A Simple Method to Calculate the Power Spectrum of Distorted Wide-Band Signals

March 14, 2014
Location: 227 Mudd
Speaker: Dr. Alessandro Piovaccari, Silicon Labs


The correct analysis of distortion products is one of the most important aspects in the design of low-power low-cost communication devices. There is a fundamental trade off between cost, power and dynamic range of the system. More precisely, the lower and upper boundaries of the dynamic range are determined respectively by the linearity and noise performance of the system, which in turn are determined by the technology choice, architecture and power consumption of the system itself. As an application example, a typical RF signal receiver is composed by a cascade of blocks performing operation of filtering, amplifying, frequency translation and data conversion. An almost century-long of literature on this topic has shown that for a given performance specification, the optimal design in terms of power consumption and cost is determined by a correct distribution of gain, filtering, and noise and distortion performance among the various blocks constituting the receiving chain. Another very important application is the determination of spurious spectral emission of a transmission system. Spectrum scarcity and pollution due to older standard (like the TV system) has forced government controlled agencies (FCC, ETSI, …) to define transmission regulations, including strict spectrum emission masks. This fact ultimately results on the architectural choice of the power amplifier of the transmitter, and the consequent trade-off between its linearity and power efficiency. As of today, the determination of the distortion products in weakly non-linear systems has been mainly relying on simplified sinusoidal analysis. While this analysis has the advantage of being simple enough to be usable in hand calculation or in spreadsheets, it produces good predictions results only for narrowband signals containing a strong carrier (FM, AM), but it is inadequate to predict the distortion effect on wide-band signals that have statistics similar to band-pass noise, like OFDM signals used in digital television (DTV) and Wireless Local Access Networks (WLAN). Several analysis has been performed in literature during the last 50 years to overcome the limitation of simple sinusoidal distortion analysis, but the math involved is generally quite complex and because of the wide availability of CAD and computation tools, system designers generally prefer to rely on time-domain simulations. This work, present a method to calculate the exact effect of distortion on wide-band signal signal that have Gaussian-like characteristics, including the determination of the exact power of the distortion products, and the prediction of effects like spectral corruption and spectral regrowth, that are not predictable by traditional sinusoidal analysis. It is important to note that, even if this method is based on results of advanced mathematics (Hermite polynomials), its results are simple enough to be usable in hand calculations, similar to sinusoidal distortion analysis. Moreover, the method can be use to calculate the exact power spectrum of the output of a non-linear system when a band-pass signal of non-negligible bandwidth and approximated by a Gaussian wide-sense stationary (WSS) random process is applied to its input, using simple matrix mathematics and without the need of a time-domain simulation.

Speaker Bio

Dr. Alessandro PiovaccariDr. Alessandro Piovaccari received the Laurea and Ph.D. degrees in electronic engineering from the University of Bologna, Bologna, Italy, in 1993 and 1998, respectively and a Post-Master's Advanced Certificate with Honors in electrical engineering from Johns Hopkins University, Baltimore, MD, in 2002. In 1997, he joined Tanner Research in Pasadena, CA as a Research Scientist in where he worked on the development of a CMOS image sensors with embedded motion detection. From 1998 to 2003 he has been part of the design services team as of Cadence Design Systems in Columbia, MD where he worked on CMOS RFICs for wireless communications and in Cary, NC where he managed the high-speed SerDes development. Since 2003, he has been part of Silicon Laboratories in Austin, TX where he contributed to the architecture definition and IC design of the single-chip FM radio, which as today sold more than 1.2 billion devices. He also managed the development and co-architected the single-chip TV tuner, currently employed in more that 55% of the TV sold world-wide. He currently holds a VP of Engineering position and he's responsible for the development of the MCU, wireless, and audio/video broadcast products. He is the author of 9 papers and 31 patents (20 currently issued). Dr. Piovaccari is a Senior Member of IEEE and Full Member of AES. He is part of the Technical Program Committee of CICC, where he also served as chair of the Analog Subcommittee. He has been reviewer for IEEE conference and journal including CICC, ISCAS, JSSC, MTT and CAS.

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