In Code Division Multiple Access (CDMA) systems, the orthogonality of the spreading codes used to achieve multiple access over a channel is severely degraded due to multi-path interference. Expensive equalization techniques are needed to recover the transmitted signal. The Linear Minimum Mean Square Error (LMMSE) is a sub-optimal equalizer that is a good compromise between computational complexity and communication system performance. It uses computationally intensive matrix inversion operations to perform equalization. In this paper, we investigate the challenges of implementing a LMMSE equalizer on a Software Defined Radio (SDR) platform which is favored by the wireless industry due to its significant benefits of reduced development costs and accelerated time-to-market. We present COordinate Rotation DIgital Computer (CORDIC) instruction set extensions that speed up the QR Decomposition (QRD) of complex matrices and LMMSE equalization algorithms. The performance benefits are evaluated on the Sandbridge Sandblaster SB3000 low-power, multithreaded SDR processor. The proposed instructions provide significant performance improvements with little hardware overhead, while improving the accuracy of the wireless algorithms under investigation.