The Art of Piecewise Linear Approximation in MMSE Estimator for Most Accurate and Fast Frequency Extraction in DIFM Receivers

Detection of wideband passive radar signals, accomplished by instantaneous frequency measurement (IFM) systems, is crucial for gaining a profound knowledge of environmental circumstances. The need for fast pulse detection has hindered the investigation of frequency extraction with higher accuracy in IFM receivers. A noteworthy research in recent years shows that fast and reliable frequency extraction in high bit-count (HBC) IFMs while attaining a better frequency accuracy [called intelligent, reliable, and design-independent (InReDI)] is feasible. In addition, some investigated process-intensive algorithms like the minimum mean squared error (MMSE) estimator promise excellent frequency accuracy. In this work, we present a new method of MMSE algorithm modified by a piecewise linear approximation [named linear approximation of MMSE (LAMMSE)]. By utilizing the InReDI methodology and the novel LAMMSE algorithm, we propose a new architecture for a fast, accurate, and reliable frequency extraction (FAREx) in HBC digital IFMs (DIFM) receivers. The proposed FAREx architecture resolves the compromise challenge between frequency accuracy and extraction speed that has been long lingered in DIFM receivers. We have implemented the new architecture using Xilinx field-programmable gate array (FPGA) on a fabricated 15 bit, 2-4 GHz, and 70 dB dynamic range IFM receiver. The measurement results show an average frequency rms error of 1.43 MHz for a CW signal, 2.49 MHz average rms error for a 50 ns pulsed input signal, and 2.7 MP/s detection speed, representing a state-of-the-art receiver and a breakthrough compared to the latest works.