1 ANALYSIS OF SWITCHING ACTIVITY IN DSP SIGNALS IN THE PRESENCE OF NOISE Asghar Havashki 1 , Lars Lundheim 1 , Per Gunnar Kjeldsberg 1 , Oscar Gustafsson 2 , Geir E. Øien 1 Abstract—Input switching activity is one of the deciding factors for power consumption in digital signal processing components. For accurate power estimation, it is essential to have knowledge about the switching activity in the input signal, including how this activity changes in different environments, e.g., in the presence of noise. The Dual Bit Type (DBT) method aims at characterizing the bit- level switching activity in a signal, using signal statistics. However, the DBT method requires that the correlation coefficient and switching activity for the most significant bit of the signal are available. In this paper we give an expression for direct calculation of the correlation coefficient for the most significant bit in a signal, using the word-level correlation coefficient. Using simulation results we examine the accuracy of the given method to calculate the switching activity and correlation coefficient for the most significant bit. Furthermore, we derive expressions for accurately calculating the variance and word-level correlation coefficient for a correlated signal, when an additional noise of a given variance is added to the signal. This can be used to estimate the bit-level switching activity in a signal in the presence of noise. Finally, based on this we study the impact the additional noise has on the switching activity of the resulting signal. Index Terms—switching activity, DSP signals, dual bit type, bit-level switching activity I. I NTRODUCTION Through the last decade, power consumption in CMOS VLSI circuits has become a major design con- straint. In order to design circuits for low power, it is now essential to be able to accurately estimate power consumption at different design stages, at circuit and logic level as well as at architectural level. Since dy- namic power consumption in a CMOS VLSI circuit depends on the number of signal transitions at its capaci- tive nodes, accurate estimation of the bit-level switching activity at the primary inputs is a key requirement in var- ious power estimation techniques. The input switching activity can subsequently be used directly or indirectly to calculate the number of transitions of all nodes in the circuit [1]. The Dual Bit Type method introduced in [2] aims at characterizing the bit-level switching activity in a data word, using the word-level statistics of data, i.e., mean, μ, variance, σ 2 , and temporal correlation, ρ. The 1: Norwegian University of Science and Technology, Trondheim, Norway. E-mail: havashki,lundheim,Per.Gunnar.Kjeldsberg,Geir.Oien@iet.ntnu.no. 2: Department of Electrical Engineering, Link¨ oping University, Link¨ oping, Sweeden. E-mail: oscarg@isy.liu.se. method is based on the assumption that the binary representation of real world signals can be divided into a few regions, with well defined switching activity for the bits in each region. In [2] the binary representation of a word is divided into three regions: the most significant bit (MSB) region or sign region (S), the uniform white noise (UWN) region, and an intermediate region. The bits in the UWN region, which are defined to last from the least significant bit to a certain breakpoint P 0 , exhibit random switching with switching activity equal to α UWN =0.5. Switching activity for the bits in the S-region, which lasts from the most significant bit to another breakpoint P 1 , is a constant, while the switching activity in the intermediate region is assumed to decrease in a linear manner from α UWN to α MSB , where α UWN and α MSB are the switching activities in the UWN and S regions, respectively. Experiments have shown that the method presented in [2] to calculate the regions boundaries, P 0 and P 1 , is not accurate for highly correlated signals. The work in [3], which builds on the principles of [2], has however developed expressions which take correlation of data into account when defining the mentioned regions. Accurate estimation of bit-level switching activity, using expressions in [3], requires accurate estimation of ρ MSB and α MSB , where ρ MSB and α MSB are the temporal correlation and the switching activity for the most sig- nificant bit, respectively. In [3] the method presented to calculate α MSB and ρ MSB is based on knowledge of a signal generation model. ρ MSB in [2] was acquired using simulation. An exact method to calculate the bit-level correlation factor ρ MSB was presented in [4]. It is again based on knowledge of a signal generation model. The estimation method calculating α MSB assumes, however, that ρ MSB is equal to the word-level correlation ρ. This is not accurate in many cases. In [5] an accurate analytical expression for calculating α MSB using the word-level correlation ρ is presented. In this paper we use this expression for α MSB to derive an expression for direct calculation of ρ MSB . We also use simulation to examine the accuracy of this method to estimate α MSB and ρ MSB . Furthermore, signals are often subjected to noise from different sources, e.g., quantization noise from fixed point DPS realization, wired and wireless communica- tion channel noise. This changes the word-level signal statistics, σ 2 and ρ. As mentioned above, the methods © 2009 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.