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This paper presents a real-valued discrete multicamer modulation approach that is based on the use of the discrete Hartley transform (DHT) and its inverseĀ ...
DISCRETE HARTLEY TRANSFORM BASED MULTICARRIER MODULATION Chin-Liang Wangt, Ching-Hsien Changt, John L. Fan*, and John M . CiofJi' 'Department of Electrical Engineering, National Tsing Hua University, Hsinchu, Taiwan 300, R.O.C. *Information Systems Laboratory, Department of Electrical Engineering, Stanford University, Stanford, CA 94305

ABSTRACT This paper presents a real-valued discrete multicamer modulation approach that is based on the use of the discrete Hartley transform (DHT) and its inverse (IDHT) to perform the modulation and demodulation operations. Since the DHT and IDHT definitions are identical, we can use the same hardware or program to implement the modulator and demodulator of the proposed multicarrier method. As compared to the complexvalued discrete Fourier transform based multicamer modulation method, the proposed one achieves the same transmission performance with reduced computational complexity and implementation cost.

1. INTRODUCTION Multicamer modulation (MCM) techniques have proved to be effective for optimization of the transmission performance over channels with moderate or severe intersymbol interference [I], [2]. Such techniques have received great attention in communication systems design recently. For example, one digital implementation form of MCM called discrete multitone (DMT) modulation has been selected by various standards institutes for asymmetric digital subscriber lines (ADSL) service which offers several megabits of data transmission per second on ordinary phone lines [3], [4]. The DMT technique is now also being considered for standards for very high-speed digital subscriber lines (VDSL) service whose data rate would be as high as 26 megabits per second [SI-[7]. Moreover, another digital form of MCM called orthogonal frequency division multiplexing (OFDM) has been standardized or extensively investigated for broadcast digital radio applications and wireless communications [8]-[101. For the current DMT-based or OFDM-based transceivers, the modulator needs to compute a long-length inverse discrete Fourier transform (IDFT), and the demodulator needs to compute a longlength DIT, where the transform length is up to 512 or more. For such long-length DITADIT computations, a great number of complex multiplications are required and each of them basically involves four real multiplications and two real additions. Clearly, the complexity of a DMT-based or OFDM-based transceiver would be reduced if the corresponding modulator/demodulator could be implemented using purely real transforms while fast algorithms similar to the fast Fourier transform (FIT) algorithm can still be applied.

architectures available for the DHT computation (see, for example, [12]-[15] and the references therein). It is shown that the proposed DHT-based MCM method achieves the same transmission performance as the DFT-based MCM method, but requires less computational complexity.

2. REVIEW OF DFT-BASED MCM Consider a real sequence of N points denoted as ( q,al. ff2, ... , f f N . 2 , ~ N . I ) .where N is a power of two. To transmit the sequence through a channel with impulse response [p,, OSnSv) by DFTbased MCM, we need to form an N-point conjugate-symmetric complex-valued sequence { X k , OSk