In the context of decoding multiple-input multiple-output (MIMO) symbols, many approaches rise as promising, such as successive interference cancellation and sphere decoding. The QR decomposition (QRD) of the channel impulse response matrix is a critical point to ensure good performance of the subsequent decoding steps for both approaches. This paper presents a low-complexity hardware architecture for the basic QRD algorithm, which is extended to two improved versions, namely the sorted QR decomposition (SQRD) and the minimum mean-square error SQRD. The main contribution of this work is a comparison of hardware implementations of the three variants and an analysis of their impact on a MIMO-BICM system regarding system communications performance and computational complexity.