neural networks (NNs) for multiple hardware impairments mitigation of a realistic direct conversion transmitter are impractical due to high computational complexity. We propose two methods to reduce the complexity without significant performance penalty. First, propose a novel NN with shortcut connections, referred to as shortcut real-valued time-delay neural network (SVDEN), where trainable neuron-wise shortcut connections are added between the input and output layers. Second, we implement a NN pruning algorithm that gradually removes connections corresponding to minimal weight magnitudes in each layer. Simulation and experimental results show that SVDEN with pruning achieves better performance for compensating frequency-dependent quadrature imbalance and power amplifier nonlinearity than other NN-based and Volterra-based models, while requiring less or similar complexity