This paper proposes two full-digital receive beamforming (BF) methods for low-complexity and high-accuracy uplink signal detection via Gaussian belief propagation (GaBP) at base stations (BSs) adopting massive multi-input multi-output (MIMO) for open radio access network (O-RAN). In addition, beyond fifth generation mobile communication (beyond 5G) systems will increase uplink capacity. In the scenarios such as O-RAN and beyond 5G, it is vital to reduce the cost of the BSs by limiting the bandwidth of fronthaul (FH) links, and the dimensionality reduction of the received signal based on the receive BF at a radio unit is a well-known strategy to reduce the amount of data transported via the FH links. In this paper, we clarify appropriate criteria for designing a BF weight considering the subsequent GaBP signal detection with the proposed methods: singular-value-decomposition-based BF and QR-decomposition-based BF with the aid of discrete-Fourier-transformation-based spreading. Both methods achieve the dimensionality reduction without compromising the desired signal power by taking advantage of a null space of channels. The proposed receive BF methods reduce correlations between the received signals in the BF domain, which improves the robustness of GaBP against spatial correlation among fading coefficients. Simulation results assuming realistic BS and user equipment arrangement show that the proposed methods improve detection capability while significantly reducing the computational cost.

An adaptive array antenna can be considered as a useful tool of combating with fading in mobile communications. We can directly obtain the optimal weight coefficients without updating in temporal sampling, if the arrival angles and signal-to-noise ratio (SNR) of the desired and the undesired signals can be accurately estimated. The Maximum Entropy Method (MEM) can estimate the arrival angles, and the SNR from spatially sampled signals by an array antenna more precisely than the Discrete Fourier Transform (DFT). Therefore, this paper proposes and investigates an adaptive array antenna based on spatial spectral estimation using MEM. We call it MEM array. In order to reduce complexity for implementation, we also propose a modified algorithm using temporal updating as well. Furthermore, we propose a method of both improving estimation accuracy and reducing the number of antenna elements. In the method, the arrival angles can be approximately estimated by using temporal sampling instead of spatial sampling. Computer simulations evaluate MEM array in comparison with DFT array and LMS array, and show improvement owing to its modified algorithm and performance of the improved method.

This paper describes a spatial and temporal multipath channel model which is useful in array antenna environments for mobile radio communications. From this model, a no distortion criterion, that is an extension of the Nyquist criterion, is derived for equalization in both spatial and temporal domains. An adaptive tapped-delay-line (TDL) array antenna is used as a tool for equalization in both spatial and temporal domains. Several criterion for such spatial and temporal equalization such as ZF (Zero Forcing) and MSE (Mean Square Error), are available to update the weights and tap coefficients. In this paper, we discuss the optimum weights based on the ZF criterion in both spatial and temporal domains. Since the ZF criterion satisfies the Nyquist criterion in case of noise free, this paper applies the ZF criterion for the spatial and temporal equalization as a simple case. The Z transform is applied to represent the spatial and temporal model of the multipath channel and to derive the optimal weights of the TDL array antenna. However, in some cases the optimal antenna weights cannot be decided uniquely. Therefore, the effect on the equalization errors due to a finite number of antenna elements and tap coefficients can be shown numerically by computer simulations.

This paper proposes and investigates a tap selectable Viterbi equalizer for mobile radio communications. When the multipath channel is modeled by a tapped delay line only, the taps which may seriously affect the data sequence estimation are selected and used to calculate the trellis metric in the Viterbi algorithm. The proposed equalization algorithm can reduce the number of path metric calculations and the number of path selections in the Viterbi algorithm. Moreover, we propose an extended equalizer which has antenna diversity. This equalizer calculates the path metric using the antenna outputs and results of channel estimators. Computer simulation is used to evaluate the BER performance of the proposed equalizer in a multipath radio channel.

Several papers have been shown equalization in the reception side. However, equalization in transmission side that is partial response signaling (PRS) or precoding is also possible in a two-way interactive communication such as time or frequency division duplex (TDD of FDD). This paper proposes and investigates a system which includes a transmission equalization and reception equalization based on an array antenna. This system is the extension in spatial and temporal domains. The channel capacity can be improved in the super channel which includes the transmitter and receiver array antenna.