Zero Forcing Decoding for QPSK Modulation in MIMO Channels

In this article, I present my custom implementation of a zero forcing decoding approach for QPSK signals in MIMO channels. I begin by explaining QPSK modulation and its role in digital communication systems, including how it encodes two bits per symbol using phase shifts. Next, I detail MIMO channel concepts and their significance in enhancing wireless communication capacity through spatial multiplexing. The core section describes the zero forcing decoding principle and its application in MIMO systems, where I implement the pseudo-inverse operation (typically using pinv() in MATLAB or np.linalg.pinv() in Python) to eliminate inter-antenna interference. The algorithm involves channel matrix inversion to separate spatially multiplexed streams, with code handling for singular value decomposition to avoid numerical instability. Finally, I analyze the advantages of this decoding method, such as computational simplicity and interference cancellation, while discussing limitations like noise enhancement in low-SNR scenarios. I propose potential improvements including regularization techniques and hybrid approaches combining with MMSE detection. Through this article, readers will gain comprehensive knowledge of QPSK, MIMO channels, and zero forcing decoding, along with practical implementation strategies for real-world applications.