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Diffstat (limited to 'ma/safety_reset.tex')
| -rw-r--r-- | ma/safety_reset.tex | 28 |
1 files changed, 20 insertions, 8 deletions
diff --git a/ma/safety_reset.tex b/ma/safety_reset.tex index f8c97f6..e403368 100644 --- a/ma/safety_reset.tex +++ b/ma/safety_reset.tex @@ -48,6 +48,7 @@ %\usepackage[pdftex]{graphicx,color} \usepackage{epstopdf} \usepackage{pdfpages} +\usepackage{minted} % pygmentized source code % Needed for murks.tex \usepackage{setspace} \usepackage[draft=false,babel,tracking=true,kerning=true,spacing=true]{microtype} % optischer Randausgleich etc. @@ -634,13 +635,24 @@ number of $0$ and $1$ bits the correlation between the sequence and uncorrelated contribution of the $+1$ terms of the correlation template approximately cancel out with the $-1$ terms when multiplied with an uncorrelated signal such as white gaussian noise or another pseudo-random sequence. -The longer the pseudo-random sequence the lower its cross-correlation with noise or other pseudorandom sequences of the -same length. Choosing a long sequence we increase modulation gain while decreasing bandwidth. For any given application -the sweet spot will be the shortest sequence that is long enough to yield sufficient SNR for subsequent processing -layers such as channel coding. - -Prototyping demodulation algorithms we have experimented by overlaying a modulated signal with actual grid frequency -measurements. At chip rates in the order of 1 chip per second we got useful results from 5 and 6 bit sequences already. +By using a family of pseudo-random sequences with low cross-correlation channel capacity can be increased. Either the +transmitter can encode data in the choice of sequence or multiple transmitters can use the same channel at once. The +longer the pseudo-random sequence the lower its cross-correlation with noise or other pseudorandom sequences of the same +length. Choosing a long sequence we increase modulation gain while decreasing bandwidth. For any given application the +sweet spot will be the shortest sequence that is long enough to yield sufficient SNR for subsequent processing layers +such as channel coding. + +A popular code used in many DSSS systems are Gold codes. A set of Gold codes has small cross-correlations. For some +value $n$ a set of Gold codes contains $2^n + 1$ sequences of length $2^n - 1$. Gold codes are generated from two +different maximum length sequences generated by linear feedback shift registers (LFSRs). For any bit count $n$ there are +certain empirically determined preferred pairs of LFSRs that produce Gold codes with especially good cross-correlation. +The $2^n + 1$ gold codes are defined as the XOR sum of both LFSR sequences shifted from $0$ to $2^n-1$ bit as well as +the two individual LFSR sequences. Given LFSR sequences \texttt{a} and \texttt{b} in numpy notation this is +\mintinline{python}{[a, b] + [ a ^ np.roll(b, shift) for shift in len(b) ]}. + +In DSSS modulation the individual bits of the DSSS sequence are called \emph{chips}. Chip duration determines modulation +bandwidth\cite{goiser01}. In our system we are directly modulating DSSS chips on mains frequency without an underlying +modulation such as BPSK as it is commonly used in DSSS systems. \subsection{Error-correcting codes} @@ -1109,7 +1121,7 @@ language such as C or rust. For prototyping these languages lack flexibility com % FIXME introduce project outline, specs -> proto -> demo above! To validate our modulation scheme we performed a series of simulations. We produced modulated frequency data that we -superimposed with either of simulated pink noise or an actual grid frequency measurement series. +superimposed with an actual grid frequency measurement series. % FIXME do test series with simulated noise emulating measured noise spectrum \section{Implementation of a demonstrator unit} |