By Hartman, E.F.; Sandia National Laboratories.; United States. Dept. of Energy.; United States. Dept. of Energy. Office of Scientific and Technical Information

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**Sample text**

The minimumdistance receiver calculates the distance between this and Wi, the response ~'f the filter to y (t). 7-9. The allpass filter has transfer function d- - :-1 HalJpa(z)= I-dz-l ' Idl < I . 108) I-dz-l and the channel model filter is (1- cz-1Xl - dz-l) . 109) (b) The zero location of the upper-path filter is outside the unit circle, since it is maximum-phase. In order to cancel this zero, the pole of the allpass filter would have to be outside the unit circle, which would make it anti-causal.

The signal power constraint now applies directly to the resulting2lJT-dimensional real-valued signal vector N N .. =1 .... 1 E[LIS.. 12] =E[1: Re(S.. m(S .. )2] = T Ps . 8-15. 255) This establishes the equivalence of the baseband and passband cases. 256) or at high SNR, SNRf' = SNRf' . lOolog1oSNR 2· 8-16. 258) Thus, for high SNR, to get the same channel capacity in half the bandwidth, the SNR (in dB) must be doubled, meaning that the SNR (not in dB) must be squared. We have M = 2, and assuming the signal constellation is ±l, a1 =1 and amin = 2, and 'YA =1.

375) where sine (x) = sin(x )/x. (d) The time domain pulses are not real. To use these pulses for orthogonal multipulse over a real channel, we need to modulate them, fonning the real-valued passband equivalent pulses h. 1 h. 376) for some roc ~ 7tIT. fi T -TI -O _. _.. D 2x T ~ CJ) 4x T Figure ~60. The Fourier transform for the orthonormal pulses in problem 6·29. The value of Hit (j CJ) in the dashed regions of the CJ) axis is determined by the requirement for conjugate symmetry. while the value in the solid regions is determined by 8(CJ).