1. HPEC_NDP-1 MAH 10/11/2015 MIT Lincoln Laboratory Efficient Multidimensional Polynomial Filtering for Nonlinear Digital Predistortion Matthew Herman, Benjamin Miller, Joel Goodman HPEC Workshop 2008 23 September 2008 This work is sponsored by the Defense Advanced Research Projects Agency under Air Force Contract FA8721-05-C-0002. Opinions, interpretations, conclusions, and recommendations are those of the author and are not necessarily endorsed by the United States Government.

2. MIT Lincoln Laboratory 999999-2 XYZ 10/11/2015 Motivation The objective of Nonlinear Digital Predistortion (NDP) is to digitally alter the input to the PA to compensate for the distortions imparted by the device. –NDP is capable improving power efficiency while reducing ACI and BER. Computationally efficient memoryless NDP techniques are not sufficient for linearizing wideband PAs that impart significant memory effects. Not feasible to use a computationally complex polynomial predistorter to model/invert state dependent nonlinearities. –Most previous polynomial approaches consider 1D subkernels as building blocks for the full PD. –Multidimensional filters more easily address asymmetric and aliasing NL. Distorted Output Constellation 12-4 QAM Constellation Frequency Power Channel N-1 Channel N+1 Power Ch. N-1 Ch. N+1 Frequency PA DAC × Standard Transmitter: Spectral regrowth from PA nonlinearities causes adjacent channel interference (ACI). PA nonlinearities also increase Error Vector Magnitude (EVM) and Bit Error Rate (BER). Full Volterra (polynomial) filter Full Volterra (polynomial) filter y(n) X x(n) Z -N+1 Z -1 X X X h 2 (0,1) X h 9 ( N-1,N-1, …,N-1 ) X + x 2 (n) x(n)x(n-1) x 9 (n-N+1) Z -N+1 The full Volterra kernel has prohibitively high computational complexity. The full Volterra kernel has prohibitively high computational complexity. h 2 (0,0) OBJECTIVE: Use small multidimensional filters to build a computationally efficient nonlinear digital predistorter.

3. MIT Lincoln Laboratory 999999-3 XYZ 10/11/2015 Methods m1m1 Full 3 rd Order Coefficient Space (Time Domain Representation) m2m2 m3m3 M 3 -1 M 2 -1 M 1 -1 Divide the full coefficient space into cube coefficient subspaces (CCS), –i.e., small hypercubes/parallelepipeds (“diagonal” CCS-D) of arbitrary dimension. Model the inverse NL by greedily selecting only the CCS components that have the greatest impact on performance. CCS allows efficient adaptation in multiple dimensions starting with the first nonlinear component selected. CCS has an efficient hardware implementation. CCS Nonlinear Digital Predistorter: x ( n ) FIR CCS Component 1 + CCS Component L + ……… v ( n ) v 0 (n) v 1 (n) v L (n) 2 Tap FIR z-αz-α × + × z-αz-α z-αz-α 2 3 4 z-αz-α 5 z-αz-α 1 conj. 2 Tap FIR z-αz-α × 2 z-αz-α 1 conj. z -1 conj. Full Kernel CCS Components CCS-D Components

4. MIT Lincoln Laboratory 999999-4 XYZ 10/11/2015 Results Measured Results using Q-Band Solid State PA: CCS reduces ACI by ~7 dB more than the state-of-the-art GMP with less than half as many operations per second. CCS reduces ACI by ~7 dB more than the state-of-the-art GMP with less than half as many operations per second. CCS NDP improves ACI by ~20 dB. CCS NDP improves ACI by ~20 dB. Architecture Complex Mult. Per Sample Complex Add. Per Sample Op’ns Per Second (GOPS) Generalized Memory Polynomial 156144147 2-D CCS/CCS-D763262 Computational Complexity: No NDP GMP NDP CCS NDP