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This is the first "essentially complete" version of the FTRSD paper.
git-svn-id: svn+ssh://svn.code.sf.net/p/wsjt/wsjt/branches/wsjtx@6385 ab8295b8-cf94-4d9e-aec4-7959e3be5d79
This commit is contained in:
Joe Taylor
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lib/ftrsd/ftrsd_paper/JT65B_EME.png
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lib/ftrsd/ftrsd_paper/JT65B_EME.png
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@ -110,6 +110,8 @@ moonbounce
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) communication, where the scattered return signals are always weak.
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It was soon found that JT65 also enables worldwide communication on the
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HF bands with low power, modest antennas, and efficient spectral usage.
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At least several thousand amateurs now use JT65 on a regular basis, making
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contacts on all bands from 160 meters through microwaves.
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\end_layout
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\begin_layout Standard
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@ -179,7 +181,7 @@ name "sec:JT65-messages-and"
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\end_inset
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JT65 messages and Reed Solomon Codes
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JT65 Messages and Reed Solomon Codes
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\end_layout
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\begin_layout Standard
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@ -771,7 +773,7 @@ name "sec:The-decoding-algorithm"
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\end_inset
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The Franke-Taylor decoding algorithm
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The Franke-Taylor Decoding Algorithm
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\end_layout
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\begin_layout Standard
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@ -849,7 +851,7 @@ The FT algorithm uses quality indices made available by a noncoherent 64-FSK
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\end_inset
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of the symbol's fractional power
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\begin_inset Formula $p_{1,\, j}$
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\begin_inset Formula $p_{1,\,j}$
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\end_inset
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in a sorted list of
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@ -919,7 +921,7 @@ t educated guesses to select symbols for erasure.
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, the soft distance between the received word and the codeword:
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\begin_inset Formula
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\begin{equation}
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d_{s}=\sum_{j=1}^{n}\alpha_{j}\,(1+p_{1,\, j}).\label{eq:soft_distance}
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d_{s}=\sum_{j=1}^{n}\alpha_{j}\,(1+p_{1,\,j}).\label{eq:soft_distance}
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\end{equation}
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\end_inset
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@ -937,7 +939,7 @@ Here
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\end_inset
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if the received symbol and codeword symbol are different, and
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\begin_inset Formula $p_{1,\, j}$
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\begin_inset Formula $p_{1,\,j}$
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\end_inset
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is the fractional power associated with received symbol
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@ -981,7 +983,7 @@ In practice we find that
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\begin_layout Standard
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\begin_inset Formula
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\begin{equation}
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u=\frac{1}{n}\sum_{j=1}^{n}S(c_{j},\, j).\label{eq:u-metric}
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u=\frac{1}{n}\sum_{j=1}^{n}S(c_{j},\,j).\label{eq:u-metric}
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\end{equation}
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\end_inset
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@ -1014,7 +1016,7 @@ The correct JT65 codeword produces a value for
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bins containing noise only.
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Thus, if the spectral array
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\begin_inset Formula $S(i,\, j)$
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\begin_inset Formula $S(i,\,j)$
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\end_inset
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has been normalized so that the average value of the noise-only bins is
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@ -1263,7 +1265,7 @@ For each received symbol, define the erasure probability as 1.3 times the
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a priori
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\emph default
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symbol-error probability determined from soft-symbol information
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\begin_inset Formula $\{p_{1}\textrm{-rank},\, p_{2}/p_{1}\}$
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\begin_inset Formula $\{p_{1}\textrm{-rank},\,p_{2}/p_{1}\}$
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\end_inset
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.
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@ -1548,7 +1550,7 @@ Deep Search
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\begin_inset Quotes erd
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\end_inset
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algorithm is presented in an accompanying text box.
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algorithm is presented as Algorithm 2 in an accompanying text box.
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\end_layout
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\begin_layout Standard
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@ -1723,8 +1725,8 @@ Simulated results on the AWGN channel
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\end_layout
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\begin_layout Standard
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Results of simulations using the BM, FT, and KV decoding algorithms on the
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JT65 code are presented in terms of word error rate versus
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Results of simulations using the BM, KV, and FT, decoding algorithms on
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the JT65 code are presented in terms of word error rate versus
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\begin_inset Formula $E_{b}/N_{o}$
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\end_inset
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@ -1871,10 +1873,10 @@ reference "fig:bodide"
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or less.
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The circumstances for minimal amateur-radio QSOs are very different, however.
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Error rates of order 0.1 or higher may be acceptable.
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In this case the essential information is better presented in a plot showing
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the percentage of transmissions copied correctly as a function of signal-to-noi
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se ratio.
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Decoding failure rates of order 0.1 or higher may be acceptable.
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In this case the essential information is more usefully presented in a
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plot showing the percentage of transmissions copied correctly as a function
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of signal-to-noise ratio.
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Figure
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\begin_inset CommandInset ref
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LatexCommand ref
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@ -2078,7 +2080,7 @@ Number of trials needed to decode a received word versus Hamming distance
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\begin_inset Formula $\mathrm{SNR}{}_{2500}=-24$
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\end_inset
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dB, which corresponds to
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dB or
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\begin_inset Formula $E_{b}/N_{o}=5.1$
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\end_inset
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@ -2123,7 +2125,7 @@ reference "fig:Psuccess"
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Hz.
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These simulated Doppler spreads are comparable to those encountered on
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HF ionospheric paths and also for EME at VHF and the lower UHF bands.
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For reference, we note that the JT65 symbol rate is about 2.69 Hz.
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For comparison we note that the JT65 symbol rate is about 2.69 Hz.
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\end_layout
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@ -2216,61 +2218,109 @@ WSJT-X
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\end_layout
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\begin_layout Section
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Summary
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On-the-air Experience
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\end_layout
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\begin_layout Standard
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...
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Still to come ...
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The JT65 protocol has proven remarkably versatile.
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Today the mode is used by thousands of amateurs around the world, communicating
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over terrestrial paths on the MF and HF bands and over terrestrial as well
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as EME paths from 50 MHz through 10 GHz.
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Three submodes are in use, together accommodating a wide range of Doppler
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spreads and potential instrumental instabilities.
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All three submodes transmit the 63 data symbols interspersed with 63 synchroniz
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ation symbols at keying rate 11025/4096 = 2.69 baud.
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Submode JT65A uses tone spacing equal to the symbol rate, so its total
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occupied bandwidth is
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\begin_inset Formula $66\times2.69=177.6$
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\end_inset
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Hz.
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Submodes B and C have tone spacings and occupied bandwidths 2 and 4 times
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larger.
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In practice JT65A is generally used at 50 MHz and below, JT65B on 144 through
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432 MHz, and JT65C at 1296 MHz and above.
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\end_layout
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\begin_layout Standard
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Possible ideas:
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\end_layout
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\begin_layout Standard
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Tie it in to
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\emph on
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WSJT-X
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\emph default
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and
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\emph on
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MAP65
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\emph default
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.
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\end_layout
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\begin_layout Subsubsection*
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Experience with FT on crowded HF bands:
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\end_layout
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\begin_layout Standard
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(Re the following paragraph and Figure
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Figure
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\begin_inset CommandInset ref
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LatexCommand ref
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reference "fig:spectrogram"
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reference "fig:JT65B_EME"
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\end_inset
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- just playing around with ideas - feel free to change, delete, etc.)
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shows portions of the main window and spectrogram displays of program
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\emph on
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WSJT-X,
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\emph default
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illustrating replies to an EME CQ from K1JT on 144.118 MHz using submode
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JT65B.
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Speckled vertical lines on the waterfall at 1494 and 1515 Hz are the synchroniz
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ing tones of signals from DL7UAE and SP6GWB.
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Other visible speckles (barely above the noise) up to about 1693 Hz are
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data tones from these two stations.
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Two lines of decoded text show that the estimated average signal strengths
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were
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\begin_inset Formula $\mathrm{SNR}{}_{2500}=-23$
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\end_inset
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and
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\begin_inset Formula $-24$
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\end_inset
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dB, respectrively, just one or two dB above the decoding threshold for
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the FT decoder.
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Note that the two signals overlap throughout 94% of their occupied bandwidths,
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yet both are decoded cleanly and without errors.
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Such behavior is typical of the JT65 protocol.
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\end_layout
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\begin_layout Standard
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The JT65 mode has proven to be remarkably versatile.
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Thousands of users regularly use the mode for two-way communication over
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terrestrial paths and the earth-moon-earth (
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\begin_inset Quotes eld
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\begin_inset Float figure
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wide false
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sideways false
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status open
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\begin_layout Plain Layout
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\align center
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\begin_inset Graphics
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filename JT65B_EME.png
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\end_inset
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moonbounce
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\begin_inset Quotes erd
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\end_layout
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\begin_layout Plain Layout
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\begin_inset Caption Standard
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\begin_layout Plain Layout
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\begin_inset CommandInset label
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LatexCommand label
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name "fig:JT65B_EME"
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\end_inset
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Examples of JT65B EME signals recorded at K1JT.
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Numbers above the spectrogram are audio frequencies in Hz, and the spectrogram'
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s vertical direction is one minute of time.
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The horizintal green bar indicates full band occupied by the second decoded
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signal, a reply from SP6GWB.
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See text for additional details.
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Plain Layout
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\end_layout
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\end_inset
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) path at frequencies from VHF to microwaves, and over multi-hop ionospheric
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reflection paths at HF.
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Use on HF was not originally an intended application for the mode, but
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at present HF use accounts for the largest number of 2-way contacts.
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\end_layout
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@ -2282,36 +2332,27 @@ reference "fig:spectrogram"
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\end_inset
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(top) shows JT65 activity in a one-minute time-segment on the 20m amateur
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band during crowded daytime band conditions (JT65 transmissions start at
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the beginning of a minute and last for approximately 47 s).
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With some straightforward signal processing to demodulate the signals and
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produce soft-symbol data for the FT decoder we are able to extract and
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decode 21 messages from the data summarized in Figure 5.
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This is achieved with a relatively small timeout parameter
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\begin_inset Formula $T=1000$
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shows activity in submode JT65A during a single minute on the 20 m amateur
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band.
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At this time the band was crowded with overlapping signals; you can probably
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count at least 19 distinct synchronizing tones (the speckled vertical lines
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in the figure), and see that in some places as many as four signals overlap.
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After straightforward signal processing to demodulate the signals and produce
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soft-symbol data for the FT decoder, program
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\emph on
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WSJT-X
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\emph default
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extracts and decodes 21 error-free messages from this recorded data segment.
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This is achieved with a relatively small timeout parameter,
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\begin_inset Formula $T=1000.$
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\end_inset
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and in spite of the fact that the 200 Hz-wide 65-FSK (sync plut 64-FSK)
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signals overlap, with as many as 4 signals superposed in some parts of
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the spectrum.
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To achieve these results we use two successive sweeps over the spectrum.
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The strongest signals are sequentially decoded and then subtracted from
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the spectrum on the first pass.
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Figure
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\begin_inset CommandInset ref
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LatexCommand ref
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reference "fig:spectrogram"
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\end_inset
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(bottom) shows the spectrogram after subtracting 12 signals that were decoded
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in the first pass.
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Another 9 signals are decoded from the data shown in the bottom figure
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on the second pass.
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Using exactly the same pre-processing, but without soft-symbol information
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the errors-only BM decoder is able to decode only 12 messages in two passes
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over the data.
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For these results the decoder uses two successive sweeps over the spectrum.
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The strongest signals (12 in this example) are sequentially decoded and
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subtracted from the raw data after the first pass.
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Another 9 signals are decoded in the second pass.
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For comparison, the hard-decision BM decoder decodes only 12 messages from
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this recording (9 in the first pass and 3 more in a second pass).
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\end_layout
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\begin_layout Standard
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@ -2331,18 +2372,6 @@ status open
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\end_inset
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\end_layout
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\begin_layout Plain Layout
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\begin_inset Graphics
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filename fig_subtracted.tiff
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width 6.5in
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BoundingBox 0bp 0bp 1126bp 202bp
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clip
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\end_inset
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\end_layout
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\begin_layout Plain Layout
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@ -2355,10 +2384,9 @@ name "fig:spectrogram"
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\end_inset
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(top) A spectrogram showing one minute of data collected under crowded band
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conditions on 20m during daytime hours.
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(bottom) The spectrogram after the subtracting all signals successfully
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decoded on the first pass.
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Spectrogram showing one minute of data collected under crowded band conditions
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on the 20 m band.
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Numbers on the scale are frequencies (in Hz) above 14.076 MHz.
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\end_layout
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@ -2377,27 +2405,60 @@ name "fig:spectrogram"
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\end_layout
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\begin_layout Standard
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Maybe one screen shot, or partial screen shot of the
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\begin_inset Quotes eld
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Our implementation of the FT decoder, written in a combination of Fortran
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and C, is freely available as open-source code
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\begin_inset CommandInset citation
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LatexCommand cite
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key "wsjt_sourceforge"
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\end_inset
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Band Activity
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\begin_inset Quotes erd
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.
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For the Berlekamp-Massey part of the algorithm we use routines written
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by Phil Karn, KA9Q
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\begin_inset CommandInset citation
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LatexCommand cite
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key "karn"
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\end_inset
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window?
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\end_layout
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, modified slightly so that the Reed-Solomon syndromes are computed only
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once in our most time-consuming loop (steps 2 through 8 in Algorithm 1).
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The FT algorithm is now an integral part of programs
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\emph on
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WSJT,
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\emph default
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\begin_layout Standard
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Some EME results needed!
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\end_layout
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\begin_layout Standard
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Something about the code repository and how to build
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\emph on
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MAP65,
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\emph default
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and
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\emph on
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WSJT-X
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\emph default
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.
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Improvement in sensitivity over the Kötter-Vardy decoder is small, only
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a few tenths of a dB, but especially on the EME path such small advantages
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are sometimes very important.
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Perhaps even more essential, programs in the
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\emph on
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WSJT
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\emph default
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suite are now entirely open source.
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We no longer need to use the patented KV algorithm or the specially licensed
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executable program
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\family typewriter
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kvasd[.exe]
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\family default
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.
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\end_layout
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\begin_layout Section
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Acknowledgments
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\end_layout
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\begin_layout Standard
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We thank X, Y, and Z for A and B...
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\end_layout
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\begin_layout Bibliography
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@ -2524,6 +2585,17 @@ IEEE Signal Processing Letters,
|
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\begin_inset CommandInset bibitem
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LatexCommand bibitem
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label "7"
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key "wsjt_sourceforge"
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\end_inset
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The WSJT project at SourceForge, https://sourceforge.net/projects/wsjt/
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\end_layout
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\begin_layout Bibliography
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\begin_inset CommandInset bibitem
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LatexCommand bibitem
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label "8"
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key "karn"
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\end_inset
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