This paper address the problem of classification of BPSK-modulated multicarrier signals with the peak-to-average power ratio (PAPR) exceeding 3/4 of the maximal possible value. By providing a simple characterization of such signals, an upper bound on their number are derived and propose a simple sufficient condition for the signals to have low PAPR. Based on this, a simple method for generation of signals with guaranteed PAPR gain of more than 2.5 dB using only two redundant tones are described.

We address the problem of classification of binary phase-shift keying-modulated multicarrier signals with the peak-to-average power ratio (PAPR) exceeding 3/4 of the maximal possible value. By providing a simple characterization of such signals, we derive an upper bound on their number, and propose a simple sufficient condition for the signals to have low PAPR. Based on this, we describe a simple method for generation of signals with guaranteed PAPR gain of more than 2.5 dB using only two redundant tones.

The spectral-null code S(n, k) of kth order and length n is the union of n-tuples with /spl plusmn/1 components, having kth-order spectral-null at zero frequency. We determine the exact asymptotic in n behavior of the size of such codes. In particular, we prove that for n satisfying some divisibility conditions, log/sub 2/|S(n, k)|=n-k/sup 2//2log/sub 2/n+c/sub k/+o(1), where c/sub k/ is a constant depending only on k and o(1) tends to zero when n grows. This is an improvement on the earlier known bounds due to Roth, Siegel, and Vardy (see ibid., vol40, p.1826-40, 1994).