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AN EFFICIENT FREQUENCY DIVISION MULTIPLEXING ALGORITHM

IP.com Disclosure Number: IPCOM000007123D
Original Publication Date: 1994-Feb-01
Included in the Prior Art Database: 2002-Feb-27
Document File: 4 page(s) / 244K

Publishing Venue

Motorola

Related People

Alex Tziortzis: AUTHOR

Abstract

Frequency division multiplexing (FDM) is the backbone for many spectrally efficient digital com- munications systems. Implementing the frequency division multiplexing in a practical system, oRen using digital signal processors, is a difftcult task since each signal (on the transmitter side, for example) to be frequency division multiplexed has to be interpo- lated, filtered, modulated (all of these being performed in the digital domain), and then summed together, If not computed in an efficient manner, these tasks take an enormous amount of processing power and therefore (for complicated modulation schemes) make the digital communications system unrealizable with one digital signal processor. One commonly used solution is the filterbank/polyphase filter implementation ofthe FDM concept. It exploits redundancies in the computation and multiplications by zeroes, allowing the computational savings. There is still a great deal of computation in the filterbank since each signal to be multiplexed together is filtered separately. A more efficient algorithm is the overlap- add algorithm. While being more computationally efficient, it does not allow arbitrary frequency spac- ing. The new invention alleviates some ofthe draw- backs of the overlap-add algorithm by allowing arbi- trary frequency spacing.

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MOTOROLA Technical Developments Volume 21 February 1994

AN EFFICIENT FREQUENCY DIVISION MULTIPLEXING ALGORITHM

by Alex Tziortzis

  Frequency division multiplexing (FDM) is the backbone for many spectrally efficient digital com- munications systems. Implementing the frequency division multiplexing in a practical system, oRen using digital signal processors, is a difftcult task since each signal (on the transmitter side, for example) to be frequency division multiplexed has to be interpo- lated, filtered, modulated (all of these being performed in the digital domain), and then summed together, If not computed in an efficient manner, these tasks take an enormous amount of processing power and therefore (for complicated modulation schemes) make the digital communications system unrealizable with one digital signal processor. One commonly used solution is the filterbank/polyphase filter implementation ofthe FDM concept. It exploits redundancies in the computation and multiplications by zeroes, allowing the computational savings. There is still a great deal of computation in the filterbank since each signal to be multiplexed together is filtered separately. A more efficient algorithm is the overlap- add algorithm. While being more computationally efficient, it does not allow arbitrary frequency spac- ing. The new invention alleviates some ofthe draw- backs of the overlap-add algorithm by allowing arbi- trary frequency spacing.

  The invention allows the use for semi-arbitrary frequency spacing in a frequency division multiplex- ing system (FDM) which uses the efficient overlap- add algorithm found in the textbook Multirate Dig- ital Signal Processing by Crochiere and Rabiner. W?th this overlap add FDM algorithm, there are only a discrete, finite number of frequency spacings possi- ble for the multiplexed signals. This can create prob- lems ifthe signals to be multiplexed together have a wider bandwidth than the discrete spacing deter- mined by the parameters of the overlap-add algo- rithm. For example, 6 signals, each with a 3 db two sided bandwidth of 15.6 kHz (assuming a 31 kHz complex valued sampling rate), are to be frequency division multiplexed together in a digital communi- cation system using the efficient overlap-add tech-

@ Motorola. 1°C. 1994

nique. Using an interpolation ratio of4 and a length 8 Fast Fourier Transform (FIT) routine, the fre- quency spacing of the signals will be 31*4/8 = 15.5 kHz. Since each of the 6 signals are 15.6 kHz in bandwidth, there will be some spectral leakage caus- ing some distortion and information loss. The inter- polation ratio and length of the FFT must be inte- ger. Ifwe change the interpolation ratio or FFI length to accommodate a wider frequency spacing, we waste spectrum. For example, if we used a 7 point FFT (which is, by the way, more computationally com- plex than an efficient 8 point FFT), the frequency spacing would be 31*4/7 = 17.7 kHz, creating unwanted 2.1 kHz "gaps" between each freq...