Adaptive beamforming for binary phase shift keying communication systems

Abstract

The paper revisits adaptive beamforming assisted receiver for multiple antenna aided multiuser systems that employ binary phase shift keying (BPSK) modulation. The standard minimum mean square error (MMSE) design is based on the criterion of minimising the mean square error (MSE) between the beamformer's desired output and complex-valued beamformer's output. Since the desired output for BPSK systems is real-valued, minimising the MSE between the beamformer's desired output and real-part of the beamformer's output can significantly improve the bit error rate (BER) performance, and we refer to this alternative MMSE design as the real-valued MMSE (RV-MMSE) to contrast to the standard complex-valued MMSE (CV-MMSE) design. The minimum BER (MBER) design however still outperforms the RV-MMSE solution, particularly for overloaded systems where degree of freedom of the antenna array is smaller than the number of BPSK users. Adaptive implementation of this RV-MMSE beamforming design is realised using a least mean square (LMS) type adaptive algorithm, which we refer to as the RV-LMS, in comparison to the standard CV-LMS algorithm. The RV-LMS adaptive beamformer is shown to have a similar computational complexity as the adaptive MBER beamforming implementation known as the least bit error rate (LBER), imposing only half of the computational requirements of the CV-LMS algorithm. r

Properties, performance and practical interest of the widely linear MMSE beamformer for nonrectilinear signals

“…WL MMSE estimation have received a great interest these last twenty years for SO noncircular (or improper) [27] signals [28], [7], [11], [12], [13], [6], [21], [25], [30]. In the context of radio communications networks using rectilinear modulations such as BPSK or ASK modulations [29], it has been shown in particular in [7], [11], [12], [13], [21] that the WL MMSE receiver allows to implement SAIC of one intra-network interference in contrast to linear MMSE receiver.…”

LSMI Beamformer with Adaptation based on Estimation Error

“…These RAB methods -SMI or LSMI -are computationally expensive when compared to the simpler methods [9], such as the DS one, as they use complex operations, such as matrix inversion. These algorithms are very robust and they can achieve very high SINR values, but sometimes the DS method is able to achieve similar SINR performance with a much lower computational cost.…”

“…The LSMI beamformer is a robust approach to the SMI beamformer and it is based on the diagonal loading of the sample covariance matrix [10]. This means that the matrixR is replaced by a diagonally loaded matrixR DL in the weight vector expression given by equation (7), as in equation (9), where γ is the diagonal loading factor and I is the identity matrix with the dimensions corresponding to the size ofR.…”

Analysis of the Loading Factor Behavior in a LSMI Beamformer

“…Adaptive beamforming is a versatile approach to detect and estimate the SOI [1], [5], [6]. It is used when the environment variables -e.g., noise, direction-of-arrival (DOA), array imperfections, etc.…”