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 low-power 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.

CVNN-based Channel Estimation and Equalization in OFDM Systems Without Cyclic Prefix

In modern communication systems operating with Orthogonal Frequency-Division Multiplexing (OFDM), channel estimation requires minimal complexity with one-tap equalizers. However, this depends on cyclic prefixes, which must be sufficiently large to cover the channel impulse response. Conversely, the use of cyclic prefix (CP) decreases the useful information that can be conveyed in an OFDM frame, thereby degrading the spectral efficiency of the system. In this context, we study the impact of CPs on channel estimation with complex-valued neural networks (CVNNs). We show that the phase-transmittance radial basis function neural network offers superior results, in terms of required energy per bit, compared to classical minimum mean-squared error and least squares algorithms in scenarios without CP.

PCA-based Channel Estimation for MIMO Communications

In multiple-input multiple-output communications, channel estimation is paramount to keep base stations and users on track. This paper proposes a novel PCA-based-principal component analysis-channel estimation approach for MIMO orthogonal frequency division multiplexing systems. The channel frequency response is firstly estimated with the least squares method, and then PCA is used to filter only the higher singular components of the channel impulse response, which is then converted back to the frequency domain. The proposed approach is compared with the MMSE, the minimum mean square error estimation, in terms of bit error rate versus Eb/N0.