Parallel Hammerstein (PH) Based Model for the Alleviation of Various Imperfections in Direct Conversion Transmitters

The parallel Hammerstein based model proposed in [18], shown in Figure 6.11, is a joint model that compensates for various imperfections in a transmitter. Prior to this model, a serial configuration based architecture that considered the effect of I/Q imbalance was presented. However, the drawback of the model was that the PA compensation and I/Q impairment compensation had to be processed separately. The joint model [18] converts this serial architecture into a parallel configuration using indirect learning architecture for parameter extraction, resulting in a single-step estimation. The serial-to-parallel conversion is detailed in [16,18, 15]:

Here, M represents the memory index, k_{1} and k_{2} are the nonlinearity indices, respectively; and dc represents the local oscillator leakage.

Two-Box Model with I/Q and DC Impairments

A generalized two-box model, inspired by the FTNTB model, was proposed in [15] for the mitigation of PA distortions and I/Q modulator imperfections. The first block is composed of dual parallel branches of Volterra series, while the second block is a static nonlinear function. The block diagram of the two-box model is shown in Figure 6.12.

x_{in}(n) is the input to the system, x(n) is the output of the nonlinear FIR filters, while y_{PA}+_{I}Q(n) is the final output of the system. The dual parallel branch Volterra series consists of only the second order cross-terms and is mathematically represented as:

Figure 6.12 Two-box model with I/Q and DC impairments

where a_{m}, b_{m}, a_{m}j, and b_{m}j represent the model coefficients, M is the memory depth of the system, and J is the time delay of the envelope of the input signal |x(-)|. The final output of the model is given by:

where H(-) is the complex static/memoryless gain of the LUT model. The coefficients of the model can be obtained using the least squares approach.

The two-box model reduces the complexity of the system more than the parallel Hammerstein model.