Orthogonal time frequency space (OTFS) is a promising technology for high-mobility wireless communications. However, the equalization realization in practical OTFS systems is a great challenge when the non-ideal rectangular waveforms are adopted. In this paper, first of all, we theoretically prove that the effective channel matrix under rectangular waveforms holds the block-circulant property and the special Fourier transform structure with time-domain channel. Then, by exploiting the proved property and structure, we further propose the corresponding low-complexity algorithms for two mainstream linear equalization methods, i.e., zero-forcing (ZF) and minimum mean square error (MMSE). Compared with the existing direct-matrixinversion-based equalization, the complexities can be reduced by a few thousand times for ZF and a few hundred times for MMSE without any performance loss, when the numbers of symbols and subcarriers are both 32 in OTFS systems.
A novel hardware Gaussian noise generator based on the Box-Muller method and the Coordinate Rotation Digital Computer (CORDIC) Algorithm is presented. The main novelties of this work are using Modified CORDIC Algorithm with Domain Folding (MDF-CORDIC) algorithm and expanding the range of convergence of the CORDIC algorithm to improve the operation accuracy for the elementary functions involved in the Box-Muller method. Due to the modified CORDIC algorithm, two 16-bit highly accurate noise samples are generated every clock cycle and the accuracy can reach 10 −7 while the conventional is 10 −3 . The noise generator can also accurately model a true Gaussian probability density function even at high σ values. This design is implemented on a Xilinx XC4VLX15 Virtex-4 device fieldprogrammable gate array (FPGA) at 155 MHz; it takes up 5% of the device and produces 155 million samples per second.
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