Icassp2003.com

Dr. Mikko Valkama, Tampere University of Technology and Prof. Visa Koivunen, Helsinki University of Technology

Abstract

Complex-valued (I/Q) signals and systems play a key role in many application areas including communication receivers, array signal processing and biomedical applications. Many spectrally efficient modulation techniques as well as some of the recent radio receiver developments are good examples of this, all being based on complex signal concepts. Moreover, in many applications signals are processed in frequency domain that leads to complex representation. In practice, a complex signal is just a combination of two real signals (real and imaginary parts) being carried, e.g., by two separate wires or bit-streams. The probabilistic structure of complex signals and the corresponding real-valued signals with twice the dimension are the same. However, the operator structure differs. Moreover, the convenience of the complex signal notations, e.g., in frequency domain analysis has made the complex signal concepts an essential ingredient in communication theoretic and communications transceiver signal processing literature.

An important feature of many complex random signals is the so-called circularity property also known as properness. At the complex signal level, this means that the signal is statistically uncorrelated with its own complex-conjugate. In case of complex random vectors it means that the so-called complementary covariance matrix or pseudo-covariance matrix vanishes. Many widely used signals such as M-QAM and 8-PSK signals and standard complex AWGN possess this circularity property. However, practical imperfections in transmitters and receivers such as I/Q imbalance may cause departures from that property. Moreover, some well known modulation schemes such as BPSK and GMSK are non-circular. The circularity property or lack of it may be exploited in designing wireless transceivers or smart antenna systems. For example, interferences may be cancelled based on their second-order non-circularity, I/Q imbalances corrected by recovering the circularity and performance of a smart antenna systems enhanced by considering the improperness of the received signal. Also, the statistical performance of the transceivers can be significantly improved by taking into account the complete second-order statistics of the signals.

This tutorial aims to provide a comprehensive overview of the circular / non-circular complex random signals, covering the basic theory as well as essential applications in the fields of communications receiver signal processing, antenna array signal processing and independent component analysis (ICA). This includes, e.g., recent developments in carrier frequency offset (CFO) estimation and compensation as well as the I/Q imbalance and mirror-frequency rejection problems in quadrature radio receivers and transmitters. Statistical performance of the signal processing algorithms is also studied using asymptotic tools. In addition to analytical work and analysis, the tutorial also contains some demonstrations with real-world measured communications waveforms.

1. Introduction and Motivation (10-15min, Mikko)
   • origins of complex (I/Q) signals and systems
   • baseband and bandpass signals and systems
2. Essential Second-Order Statistics and Nature of Complex Random Signals (~1h, Visa/Mikko)
   • second-order statistics of complex random signals
   • covariance and pseudo-covariance
   • structure of covariance and pseudo-covariance matrices
   • widely linear transformations
3. Applications, Part I - Independent Component Analysis (ICA) (30min, Visa)
   • blind signal separation of complex-valued signals: identifiability
   • Takagi-transformation
   • example: separating circular and non-circular signals
4. Applications, Part II - Communications Receiver Signal Processing (~1h, Visa/Mikko)
   • carrier-frequency offset (CFO) estimation and compensation in receivers
   • I/Q imbalance compensation and mirror-frequency rejection in quadrature radio receivers and transmitters
   • examples with real-world measured signals
5. Conclusions and References (10-15min)

Target Audience and Prerequisites

This tutorial is targeted for graduate students, researchers and engineers in both academia and industry, working on the physical layer technologies and signal processing aspects of wireless communications systems. As a background information, basic knowledge of statistics and signal processing is recommended.

Speaker Biographies

Mikko Valkama (Member, IEEE) was born in Pirkkala, Finland, on November 27, 1975. He received the M.Sc. and Ph.D. degrees (both with honors) in Electrical Engineering (EE) from Tampere University of Technology (TUT), Finland, in 2000 and 2001, respectively. In 2002 he received the Best Ph.D. Thesis -award by the Finnish Academy of Science and Letters for his thesis entitled “Advanced I/Q Signal Processing for Wideband Receivers: Models and Algorithms”. In 2003, he was working as a visiting researcher with the Communications Systems and Signal Processing Institute at SDSU, San Diego, CA. Currently, he is working as a senior researcher with the Institute of Communications Engineering at TUT, Finland. He is also involved in the organization of the IEEE SPAWC’07 conference (Publications Chair) to be held in Helsinki, Finland. His general research interests include communications signal processing, estimation and detection techniques, signal processing algorithms for software defined flexible radios, and digital transmission techniques such as different variants of multicarrier modulation methods and OFDM.

Visa Koivunen (Senior Member, IEEE) received his D.Sc. (Tech) degree with honors from the University of Oulu, Dept. of Electrical Engineering. He received the primus doctor (best graduate) award among the doctoral graduates in years 1989-1994. From 1992 to 1995 he was a visiting researcher at the University of Pennsylvania, Philadelphia, USA. Year 1996 he held a faculty position at the Department of Electrical Engineering, University of Oulu. From August 1997 to August 1999 he was an Associate Professor at the Signal Processing Laboratory, Tampere University of Technology. Since 1999 he has been a Professor of Signal Processing at the Department of Electrical and Communications Engineering, Helsinki University of Technology (HUT), Finland. He is one of the Principal Investigators in SMARAD (Smart and Novel Radios) Center of Excellence in Radio and Communications Engineering nominated by the Academy of Finland. Since year 2003 he has been also adjunct full professor at the University of Pennsylvania, Philadelphia, USA.

Dr. Koivunen’s research interest include statistical, communications and sensor array signal processing. He has published more than 200 papers in international scientific conferences and journals. He received the best paper award in IEEE PIMRC 2005 (co-authored with C. Ribeiro and A. Richter). He also co-authored a paper receiving best student paper award in EUSIPCO 2006 and best paper in 2006 European Conference on Antennas and Propagation. He served as an associate editor for IEEE Signal Processing Letters. He is a member of the editorial board for the Signal Processing Journal and Journal of Wireless Communication and Networking. He is also a member of the IEEE Signal Processing for Communication Technical Committee (SPCOM-TC). He is the general chair of the IEEE SPAWC (Signal Processing Advances in Wireless Communication) 2007 conference in Helsinki, June 2007.