In the pursuit of energy efficiency in next-generation communication systems, approximate computing is emerging as a promising technique. In the proposed work, efforts are made to address the challenge of bridging the gap between the level of approximation and the Quality-of-Service (QoS) of the system. The application of approximate multiplication to wireless signal detection is explored systematically, illustrated by employing Truncated Multiplication (TM) on Quadrature Phase Shift Keying (QPSK) Minimum Mean Square Error (MMSE) detection. The irregularities induced by approximation in the multiplication operation employed in wireless signal detection are captured by the Approximate Multiplication Noise (AMN) model, which aids in the analysis of signal fidelity and resiliency of the system. The energy efficiency gains through approximation are highlighted in the approximation analysis. Signal fidelity analysis provides the capability to predict system output for varying levels of approximation, which aids in improving the stability of the system. The higher approximation levels are advantageous in low Signal-to-Noise Ratio (SNR) regimes, whereas lower approximation levels prove beneficial in high SNR regimes.