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Complex QR factorisation is a fundamental operation used in various applications such as adaptive beamforming and MIMO signal detection. In this paper, based on Givens rotation scheme, a high-throughput, fully parallel complex-valued QR factorisation (CQRF) design is presented. It features the lowest computing complexity in various factorising schemes and indicates no BER performance loss when applied to a MIMO signal detection system. Via carefully plotted scheduling, one CQRF computation can be completed in eight clock cycles. In hardware design, a low complexity and look-up-table-free CORDIC algorithm is employed to implement the rotation operations. Further design optimisations, such as hardware sharing of common modules and reduction of register usage by shortening the variable's life span, are also applied. Sized 2×2 and 4×4 chip designs largely following the IEEE 802.11n standard are developed. The implementation results in TSMC 0.18 um process technology show that the proposed 4×4 design, with a gate count of only 134.6 K, is capable of performing 15 M CQRFs per second. The measured power consumption is 196.3 mW at 120 MHz. Compound performance indexes such as area-time product and energy consumption per CQRF also indicate significant performance edges of the proposed designs.