Codebook Design and Performance Analysis of Quantized Beamforming under Perfect and Imperfect Channel State Information

  • Samuel Tumelero Valduga GTEL-UFC
  • André L. F. de Almeida GTEL-UFC
  • Renato Machado UFSM
  • Andrei P. Legg UFSM
  • Murilo B. Loiola UFABC
  • Dimas Alves Unipampa
Keywords: MIMO, beamforming, quantized feedback, BER, channel estimation


This paper presents a codebook design to multiple transmit and multiple receive antenna system with quantized feedback channel. The codebook design is based on trigonometrical expressions that give a quasi-orthogonal structure to the codes. The codebook is designed to a specific number of transmit antennas and can easily be adapted to different number of feedback bits. An instantaneous signal-to-noise ratio analysis is performed which is used to optimize the codebooks. An upper bound on the bit error rate (BER) performance for the proposed scheme is provided as well. We also investigate the system performance under more realisticconditions, and for this purpose we consider a time-varying and spatially-correlated channel model. We compare the BER performance of the proposed scheme with other closed-loop codebook-based schemes. Results show that the proposed schemeoutperforms other good schemes in terms of array gain.

Author Biographies

Samuel Tumelero Valduga, GTEL-UFC
Samuel Tumelero Valduga received the B.S.E.E.and M.Sc. degrees in electrical engineering andcomputer science from Federal University of SantaMaria (UFSM), Santa Maria, RS, Brazil, in 2012and 2014, respectively.He is currently pursuing his Ph.D. degree atFederal University of Ceará (UFC). He is memberof Wireless Telecommunications Research Group(GTEL), Fortaleza, Brazil. From 2016 to 2017,he held a one-year research position at the I3SLaboratory, CNRS, France. His research interestsare massive MIMO, matrix and tensor completion, pilot contamination,beamforming, precoding, and channel estimation.
André L. F. de Almeida, GTEL-UFC
André L. F. de Almeida received the double in Sciences and Teleinformatics Engineeringfrom the University of Nice, Sophia Antipolis,France, and the Federal University of Ceará,Fortaleza, Brazil, in 2007.He is currently an Assistant Professor with theDepartment of Teleinformatics Engineering of theFederal University of Ceará. During fall 2002, hewas a visiting researcher at Ericsson Research Labs,Stockholm, Sweden. From 2007 to 2008, he helda one-year research position at the I3S Laboratory,CNRS, France. In 2008, he was awarded a CAPES/COFECUB researchfellowship with the I3S Laboratory, CNRS, France. He currently holds aproductivity research fellowship from CNPq (the Brazilian National Councilfor Scientific and Technological Development). In 2012, 2013 and 2015,he was a Visiting Professor at the University of Nice Sophia Antipolis,France. He served as an Associate Editor of the IEEE Transactions onSignal Processing (2012-1016). He is currently an Associate Editor ofthe IEEE Signal Processing Letters and serves as a general co-chair ofIEEE CAMSAP2017. His research interests lie in the areas of signalprocessing for communications and sensor array processing, and include blindmethods for channel identification, equalization and source separation, MIMOreceivers, multilinear algebra and tensor-based signal processing applied tocommunications and data analysis.
Renato Machado, UFSM
Renato Machado received the B.S. degree inElectrical Engineering from the São Paulo StateUniversity, Brazil, in 2001, and the M.Sc. degreeand the Ph.D. degree in Electrical Engineering fromthe Federal University of Santa Catarina (UFSC),Brazil, in 2004 and 2008, respectively.He was a visiting Ph.D. researcher in theDepartment of Electrical Engineering, Arizona StateUniversity, from Aug. 2006 to Jun. 2007. He workedas a researcher at Nokia Institute of Technology, in2007 and 2008. Between Aug. 2009 and Dec. 2017,he was a professor in the Department of Electronics and Computing, FederalUniversity of Santa Maria, Brazil. From Dec. 2011 to Oct. 2013 he wasthe director of the Santa Maria Space Science Laboratory. Between Nov.2013 and Mar. 2015, Dr. Machado spent his sabbatical license as a visitingresearcher fellow at Blekinge Institute of Technology, Karlskrona, Sweden,working in partnership with the Saab Electronic Defence Systems group. Dr.Machado is a member of the IEEE Communications Society, IEEE Aerospaceand Electronic Systems Society, and the Brazilian Telecommunications andSignal Processing Society (SBrT). Since Dec. 2017, Dr. Machado has been anAssociate Professor at the Aeronautics Institute of Technology. His researchinterests include SAR image processing, wireless communications, MIMOsystems, power line communications and sensor networks.
Andrei P. Legg, UFSM
Andrei Piccinini Legg received his B.S. degree in2005, M.S. in 2007, and Ph.D. in 2011 in electricalengineering from the Federal University of SantaCatarina - Brazil.He is currently an Associate Professor atthe Federal University of Santa Maria - Brazil.His research focus includes image processing,electronic design, error correction codes, and wirelesscommunications.
Murilo B. Loiola, UFABC
Murilo Bellezoni Loiola received the titles ofElectrical Engineer (2002), Master in ElectricalEngineering (2005) and Doctor in ElectricalEngineering (2009) from the University ofCampinas (UNICAMP), Brazil.He is currently an Assistant Professor at FederalUniversity of ABC (UFABC). His main researchinterests lie in the areas of adaptive and statisticalsignal processing, wireless communications,wireless physical-layer security, and machinelearning.
Dimas Alves, Unipampa
Dimas Irion Alves received the B.S.E.E degree fromthe Federal University of Santa Maria, Santa Maria,RS, Brazil, in 2013. He received his M.Sc. degree inelectrical engineering from the Federal University ofSanta Catarina, Florianópolis, SC, Brazil, in 2015.He is currently a Ph.D. student at UFSC and amember of the Communications Research Group(GPqCom/UFSC). Since October 2015 he hasbeen a Professor in Federal University of Pampa(Unipampa), Alegrete, RS, Brazil. His researchinterests include digital signal processing, MIMOsystems, wireless communications, SAR systems and image processing.
How to Cite
Valduga, S., de Almeida, A., Machado, R., Legg, A., Loiola, M., & Alves, D. (2017). Codebook Design and Performance Analysis of Quantized Beamforming under Perfect and Imperfect Channel State Information. Journal of Communication and Information Systems, 32(1).
Regular Papers