Digital communications in Software Printer Code 128B in Software Digital communications

Digital communications using barcode maker for software control to generate, create code 128 code set c image in software applications. USS-128 Table 6.1. Spectral densities of channel and shaping filters f . C(f ). 2 . S1(f ). 2 . S2(f ). 2 0 0 0 0 1 1 0 0 2 25 0 1/16 3 225 1/8 1/8 4 400 1/4 1/8 5 625 1/4 1/8 6 900 1/4 1/8 7 400 1/8 1/8 8 100 0 1/8 9 25 0 1/8 10 1 0 1/16 11 0 0 0. T q 2p p=T Z  ln  N0 d!: X ej!T N0 p=T Thus, the DFE is clearly less sensitive to variations in the folded spectrum than the linear equalizer. The optimal shaping filter to use with a DFE is well approximated in most situations by a flat allocation of power across the Nyquist band for high SNR, and water-filling (see 2) on the inverse of the folded spectrum otherwise..

Example 6.8 Comparison of USS Code 128 for None infinite length MMSE linear equalizer (LEQ) and DFE For a particular channel c(t), infinite length linear equalizers are compared at two different symbol rate/carrier frequency pairs. Data for the psd are given in Table 6.

1. (a) Compute . H1(f ). 2 . C(f ). 2. S1(f). 2, and then compare the M Code128 for None SE J for a LEQ with the ZF and MMSE criteria, and the DFE under the MMSE criterion. (b) Repeat using S2(f ). Solution (a) This is simply a matter of substituting into the appropriate equations, replacing the integration by a summation, and changing variable to f 2p!.

Note that in this case the shaping filter 3 dB points are separated by 1/T 4. Thus the calculation for the ZF LEQ becomes. 1=2T Z 1=2T. df % 1=16 jHf1 f j2 6 X 3. 1 jHf1 f j2 where Hf1 denotes the fol Code 128A for None ding of the points separated by 1/T, and (f 1). The folding is from f 7 down onto f 3. Hence, J (1/16) [(8/(225 400) 4/400 4/625 4/900)]; in dB, J 26.

8 dB. Since the rectangle rule integration of . S(f ). 2 1 (the transmitted po Software Code 128 Code Set A wer), the SNR is thus 26.8 dB. The MMSE LEQ calculation differs only in adding a 1 to the denominator of each term in the sum, resulting in a negligible change.

This is expected since the SNR is high over the whole of the folded spectrum. The calculation for the DFE is J eln 2= 225 400 ln 1=400 ln 1=625 ln 1=900 =4 ; yielding an SNR of 27.1 dB.

The small improvement reflects slightly less noise enhancement, as the folded spectrum is not completely flat. (b) Now 1/T 8, and the sum is from 2 to 9, with the term for f 10 folded onto f 2. The SNR results are 17.

5 dB for the ZF LEQ, 17.7 dB for the MMSE LEQ, and 22.3 dB for the DFE.

The much larger variations in the folded spectrum account for the difference in. 6.4 Communication over dispersive channels performances among the eq Software Code 128 Code Set B ualizers, with the linear equalizers enhancing noise at the band edges. The lower SNR for the DFE compared with the first situation reflects use of a part of the spectrum with lower average SNR..

For the finite length, fr actionally spaced DFE, the MMSE filter coefficients can be derived using a procedure similar to that used for the LEQ. Model the received signal prior to the equalizer by r t . 1 X k 1 Ik h t kT n t (6:17). and sample it at the rate 1/. Then element (i, j) of the autocorrelation matrix R is given by Rij . 1 X k 1 h hk j Nij ; k i (6:18). where Nij is the correspo nding entry of the noise autocorrelation matrix (zero for off-diagonal entries if the noise is white, but in general derived from the noise autocorrelation function). Define hT hD ; hD  ; : : : ; hD N 1  T . Then the forward filter coefficients are given by c W 1 h ; where Wij Rij .

D M X k D 1 (6:19). h hk j ; k i and then the feedback coefficients are given by bj N 1 X k 0 ck hD j k ; j 1; 2; . . .

; M:. (6:20). The MMSE, assuming unit energy for the channel, is then J 1 N 1 X k 0 ck hD k :. (6:21). The optimal delay D for f inite filter lengths can be selected by trial and error. Note that for finite filter lengths, the forward filter is only approximately a noise-whitening matched filter. It must also work to reduce the postcursor ISI outside the span of the feedback filter.

Consequently, J is larger than for the infinite length DFE.. Example 6.9 DFE for a two Code 128 Code Set A for None -tap channel Determine the MMSE DFE for the channel 1 0:5Z 1 , where AWGN of variance 0.05 is added.

Determine the MSE. Solution This situation is simple enough not to need to resort to the above equations. As there is no precursor ISI, all that is required is a single feedback coefficient to cancel the second term in.

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