Fast Determination of Similarity Between Two Vectors by Means of Analog CMOS Technique

In this paper, an analog approach to determining a resemblance between two multidimensional vectors is proposed. As the resemblance measure, Euclidean distance is used. The main advantage of the presented method is a very high speed of the Euclidean-distance-measure calculations. The achieved high speed results from the fact that most of arithmetic operations needed to realize the calculations are carried out in parallel. This concerns the required operations of squaring a difference of two corresponding components of the compared vectors. Operating in a transconductane mode (voltage difference squaring transconductors) and a current mode (output square-root extracting circuit), our CMOS circuit is power saving. Its low-power operation results from the fact that sub-circuits of our calculator responsible for the squaring operations (a great number of them in case of large multidimensional vectors) consume no power in the absence of input signals. This takes place when corresponding components of the compared vectors are both equal to zero. The circuit also consumes a reasonably low amount of energy when processing (comparing) a different from zero input data (corresponding vector components). A simplified description of the applied differential squaring transconductors as well as the output current-mode square-root extraction circuit is given and a problem of good cooperation between them is discussed and proper solutions indicated. SPICE simulation results are shown to be in a good agreement with the theory presented.