T. Sansaloni

The use of CORDIC in software defined radios: a tutorial

CORDIC is a versatile algorithm widely used for VLSI implementation of digital signal processing applications. This article presents a tutorial of how to use CORDIC to implement different communication subsystems that can be found in a software defined radio. Specifically, it shows how to use CORDIC to implement direct digital synthesizers, AM, PM, and FM analog modulators and ASK, PSK and FSK modulators, up-/down-converters of in-phase and quadrature signals, full mixers for complex signals, and phase detection for synchronizers. The article also shows some tricks to efficiently implement the algorithm

Efficient FPGA implementation of Cordic algorithm for circular and linear coordinates

This paper proposes an efficient FPGA implementation of a common CORDIC architecture for circular and linear coordinates. The proposed circuit is derived from the single coordinate CORDIC architectures and the mapping on the Xilinx slices is fully detailed. Relative placed macros in VHDL have been designed to show the goodness of the proposed architecture. All the circuits have been implemented in Virtex-E and Virtex-II devices and the results show that the area of the common architecture is hardly larger than the area of a single coordinate or single mode CORDIC architecture. It is also shown that if a common architecture is modeled with RTL style its implementation requires the double of area and the maximum throughput decreases more than a half.

Design and FPGA implementation of digit-serial FIR filters

In this paper the design of a family of digit-serial 8th-order FIR filters with programmable coefficients is presented. Both input data and coefficient size are 8 bits, but every filter of the family allows the computation with full precision of the intermediate data. The output data is truncated to 8 bits. The design of both, the digit-serial multiple precision multiply-and-accumulate and the digit-serial multiple-to-single precision converter, is detailed. All filters were implemented using an ALTERA FPGA being useful in applications with sample rate range from 5 to 22 MHz.

A study about FPGA-based digital filters

A set of operators suitable for digit-serial FIR filtering is presented. The canonical and inverted forms are studied. In each of these structures both the symmetrical and anti-symmetrical particular cases are also covered. All circuits have been implemented using an EPF10K50 Altera FPGA. The main results show that the canonical form presents less occupation and higher throughput. The 8-tap filter versions implemented can be applied in real-time processing with sample rate ranging up to 7 MHz using the bit-serial versions and up to 25 MHz with the bit-parallel ones.

Efficient Mapping of CORDIC Algorithm for OFDM-Based WLAN

In an orthogonal frequency division multiplexing-based wireless local area network receiver there are three operations that can be performed by a unique coordinate rotation digital computer (CORDIC) processor since they are needed in different time instants. These are the rotation of a vector, the computation of the angle of a vector and the computation of the reciprocal. This paper proposes a common architecture of CORDIC algorithm suitable to implement the three operations with a reduced increase of the hardware cost with respect to a single operation CORDIC. The proposed architecture has been validated on field programmable gate-arrays devices and the results of the implementation show that area saving around 28% and throughput increment of 64% are obtained.

FPGA-based radix-4 butterflies for HIPERLAN/2

This paper presents two different FPGA-implementation of radix-4 butterflies suitable for HIPERLAN 2. The two approaches lead to an efficient use of the hardware resources available in the target device and reduces the area with respect to the direct implementation of the radix-4 butterfly. Both methods reduce the area required storing the coefficients. The first one uses the symmetries of coefficients for reducing the number of functions to store; the second one takes advantage of the dual-port capability of the embedded block-RAM.

Fast FPGA-based pipelined digit-serial/parallel multipliers

In this paper fast pipelined digit-serial/parallel multipliers are proposed. The conventional digit-serial/parallel multipliers and their pipelined versions are presented. Every structure has been implemented on FPGA and the results are given. These results have been analysed and it is detected that the pipelined ones do not have the throughput improvement expected because of a logic depth increment. As a consequence, a new structure based on the fast serial/parallel multiplier proposed by Gnanasekaran [1985] has been developed. The new multipliers designed achieve better performance than the previous ones: their throughput is higher than it in the pipelined serial/parallel multipliers with nearly the same cost in area.

A comparison between lattice, cascade and direct form FIR filter structures by using a FPGA bit-serial distributed arithmetic implementation

In this paper, several bit-serial, high-order implementations of cascade, lattice and direct-form FIR filters using Distributed Arithmetic (DA) are studied. Although lattice and cascade structures present many interesting properties related to quantification error and stability, the DA versions have not been thoroughly compared. Three types of filters with their particular bit-serial DA model error have been built using an ALTERA 10K50 FPGA and their area-time figure is analysed. The results show that a 60th order bit-serial cascade and direct-form implementation at nearly 4 MHz and a 40th order lattice structure at 7.5 MHz can be implemented. Moreover, the lattice filter presents the lower quantification error.

Scheme for Reducing the Storage Requirements of FFT Twiddle Factors on FPGAs

A scheme for reducing the hardware resources to implement on LUT-based FPGA devices the twiddle factors required in Fast Fourier Transform (FFT) processors is presented. The proposed scheme reduces the number of embedded block RAM for large FFTs and the number of slices for FFT lengths higher than 128 points. Results are given for Xilinx devices, but they can be generalized for other advanced LUT-based devices like ALTERA Stratix.

Efficient mapping on FPGA of a Viterbi decoder for wireless LANs

In this paper an optimized hardware implementation on FPGA of a Viterbi decoder is presented for WLAN. A fixed-point analysis is made and its performance is compared with a soft decision decoding floating point model with CSI weight. Only 6 bits are needed to perform the soft quantification and 7 bits to the CSI, in order to maintain the performance of the floating point model. A normalization method is proposed to increase the throughput of the decoder, being possible to decode 172 Mbps when it is implemented in a Virtex 2 device. Power consumption results of the decoder implementation are presented for Hiperlan/2 maximum rate. Moreover, it has been shown that it is possible to reduce the power consumption disabling the unnecessary hardware depending on the WLAN modes.