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. The first paper in which it found application was in 1991 as seen here. 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. 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.

Advantages

Just as the digital pre-distortion in MDDPD is applied to the channels independently, the feedback sampling of the channels may also be done independently. In addition, as was mentioned previously, MDDPD allows the pre-distortion to be applied to channels that are generated independently.