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Multidimensional Digital Pre-distortion
Multidimensional Digital Pre-distortion (MDDPD), often referred to as multiband digital pre-distortion (MBDPD), is a subset of digital predistortion (DPD) that enables DPD to be applied to signals (channels) that cannot or do not pass through the same digital pre-distorter but do concurrently pass through the same nonlinear system. Its ability to do so comes from the portion of multidimensional signal theory that deals with one dimensional discrete time vector input - 1-D discrete time vector output systems as defined in ''Multidimensional Digital Signal Processing''.〔Dan E. Dudgeon and Russell M. Mersereau, ''Multidimensional Digital Signal Processing'', Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1984.〕 The first paper in which it found application was in 1991 as seen here.〔Kaprielian, S.; Turi, J.; Hunt, L.R., "Vector input-output linearization for a class of descriptor systems (AC/DC power system )", ''Decision and Control'', 1991, Proceedings of the 30th IEEE Conference on , vol., no., pp. 1949, 1954 vol. 2, 11-13 Dec 1991 doi: 10.1109/CDC.1991.261756〕 None of the applications of MDDPD are able to make use of the linear shift invariant (LSI) system properties as by definition they are nonlinear and not shift-invariant although they are often approximated as shift-invariant (memoryless).
==Motivation==
Although MDDPD enables the use of DPD in multi source systems, there is another advantage from implementing MDDPD over DPD which is the prime motivation of the initial studies.〔S. A. Bassam, M. Helaoui, and F. M. Ghannouchi, “2-D digital predistortion (2-D-DPD) architecture for concurrent dual-band transmitters,” IEEE Trans. Microwave theory Tech., vol. 59, pp. 2547–2553, Oct. 2011〕 In one dimensional polynomial-based memory (or memoryless) DPD, in order to solve for the digital pre-distorter polynomials coefficients and minimize the mean squared error (MSE), the distorted output of the nonlinear system must be over-sampled at a rate that enables the capture of the nonlinear products of the order of the digital pre-distorter. In systems where there is considerable spacing between carriers or the channel bandwidths are very wide, this leads to a significant increase in the minimum acceptable sampling rate of the analog-to-digital converter (ADC) used for feedback sampling over that of systems that are single channel or have tightly spaced carriers. As ADCs are more expensive and harder to design than the digital-to-analog converter (DAC) used to generate the channels and ADCs get very expensive when the sampling rate approaches 1 Gs/s and higher, it is highly desirable to reduce the sampling rate of the ADC required to perform DPD. MDDPD does just this.
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