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In this brief, a high-throughput and low-complexity fast Fourier transform (FFT) processor for wideband orthogonal frequency division multiplexing communication systems is presented. A new indexed-scaling method is proposed to reduce both the critical-path delay and hardware cost by employing shorter wordlength. Together with the mixed-radix multipath delay feedback structure, the proposed FFT processor can achieve very high throughput with low hardware cost. From analysis, it is shown that the proposed indexed-scaling method can save at least 11% memory utilizations compared to other state-of-the-art scaling algorithms. Also, a test chip of a 1.2 Gsample/s 2048-point FFT processor has been designed using UMC 90-nm 1P9M process with a core area of 0.97 mm2. The signal-to-quantization-noise ratio (SQNR) performance of this test chip is over 32.7 dB to support 16-QAM modulation and the power consumption is about 117 mW at 300 MHz. Compared to the fixed-point FFT processors, about 26% area and 28% power can be saved under the same throughput and SQNR specifications.