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Tone-independent orthogonalizing lattice per tone equalizer (TOL-PTEQ) is introduced and its convergence is analyzed. Cyclic-prefix redundancy, one of the major drawbacks of orthogonal frequency division multiplexing (OFDM), can be reduced by TOL-PTEQ. Fast convergence and low computational complexity of TOL-PTEQ are also suitable properties for packet-based wireless communications and detections in which OFDM is widely deployed for their modulation technique.