,” IEEE Transactions on Wireless Communications, vol. 9, no. 4, pp. 1536–1276, April 2010.
› J. T. Wang, “Joint MMSE equalization and power control for MIMO system under multi-user interference,”
IEEE Communications Letters, vol. 16, no. 1, pp. 54–56, January 2012. › B. Shim, J. W. Choi, and I. Kang, “Towards the performance of ML and the complexity of MMSE: A hybrid approach for multiuser detection,”
IEEE Transactions on Wireless Communications, vol. 11, no. 7, pp. 2508–2519, July 2012.
› E. Eraslan, B. Daneshrad, and C.-Y. Lou, “Performance indicator for MIMO MMSE receivers in the presence of channel estimation error,” IEEE Wireless Communications Letters, vol. 2, no. 2, pp. 211–214, April 2013.
› Y. Dong and L. Qiu, “Spectral efficiency of massive MIMO systems with low-resolution ADCs and MMSE receiver,” IEEE Communications Letters, vol. 21, no. 8, pp. 1771–1774, August 2017.
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ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐəǽẀẁẂẃẄẅỲỳ№
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Minimizing the MSE with CSI Errors | KTH Seminar | 2018-04-25 | Page 5
Related Works (MMSE Receiver)
› M. R. McKay, I. B. Collings, and A. M. Tulino, “Achievable sum rate of MIMO MMSE receivers: A general analytic framework,” IEEE Transactions on Information Theory, vol. 56, no. 1, pp. 396 – 410, January 2010.
› Y. Wu and S. Verdu, “MMSE dimension,” IEEE Transactions on Information Theory, vol. 57, no. 8, pp. 4857 – 4879, August 2011.
› C. Artigue and P. Loubaton, “On the precoder design of flat fading MIMO systems equipped with MMSE receivers: A large-system approach,” IEEE Transactions on Information Theory, vol. 57, no. 7, pp. 4138 – 4155, July 2011.
› Y. Jiang, M. K. Varanasi, and J. Li, “Performance analysis of ZF and MMSE equalizers for MIMO systems: An in-depth study of the high SNR regime,” IEEE Transactions on Information Theory, vol. 57, no. 4, pp. 2008–2026, March 2011.
› B. Wang, Y. Chang, and D. Yang, “On the SINR in massive MIMO networks with MMSE receivers,” IEEE Communications Letters, vol. 18, no. 11, pp. 1979 – 1982, September 2014.
› G. Han and J. Song, “Extensions of the I-MMSE relationship to Gaussian channels with feedback and memory,” IEEE Transactions on Information Theory, vol. 62, no. 10, pp. 5422 – 5445, October 2016.
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› Channel Estimation – Toy Model
› Channel Estimation and Receiver Design for Multiuser Systems
Outline
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› Channel Estimation – Toy Model
› Channel Estimation and Receiver Design for Multiuser Systems
Outline
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Characters for Embedded font: !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~¡¢£¤¥¦§¨©ª«¬®¯°±²³´¶·¸¹º»¼½ÀÁÂÃÄÅÆÇÈËÌÍÎÏÐÑÒÓÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷øùúûüýþÿĀāĂăąĆćĊċČĎďĐđĒĖėĘęĚěĞğĠġĢģĪīĮįİıĶķĹĺĻļĽľŁłŃńŅņŇňŌŐőŒœŔŕŖŗŘřŚśŞşŠšŢţŤťŪūŮůŰűŲųŴŵŶŷŸŹźŻżŽžƒȘșˆˇ˘˙˚˛˜˝ẀẁẃẄẅỲỳ–—‘’‚“”„†‡•…‰‹›⁄€™ĀĀĂĂĄĄĆĆĊĊČČĎĎĐĐĒĒĖĖĘĘĚĚĞĞĠĠĢĢĪĪĮĮİĶĶĹĹĻĻĽĽŃŃŅŅŇŇŌŌŐŐŔŔŖŖŘŘŚŚŞŞŢŢŤŤŪŪŮŮŰŰŲŲŴŴŶŶŹŹŻŻȘș−≤≥fifl
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ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐəǽẀẁẂẃẄẅỲỳ№
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Channeles)ma)onatthereceiverfromthereceivedsignal:
Channel Estimation – Toy Model
Tagged User
(path loss)
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Characters for Embedded font: !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~¡¢£¤¥¦§¨©ª«¬®¯°±²³´¶·¸¹º»¼½ÀÁÂÃÄÅÆÇÈËÌÍÎÏÐÑÒÓÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷øùúûüýþÿĀāĂăąĆćĊċČĎďĐđĒĖėĘęĚěĞğĠġĢģĪīĮįİıĶķĹĺĻļĽľŁłŃńŅņŇňŌŐőŒœŔŕŖŗŘřŚśŞşŠšŢţŤťŪūŮůŰűŲųŴŵŶŷŸŹźŻżŽžƒȘșˆˇ˘˙˚˛˜˝ẀẁẃẄẅỲỳ–—‘’‚“”„†‡•…‰‹›⁄€™ĀĀĂĂĄĄĆĆĊĊČČĎĎĐĐĒĒĖĖĘĘĚĚĞĞĠĠĢĢĪĪĮĮİĶĶĹĹĻĻĽĽŃŃŅŅŇŇŌŌŐŐŔŔŖŖŘŘŚŚŞŞŢŢŤŤŪŪŮŮŰŰŲŲŴŴŶŶŹŹŻŻȘș−≤≥fifl
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ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐəǽẀẁẂẃẄẅỲỳ№
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LinearcombinaLonofGaussianvariables
arejointlyGaussian(mul$variatenormal)!andh h^
Channel Estimation – Toy Model
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Characters for Embedded font: !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~¡¢£¤¥¦§¨©ª«¬®¯°±²³´¶·¸¹º»¼½ÀÁÂÃÄÅÆÇÈËÌÍÎÏÐÑÒÓÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷øùúûüýþÿĀāĂăąĆćĊċČĎďĐđĒĖėĘęĚěĞğĠġĢģĪīĮįİıĶķĹĺĻļĽľŁłŃńŅņŇňŌŐőŒœŔŕŖŗŘřŚśŞşŠšŢţŤťŪūŮůŰűŲųŴŵŶŷŸŹźŻżŽžƒȘșˆˇ˘˙˚˛˜˝ẀẁẃẄẅỲỳ–—‘’‚“”„†‡•…‰‹›⁄€™ĀĀĂĂĄĄĆĆĊĊČČĎĎĐĐĒĒĖĖĘĘĚĚĞĞĠĠĢĢĪĪĮĮİĶĶĹĹĻĻĽĽŃŃŅŅŇŇŌŌŐŐŔŔŖŖŘŘŚŚŞŞŢŢŤŤŪŪŮŮŰŰŲŲŴŴŶŶŹŹŻŻȘș−≤≥fifl
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ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐəǽẀẁẂẃẄẅỲỳ№
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Minimizing the MSE with CSI Errors | KTH Seminar | 2018-04-25 | Page 10
› DeterminingtheCondi)onalChannelDistribu)on
› DeterminingtheMeanSquaredError(MSE)
› DeterminingtheaverageMSEasafunc)onofthepilotanddatapower
1
2
3
Three Steps to determine the Mean Squared Error of the Received Data Symbols
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Characters for Embedded font: !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~¡¢£¤¥¦§¨©ª«¬®¯°±²³´¶·¸¹º»¼½ÀÁÂÃÄÅÆÇÈËÌÍÎÏÐÑÒÓÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷øùúûüýþÿĀāĂăąĆćĊċČĎďĐđĒĖėĘęĚěĞğĠġĢģĪīĮįİıĶķĹĺĻļĽľŁłŃńŅņŇňŌŐőŒœŔŕŖŗŘřŚśŞşŠšŢţŤťŪūŮůŰűŲųŴŵŶŷŸŹźŻżŽžƒȘșˆˇ˘˙˚˛˜˝ẀẁẃẄẅỲỳ–—‘’‚“”„†‡•…‰‹›⁄€™ĀĀĂĂĄĄĆĆĊĊČČĎĎĐĐĒĒĖĖĘĘĚĚĞĞĠĠĢĢĪĪĮĮİĶĶĹĹĻĻĽĽŃŃŅŅŇŇŌŌŐŐŔŔŖŖŘŘŚŚŞŞŢŢŤŤŪŪŮŮŰŰŲŲŴŴŶŶŹŹŻŻȘș−≤≥fifl
ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰαβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ
ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐəǽẀẁẂẃẄẅỲỳ№
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Multivariate Normal Distribution
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Characters for Embedded font: !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~¡¢£¤¥¦§¨©ª«¬®¯°±²³´¶·¸¹º»¼½ÀÁÂÃÄÅÆÇÈËÌÍÎÏÐÑÒÓÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷øùúûüýþÿĀāĂăąĆćĊċČĎďĐđĒĖėĘęĚěĞğĠġĢģĪīĮįİıĶķĹĺĻļĽľŁłŃńŅņŇňŌŐőŒœŔŕŖŗŘřŚśŞşŠšŢţŤťŪūŮůŰűŲųŴŵŶŷŸŹźŻżŽžƒȘșˆˇ˘˙˚˛˜˝ẀẁẃẄẅỲỳ–—‘’‚“”„†‡•…‰‹›⁄€™ĀĀĂĂĄĄĆĆĊĊČČĎĎĐĐĒĒĖĖĘĘĚĚĞĞĠĠĢĢĪĪĮĮİĶĶĹĹĻĻĽĽŃŃŅŅŇŇŌŌŐŐŔŔŖŖŘŘŚŚŞŞŢŢŤŤŪŪŮŮŰŰŲŲŴŴŶŶŹŹŻŻȘș−≤≥fifl
ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰαβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ
ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐəǽẀẁẂẃẄẅỲỳ№
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Recall:
Multivariate Normal Distribution
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ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰαβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ
ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐəǽẀẁẂẃẄẅỲỳ№
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What is the distribution of ?
› ApplyingtheTheoremofMVGaussian[seee.g.Kay’93]:
› ApplyingtheBayesianLinearModelof[seee.g.Kay’93]:
1
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Pilotpower
Datapower
”perfect”CSI
Minimumpilot
SNR1SNR2
Feasibleregionundersumpower
constraint
SNRtargetfordata
› Intui)vetradeoffbetweenthepilotandthedatapowerwhensustainingagivenSNR(nointerference!):
The Pilot Power – Data Power Trade-off
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ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰαβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ
ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐəǽẀẁẂẃẄẅỲỳ№
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MSE – 20 un-correlated / correlated antennas
AgivenMSEoftheequalizeddatasymbolscanbereachedbydifferentpilotanddatapowerse\ng.
Uncorrelated Correlated
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Characters for Embedded font: !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~¡¢£¤¥¦§¨©ª«¬®¯°±²³´¶·¸¹º»¼½ÀÁÂÃÄÅÆÇÈËÌÍÎÏÐÑÒÓÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷øùúûüýþÿĀāĂăąĆćĊċČĎďĐđĒĖėĘęĚěĞğĠġĢģĪīĮįİıĶķĹĺĻļĽľŁłŃńŅņŇňŌŐőŒœŔŕŖŗŘřŚśŞşŠšŢţŤťŪūŮůŰűŲųŴŵŶŷŸŹźŻżŽžƒȘșˆˇ˘˙˚˛˜˝ẀẁẃẄẅỲỳ–—‘’‚“”„†‡•…‰‹›⁄€™ĀĀĂĂĄĄĆĆĊĊČČĎĎĐĐĒĒĖĖĘĘĚĚĞĞĠĠĢĢĪĪĮĮİĶĶĹĹĻĻĽĽŃŃŅŅŇŇŌŌŐŐŔŔŖŖŘŘŚŚŞŞŢŢŤŤŪŪŮŮŰŰŲŲŴŴŶŶŹŹŻŻȘș−≤≥fifl
ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰαβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ
ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐəǽẀẁẂẃẄẅỲỳ№
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› Channel Estimation – Toy Model
› Channel Estimation and Receiver Design for Multiuser Systems
Outline
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Characters for Embedded font: !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~¡¢£¤¥¦§¨©ª«¬®¯°±²³´¶·¸¹º»¼½ÀÁÂÃÄÅÆÇÈËÌÍÎÏÐÑÒÓÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷øùúûüýþÿĀāĂăąĆćĊċČĎďĐđĒĖėĘęĚěĞğĠġĢģĪīĮįİıĶķĹĺĻļĽľŁłŃńŅņŇňŌŐőŒœŔŕŖŗŘřŚśŞşŠšŢţŤťŪūŮůŰűŲųŴŵŶŷŸŹźŻżŽžƒȘșˆˇ˘˙˚˛˜˝ẀẁẃẄẅỲỳ–—‘’‚“”„†‡•…‰‹›⁄€™ĀĀĂĂĄĄĆĆĊĊČČĎĎĐĐĒĒĖĖĘĘĚĚĞĞĠĠĢĢĪĪĮĮİĶĶĹĹĻĻĽĽŃŃŅŅŇŇŌŌŐŐŔŔŖŖŘŘŚŚŞŞŢŢŤŤŪŪŮŮŰŰŲŲŴŴŶŶŹŹŻŻȘș−≤≥fifl
ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰαβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ
ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐəǽẀẁẂẃẄẅỲỳ№
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Minimizing the MSE with CSI Errors | KTH Seminar | 2018-04-25 | Page 17
Pilot-Based Channel Estimation
Trade-offs:
Higherpilotpower
BeWerchanneles)mate
SNRdegrada)onfordata+increasedpilotcontamina)on
Morepilotsymbols
BeWerchanneles)mateLessaggressivepilotreuseMoreusersforMUmul)plexing
Lessdatasymbols
MU: Multi user SNR: Signal-to-Noise-Ratio
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Characters for Embedded font: !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~¡¢£¤¥¦§¨©ª«¬®¯°±²³´¶·¸¹º»¼½ÀÁÂÃÄÅÆÇÈËÌÍÎÏÐÑÒÓÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷øùúûüýþÿĀāĂăąĆćĊċČĎďĐđĒĖėĘęĚěĞğĠġĢģĪīĮįİıĶķĹĺĻļĽľŁłŃńŅņŇňŌŐőŒœŔŕŖŗŘřŚśŞşŠšŢţŤťŪūŮůŰűŲųŴŵŶŷŸŹźŻżŽžƒȘșˆˇ˘˙˚˛˜˝ẀẁẃẄẅỲỳ–—‘’‚“”„†‡•…‰‹›⁄€™ĀĀĂĂĄĄĆĆĊĊČČĎĎĐĐĒĒĖĖĘĘĚĚĞĞĠĠĢĢĪĪĮĮİĶĶĹĹĻĻĽĽŃŃŅŅŇŇŌŌŐŐŔŔŖŖŘŘŚŚŞŞŢŢŤŤŪŪŮŮŰŰŲŲŴŴŶŶŹŹŻŻȘș−≤≥fifl
ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰαβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ
ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐəǽẀẁẂẃẄẅỲỳ№
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Minimizing the MSE with CSI Errors | KTH Seminar | 2018-04-25 | Page 18
MU MIMO Signal Model
ThenaïveGminimizestheMSEofthereceiveddatasymbolswhenperfectchanneles)ma)onisavailableatthereceiver.
Tagged User
Data signal model:
G.Fodor,P.DiMarco,M.Telek“OnMinimizingtheMSEinMulLpleAntennaSystemsinthePresenceofChannelStateInformaLonErrors”,IEEECommunicaLonsLebers,Vol.19,No.9,pp.1604-1607,September2015.
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ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰαβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ
ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐəǽẀẁẂẃẄẅỲỳ№
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Minimizing the MSE with CSI Errors | KTH Seminar | 2018-04-25 | Page 19
Preliminaries I
Pilot signal model:
Estimated channel:
Pilot sequence:
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Characters for Embedded font: !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~¡¢£¤¥¦§¨©ª«¬®¯°±²³´¶·¸¹º»¼½ÀÁÂÃÄÅÆÇÈËÌÍÎÏÐÑÒÓÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷øùúûüýþÿĀāĂăąĆćĊċČĎďĐđĒĖėĘęĚěĞğĠġĢģĪīĮįİıĶķĹĺĻļĽľŁłŃńŅņŇňŌŐőŒœŔŕŖŗŘřŚśŞşŠšŢţŤťŪūŮůŰűŲųŴŵŶŷŸŹźŻżŽžƒȘșˆˇ˘˙˚˛˜˝ẀẁẃẄẅỲỳ–—‘’‚“”„†‡•…‰‹›⁄€™ĀĀĂĂĄĄĆĆĊĊČČĎĎĐĐĒĒĖĖĘĘĚĚĞĞĠĠĢĢĪĪĮĮİĶĶĹĹĻĻĽĽŃŃŅŅŇŇŌŌŐŐŔŔŖŖŘŘŚŚŞŞŢŢŤŤŪŪŮŮŰŰŲŲŴŴŶŶŹŹŻŻȘș−≤≥fifl
ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰαβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ
ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐəǽẀẁẂẃẄẅỲỳ№
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Minimizing the MSE with CSI Errors | KTH Seminar | 2018-04-25 | Page 20
Preliminaries II
Data signal model:
MU MIMO Receiver at the BS:
N.Rajatheva,S.Suyama,W.Zirwas,L.Thiele,G.Fodor,A.Tölli,E.Carvalho,J.H.Sorensen,"MassiveMulLpleInputMulLpleOutput(MIMO)Systems",Chapter8in:A.Osseiran,J.F.Monserrat,P.Marsch,"5GMobileandWirelessCommunicaLonsTechnology",CambridgeUniversityPress,June2016.ISBN:9781107130098
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ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰαβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ
ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐəǽẀẁẂẃẄẅỲỳ№
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How to find the (true) MMSE Receiver ?
› Tofindtheop=malreceiverinthepresenceofchanneles)ma)onerrors:
› Step1:DeterminetheMSEofataggedUserasafunc)onofGinthecaseofperfectCSI
› Step3:Determinethatminimizes
› Step2:DeterminetheMSEofataggedUserasafunc)onofGandthees)matedchannel
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ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰαβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ
ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐəǽẀẁẂẃẄẅỲỳ№
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Results
› ClosedformexpressionfortheMMSEreceiverinthepresenceofCSIerrors
› ClosedformexpressionfortheMSEwhenusingthenaïveandtheMMSEreceiver
› Closedformexpressionsfortheop)mumpilot-to-datapowerra)owhenusingtheMMSEreceiver
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ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐəǽẀẁẂẃẄẅỲỳ№
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How to find the (true) MMSE Receiver ?
Elementsofproof: Quadra)cForm:
G.Fodor,P.DiMarcoandM.Telek,"OntheImpactofAntennaCorrelaLonandCSIErrorsonthePilot-to-DataPowerRaLo",IEEETransacLonsonCommunicaLons,Volume64,Issue6,pp.2622-2633,April2016.
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Characters for Embedded font: !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~¡¢£¤¥¦§¨©ª«¬®¯°±²³´¶·¸¹º»¼½ÀÁÂÃÄÅÆÇÈËÌÍÎÏÐÑÒÓÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷øùúûüýþÿĀāĂăąĆćĊċČĎďĐđĒĖėĘęĚěĞğĠġĢģĪīĮįİıĶķĹĺĻļĽľŁłŃńŅņŇňŌŐőŒœŔŕŖŗŘřŚśŞşŠšŢţŤťŪūŮůŰűŲųŴŵŶŷŸŹźŻżŽžƒȘșˆˇ˘˙˚˛˜˝ẀẁẃẄẅỲỳ–—‘’‚“”„†‡•…‰‹›⁄€™ĀĀĂĂĄĄĆĆĊĊČČĎĎĐĐĒĒĖĖĘĘĚĚĞĞĠĠĢĢĪĪĮĮİĶĶĹĹĻĻĽĽŃŃŅŅŇŇŌŌŐŐŔŔŖŖŘŘŚŚŞŞŢŢŤŤŪŪŮŮŰŰŲŲŴŴŶŶŹŹŻŻȘș−≤≥fifl
ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰαβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ
ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐəǽẀẁẂẃẄẅỲỳ№
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PL=50 dB
PL=45 dB PL=40 dB
PL=40 dB PL=45 dB
PL=50 dB MMSE
Naïve
Gain of using the (true) MMSE Detector
over Naïve ~8 dB
The optimal receiver yields significant gains over the whole CDF, including the 10 and 90 percentiles and for various levels of the path loss.
Sq.Error
G.Fodor,P.DiMarcoandM.Telek,"OntheImpactofAntennaCorrelaLonandCSIErrorsonthePilot-to-DataPowerRaLo",IEEETransacLonsonCommunicaLons,Volume64,Issue6,pp.2622-2633,April2016.
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ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰαβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ
ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐəǽẀẁẂẃẄẅỲỳ№
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Minimizing the MSE with CSI Errors | KTH Seminar | 2018-04-25 | Page 25
Naïve
MMSE
Naïve
MMSE
Minimum value
Gain
The gain increases as the number of antennas increases.
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ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰαβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ
ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐəǽẀẁẂẃẄẅỲỳ№
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Naïve MMSE
Optimal MMSE
How does the Gain depend on the Number of Antennas ?
Gain increases
This plot shows the minimum MSE, that is the MSE that is achieved when using the optimal pilot power.
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ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰαβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ
ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐəǽẀẁẂẃẄẅỲỳ№
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Comparison With Perfect CSI
Nr=4
Nr=20
Nr=100
naive
opt
perfect
Data transmit power decreases
With large number of antennas, the MSE performance of the optimal receiver remains close to the perfect CSI performance, whereas the performance of the naïve receiver is far from the perfect CSI case. Therefore, with larger number of antennas, the importance of applying the optimal receiver increases.
Pilotpower[mW]
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Characters for Embedded font: !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~¡¢£¤¥¦§¨©ª«¬®¯°±²³´¶·¸¹º»¼½ÀÁÂÃÄÅÆÇÈËÌÍÎÏÐÑÒÓÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷øùúûüýþÿĀāĂăąĆćĊċČĎďĐđĒĖėĘęĚěĞğĠġĢģĪīĮįİıĶķĹĺĻļĽľŁłŃńŅņŇňŌŐőŒœŔŕŖŗŘřŚśŞşŠšŢţŤťŪūŮůŰűŲųŴŵŶŷŸŹźŻżŽžƒȘșˆˇ˘˙˚˛˜˝ẀẁẃẄẅỲỳ–—‘’‚“”„†‡•…‰‹›⁄€™ĀĀĂĂĄĄĆĆĊĊČČĎĎĐĐĒĒĖĖĘĘĚĚĞĞĠĠĢĢĪĪĮĮİĶĶĹĹĻĻĽĽŃŃŅŅŇŇŌŌŐŐŔŔŖŖŘŘŚŚŞŞŢŢŤŤŪŪŮŮŰŰŲŲŴŴŶŶŹŹŻŻȘș−≤≥fifl
ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰαβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ
ЁЂЃЄЅІЇЈЉЊЋЌЎЏАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯАБВГДЕЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯЁЂЃЄЅІЇЈЉЊЋЌЎЏѢѢѲѲѴѴҐҐəǽẀẁẂẃẄẅỲỳ№
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50 100 150 200P mW
0.005
0.010
0.050
0.100
0.500
MSE
50 100 150 200P mW
2
3
4
5
6SE
MSE And SE With Comb Pilot Pattern
#antennas=10
#antennas=100
#antennas=10
#antennas=100
#antennas=500
#antennas=500
Gain due to optimal MMSE receiver (over naïve MMSE)
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ΆΈΉΊΌΎΏΐΑΒΓΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΪΫΆΈΉΊΰαβγδεζηθικλνξορςΣΤΥΦΧΨΩΪΫΌΎΏ
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› The gain of the optimal receiver increases with increasing number of antennas. In the massive MIMO domain, this gain can be up to 8-10 dB in terms of MSE;
› The true MMSE receiver well approximates the perfect channel estimation case, independently of the number of antennas (as opposed to the naïve receiver);
› With the true MMSE, the transmit power that minimizes the MSE, does not depend on the number of receive antennas (as opposed to the naïve receiver);
› Impact of antenna spacing and angular spread on MSE decreases with increasing number of antennas.
Take Away
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Minimizing the MSE with CSI Errors | KTH Seminar | 2018-04-25 | Page 30
› 3GPP Technical Report: Study on Elevation Beamforming and FD-MIMO for LTE
› See also: - 36.873 Study on 3D Channel Model for LTE - 37.105 Active Antenna System BS Radio Transmission and Reception
› Full Dimension MIMO (FD-MIMO) › Greater number of antenna ports › Efficient MU MIMO Spatial Multiplexing › Robustness against CSI Impairments (e.g. intercell interference)
Full Dimension in 3GPP