Constant Envelope OFDM Phase Modulation - Dr. James R. Zeidler

27In general, modeling nonlinear power amplifiers is complicated (see [233, chap. 5]).A common simplification is to assume that the PA is a memoryless nonlinearity, andtherefore has a frequency-nonselective response. For example, if the PA input iss in (t) = A(t) exp[jφ(t)], (2.32)the output iss out (t) = G[A(t)] exp [ j{φ(t) + Φ[A(t)]} ] , (2.33)where G(·) and Φ(·) are known as the AM/AM and AM/PM conversions, respectively.The SSPA model is expressed asG(A) =g 0 A[1 + (A/A sat ) 2p] , and Φ(A) = 0, (2.34)1/2pwhere g 0 is the amplifier gain, A sat is the input saturation level, and p controls theAM/AM sharpness of the saturation region. For this model the AM/PM conversion isassumed to be negligibly small.Though widely known as the Rapp model [426], (2.34) should be credited to theoriginal work by A. J. Cann, published a decade earlier in the IEEE literature [71].Cann’s formula is obtained with the simple manipulation:AG(A) =g 0 [1 + (A/A sat ) 2p] 1/2pA=g 0 [1 + (A/A sat ) 2p] 1/2p × [(A sat/A) 2p ] 1/2p[(A sat /A) 2p ] 1/2p(2.35)A sat=g 0 [1 + (A sat /A) 2p] 1/2p ,which is precisely the nonlinearity presented in Cann’s paper.Saleh’s TWTA model is expressed as [110]G(A) =g 0 A1 + (A/A sat ) 2 , and Φ(A) = α φA 21 + β φ A 2 . (2.36)Notice that the AM/PM conversion, determined by the constants α φ and β φ , is non-zero.The TWTA model is therefore more nonlinear than the SSPA model.