Zero-Forcing Frequency-Domain Equalization for Generalized DMT Transceivers with Insufficient Guard Interval
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Zero-Forcing Frequency-Domain Equalization for Generalized DMT Transceivers with Insufficient Guard Interval Tanja Karp Department of Electrical and Computer Engineering, Texas Tech University, Lubbock, TX 79409, USA Email: [email protected]
Steffen Trautmann Infineon Technologies Austria AG, Development Center Villach Siemens Strasse 2, 9500 Villach, Austria Email: steff[email protected]
Norbert J. Fliege Institute of Computer Engineering, Mannheim University, 68131 Mannheim, Germany Email: [email protected] Received 28 February 2003; Revised 16 September 2003 We propose a zero-forcing frequency domain block equalizer for discrete multitone (DMT) systems with a guard interval of insufficient length. In addition to the insufficient guard interval in the time domain, the equalizer takes advantage of frequency domain redundancy in the form of subcarriers that do not transmit any data. After deriving sufficient conditions for zero-forcing equalization, that is, complete removal of intersymbol and intercarrier interference, we calculate the noise enhancement of the equalizer by evaluating the signal-to-noise ratio (SNR) for each subcarrier. The SNRs are used by an adaptive loading algorithm. It decides how many bits are assigned to each subcarrier in order to achieve a maximum data rate at a fixed error probability. We show that redundancy in the time domain can be traded off for redundancy in the frequency domain resulting in a transceiver with a lower system latency time. The derived equalizer matrix is sparse, thus resulting in a low computational complexity. Keywords and phrases: discrete multitone modulation, insufficient guard interval, zero-forcing frequency domain equalization, noise enhancement, system latency time.
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INTRODUCTION
Discrete multitone (DMT) modulation has been standardized for high data rate transmission over twisted-pair copper wires such as in asymmetric digital subscriber lines (ADSL) and very high bitrate digital subscriber lines (VDSL), which allow transmission speeds up to 8 Mbps, or 50 Mbps, respectively, over ordinary twisted-pair copper lines of distances up to 4 km. The block diagram of a DMT transceiver is shown in Figure 1. In order to achieve easy equalization at the receiver, a guard interval is introduced at the transmitter in form of a cyclic prefix. Its length has to be at least as long as the memory of the channel. Coupling the guard interval to the length of the channel impulse response has turned out to be a severe limitation of DMT. For twisted-pair copper wires, the length of the impulse response increases with the length of the line. Thus, if the guard interval is fixed to a maximum
length, the channel length has to be restricted to a maximum, too, resulting in applications over short distances, as, for example, VDSL. Increasing the guard interval for a fixed block length M reduces the channel throughput, since the guard interval contains redundant samples only. If we increase the block length by the same amount as the guard interval, in order to mainta
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