Contributions to Low-Complexity Linearization, Equalization, and Synchronization

Firstly, the design of low-complexity digital linearizers for ADIs is addressed. Several novel linearizers are introduced that are inspired by neuralnetwork architectures, but avoid the high training complexity associated with neural-network-based approaches. These linearizers can outperform classical linearizers, such as Wiener and Hammerstein, while requiring lower implementation complexity. The proposed designs cover both memoryless and memory (frequency-dependent) linearizers and are applicable to nonlinear distortion occurring either before or after sampling. All designs enable closed-form parameter estimation via matrix inversion, thereby eliminating the need for unpredictable iterative nonconvex optimization. In addition,an efficient memoryless linearizer based on 1-bit quantization is introduced,enabling lookup-table-based implementations with only one multiplication per corrected sample.

Secondly, equalization of digital-to-analog converters (DACs) frequency response using linear-phase finite impulse response (FIR) filters is considered. For several DAC pulse shapes operating across multiple Nyquist bands,minimax-optimal equalizers are designed, and their properties are analyzed. Based on these designs, expressions for the required filter order are derived as explicit functions of bandwidth and target equalization accuracy, using symbolic regression followed by further refinement. The resulting expressions provide accurate order estimates across different pulse shapes and operating conditions.

Thirdly, a low-complexity time-domain sampling frequency offset (SFO)estimation and compensation framework based on the Farrow structure for interpolation is presented. By reusing the Farrow structure already employed for SFO compensation, the proposed approach enables a unified estimation and compensation architecture with significantly reduced overall implementation complexity. The method operates on arbitrary bandlimited signals, supports joint estimation of SFO and sampling time offset, and allows estimation using only a single component (real or imaginary) of a complex signal. A Newton-based estimator exploiting the structure of the problem is developed to reduce computational complexity, while an alternative iterative least-squares-based design provides an even lower-complexity solution. The resulting estimators are robust to other synchronization errors and are well suited for practical receiver implementations. In addition, motivated by the appearance of low-order time-index-powered sums in the Farrow-based formulation, a general cascaded-accumulator framework is developed as a supplementary contribution, enabling efficient causal computation of time-index-powered weighted sums of arbitrary order without data buffering and reducing the multiplicative complexity from order K N to only K+1 constant multiplications (where N is the number of terms and K is the power in the sum), which is applicable both to SFO estimators and to other signal processing applications beyond the SFO problem.