Performance of M-ary noncoherent orthogonal signaling in Java Printer PDF417 in Java Performance of M-ary noncoherent orthogonal signaling

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4.5.3 Performance of M-ary noncoherent orthogonal signaling using barcode generation for j2se control to generate, create pdf417 2d barcode image in j2se applications. SQL Server 2000/2005/2008/2012 An important class of barcode pdf417 for Java noncoherent systems is M-ary orthogonal signaling. We have shown in 3 that coherent orthogonal signaling attains fundamental limits of power efficiency as M . We now show that this property holds for noncoherent orthogonal signaling as well.

We consider equal-energy M-ary orthogonal signaling with symbol energy Es = Eb log2 M.. Synchronization and noncoherent communication Exact error probability As shown in Problem 4.8, this is given by the expression Pe = M 1 k 1 k+1 k Es exp k+1 k + 1 N0 (4.59). Union bound For equal -energy orthogonal signaling with symbol energy Es , Proposition 4.5.6 provides a formula for the pairwise error probability.

We therefore obtain the following union bound: Pe M 1 E exp s 2 2N0 (4.60). Note that the union b PDF417 for Java ound coincides with the first term in the summation (4.59) for the exact error probability. As for coherent orthogonal signaling in 2, we can take the limit of the union bound as M to infer that Pe 0 if Eb /N0 is larger than a threshold.

However, as before, the threshold obtained from the union bound is off by 3 dB. As we show in Problem 4.9, the threshold for reliable communication for M-ary noncoherent orthogonal signaling is actually Eb /N0 > ln 2 ( 1 6 dB).

That is, coherent and noncoherent M-ary orthogonal signaling achieve the same asymptotically optimal power efficiency as M gets large. Figure 4.8 shows the probability of symbol error as a function of Eb /N0 for several values of M.

As for coherent demodulation (see Figure 3.20), we see that the performance for the values of M considered is quite far from the asymptotic limit of 1 6 dB..

Figure 4.8 Symbol err or probabilities for M-ary orthogonal signaling with noncoherent demodulation. .

Probability of symbol barcode pdf417 for Java error (log scale). 10 1. 10 2. M = 16. 10 3. 10 4. 10 5. 10 6 5. 1.6. 5 Eb / N0 (dB). 4.5 Performance of noncoherent communication 4.5.4 Performance of DPSK Exact analysis of the barcode pdf417 for Java performance of M-ary DPSK suffers from the same complication as the exact analysis of noncoherent demodulation of correlated signals. However, an exact result is available for the special case of binary DPSK, as follows. Proposition 4.

5.7 (Performance of binary DPSK) For an AWGN channel with unknown phase, the error probability for demodulation of binary DPSK over a two-symbol window is given by Pe = 1 E exp b 2 N0 Binary DPSK (4.61).

Proof of Proposition 4.5.7 Demodulation of binary DPSK over two symbols corresponds to noncoherent demodulation of binary, equal-energy, orthogonal signaling using the signals s+1 = 1 1 T and s 1 = 1 1 T in (4.

38), so that the error probability is given by the formula 1/2 exp Es /2N0 . The result follows upon noting that Es = 2Eb , since the signal sa spans two bit intervals, a = 1. Remark 4.

5.7 (Comparison of binary DPSK and coherent BPSK) The error probability for coherent BPSK, which is given by Q 2Eb /N0 exp Eb /N0 . Comparing with (4.

61), note that the high SNR asymptotics are not degraded due to differential demodulation in this case. For M-ary DPSK, Proposition 4.5.

5 implies that the high SNR asymptotics for , where the pairwise error probabilities are given by exp Es /2N0 1 is the pairwise correlation coefficient between signals drawn from the set sa a A , and Es = 2Eb log2 M. The worst-case value of dominates the high SNR asymptotics. For example, if a n are drawn from a QPSK constellation 1 j , the largest value of can be obtained by correlating the signals 1 1 T and 1 j T , which yields = 1/ 2.

We therefore find that the high SNR asymptotics for DQPSK, demodulated over two successive symbols, are given by Pe DQPSK exp Eb 2 2 N0. Comparing with the er spring framework pdf417 2d barcode ror probability for coherent QPSK, which is given by = Q 2Eb /N0 exp Eb /N0 , we note that there is a degradation of 2.3 dB (10 log10 2 2 = 2 3). It can be checked using similar methods that the degradation relative to coherent demodulation gets worse with the size of the constellation.

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