On the Computational Complexities of Complex-valued Neural Networks

Complex-valued neural networks (CVNNs) are nonlinear filters used in the digital signal processing of complex-domain data. Compared with real-valued neural networks (RVNNs), CVNNs can directly handle complex-valued input and output signals due to their complex domain parameters and activation functions. With the trend toward lowpower systems, computational complexity analysis has become essential for measuring an algorithm's power consumption. Therefore, this paper presents both the quantitative and asymptotic computational complexities of CVNNs. This is a crucial tool in deciding which algorithm to implement. The mathematical operations are described in terms of the number of real-valued multiplications, as these are the most demanding operations. To determine which CVNN can be implemented in a low-power system, quantitative computational complexities can be used to accurately estimate the number of floating-point operations. We have also investigated the computational complexities of CVNNs discussed in some studies presented in the literature.