Embodiments are described herein to provide better predistortion solutions for the linearization of high power amplifiers, especially those with memory effects. Many embodiments involve a method in which a predistorted signal zn is generated from input signal xn in accordance with z n = ⁢ ∑ k = 1 K ⁢ ∏ q = 1 Q ⁢ ⁢ P kq ⁡ ( x n - q - 1 ) = ⁢ P 11 ⁡ ( x n ) ⁢ P 12 ⁡ ( x n - 1 ) ⁢ ⁢ … ⁢ ⁢ P 1 ⁢ Q ⁡ ( x n - Q - 1 ) + ⁢ P 21 ⁡ ( x n ) ⁢ P 22 ⁡ ( x n - 1 ) ⁢ ⁢ … ⁢ ⁢ P 2 ⁢ Q ⁡ ( x n - Q - 1 ) + … + ⁢ P K ⁢ ⁢ 1 ⁡ ( x n ) ⁢ P K ⁢ ⁢ 2 ⁡ ( x n - 1 ) ⁢ ⁢ … ⁢ ⁢ P KQ ⁡ ( x n - Q - 1 ) for K terms and Q−1 delays, wherein each Pkq is a complex valued function of a single complex variable. Also described are predistorter apparatus embodiments in which a predistorter includes complex multipliers for multiplying the value of each Pkq having the same value of k to produce K products and at least one adder for adding the K products to generate predistorted signal zn from input signal xn in accordance with the equation above.