Efficient Multidimensional Polynomial Filtering for Nonlinear Digital Predistortion

1. 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. Motivation h2(0,0) Spectral regrowth from PA nonlinearities causes adjacent channel interference (ACI). Full Volterra (polynomial) filter x2(n) Ch. N-1 Ch. N+1 Channel N+1 Channel N-1 X X Power h2(0,1) Power x(n)x(n-1) X X Z-1 Standard Transmitter: y(n) Frequency Frequency x(n) + PA DAC × x9(n-N+1) h9(N-1,N-1,…,N-1) Z-N+1 X X PA nonlinearities also increase Error Vector Magnitude (EVM) and Bit Error Rate (BER). Z-N+1 The full Volterra kernel has prohibitively high computational complexity. Z-N+1 12-4 QAM Constellation Distorted Output Constellation • 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. OBJECTIVE: Use small multidimensional filters to build a computationally efficient nonlinear digital predistorter.

3. Methods ( ( ) ) v x n n Full Kernel CCS Components CCS-D Components z-α 2 Tap FIR 1 × conj. z-α 2 × + z-α 2 Tap FIR 1 × conj. z-α z-1 2 z-α 3 z-α 4 z-α conj. 5 Full 3rd Order Coefficient Space (Time Domain Representation) • 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. m3 M3-1 M2-1 m2 m1 M1-1 CCS Nonlinear Digital Predistorter: v0(n) + FIR v1(n) + CCS Component 1 … … … vL(n) CCS Component L

4. Results Measured Results using Q-Band Solid State PA: Computational Complexity: No NDP GMP NDP CCS NDP 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.