//status: edited

[[PROTOCOL_OVERVIEW]]
=== Overview

All QSO modes use structured messages that compress
user-readable information into fixed-length packets.  JT4, JT9, and JT65
use 72-bit payloads.  Standard messages consist of two
28-bit fields normally used for callsigns and a 15-bit field for a
grid locator, report, acknowledgment, or 73.  An additional bit flags
a message containing arbitrary free text, up to 13 characters.
Special cases allow other information such as add-on callsign prefixes
(e.g., ZA/K1ABC) or suffixes (e.g., K1ABC/P) to be encoded. The basic
aim is to compress the most common messages used for minimally valid
QSOs into a fixed 72-bit length.

Information payloads for FST4, FT4, FT8, Q65, and MSK144 contain 77 bits.
The 5 additional bits are used to flag special message types used for
nonstandard callsigns, contest exchanges, FT8 DXpedition Mode, and a
few other possibilities.  Full details have been published in QEX, see
{ft4_ft8_protocols}.

A standard amateur callsign consists of a one- or two-character
prefix, at least one of which must be a letter, followed by a digit
and a suffix of one to three letters. Within these rules, the number
of possible callsigns is equal to 37×36×10×27×27×27, or somewhat over
262 million. (The numbers 27 and 37 arise because in the first and
last three positions a character may be absent, or a letter, or
perhaps a digit.) Since 2^28^ is more than 268 million, 28 bits are
enough to encode any standard callsign uniquely. Similarly, the number
of 4-digit Maidenhead grid locators on earth is 180×180 = 32,400,
which is less than 2^15^ = 32,768; so a grid locator requires 15 bits.

Some 6 million of the possible 28-bit values are not needed for
callsigns.  A few of these slots are assigned to special message
components such as `CQ`, `DE`, and `QRZ`. `CQ` may be followed by three
digits to indicate a desired callback frequency. (If K1ABC transmits
on a standard calling frequency such as 50.280, and sends `CQ 290 K1ABC
FN42`, it means that s/he will listen on 50.290 and respond there to
any replies.) A numerical signal report of the form `–nn` or
`R–nn` can be sent in place of a grid locator.  (As originally
defined, numerical signal reports `nn` were required to fall between -01
and -30 dB.  Recent program versions 2.3 and later accommodate reports between
-50 and +49 dB.) A country prefix or portable suffix may be
attached to one of the callsigns.  When this feature is used, the
additional information is sent in place of the grid locator or by
encoding additional information into some of the 6 million available
slots mentioned above.

As a convenience for sending directed CQ messages, the 72-bit
compression algorithm supports messages starting with `CQ AA` through
`CQ ZZ`.  These message fragments are encoded internally as if they
were the callsigns `E9AA` through `E9ZZ`.  Upon reception they are
converted back to the form `CQ AA` through `CQ ZZ`, for display to the
user.

To be useful on channels with low signal-to-noise ratio, this kind of
lossless message compression requires use of a strong forward error
correcting (FEC) code.  Different codes are used for each mode.
Accurate synchronization of time and frequency is required between
transmitting and receiving stations.  As an aid to the decoders, each
protocol includes a "`sync vector`" of known symbols interspersed with
the information-carrying symbols.  Generated waveforms for all of the
_WSJT-X_ modes have continuous phase and constant envelope.

[[SLOW_MODES]]
=== Slow Modes

[[FST4PRO]]
==== FST4

FST4 offers T/R sequence lengths of 15, 30, 60, 120, 300, 900, and
1800 seconds.  Submodes are given names like FST4-60, FST4-120, etc.,
the appended numbers indicating sequence length in seconds.  A 24-bit
cyclic redundancy check (CRC) is appended to the 77-bit message
payload to create a 101-bit message-plus-CRC word.  Forward error
correction is accomplished using a (240,101) LDPC code.  Transmissions
consist of 160 symbols: 120 information-carrying symbols of two bits
each, interspersed with five groups of eight predefined
synchronization symbols.  Modulation uses 4-tone frequency-shift
keying (4-GFSK) with Gaussian smoothing of frequency transitions.

[[FT4PRO]]
==== FT4

Forward error correction (FEC) in FT4 uses a low-density parity check
(LDPC) code with 77 information bits, a 14-bit cyclic redundancy check
(CRC), and 83 parity bits making a 174-bit codeword.  It is thus
called an LDPC (174,91) code.  Synchronization uses four 4×4 Costas
arrays, and ramp-up and ramp-down symbols are inserted at the start
and end of each transmission.  Modulation is 4-tone frequency-shift
keying (4-GFSK) with Gaussian smoothing of frequency transitions.  The
keying rate is 12000/576 = 20.8333 baud.  Each transmitted symbol
conveys two bits, so the total number of channel symbols is 174/2 + 16
+ 2 = 105.  The total bandwidth is 4 × 20.8333 = 83.3 Hz.

[[FT8PRO]]
==== FT8

FT8 uses the same LDPC (174,91) code as FT4.  Modulation is 8-tone
frequency-shift keying (8-GFSK) at 12000/1920 = 6.25 baud.
Synchronization uses 7×7 Costas arrays at the beginning, middle, and
end of each transmission.  Transmitted symbols carry three bits, so
the total number of channel symbols is 174/3 + 21 = 79.  The total
occupied bandwidth is 8 × 6.25 = 50 Hz.

[[JT4PRO]]
==== JT4

FEC in JT4 uses a strong convolutional code with constraint length
K=32, rate r=1/2, and a zero tail. This choice leads to an encoded
message length of (72+31) x 2 = 206 information-carrying bits.
Modulation is 4-tone frequency-shift keying (4-FSK) at 11025 / 2520 =
4.375 baud.  Each symbol carries one information bit (the most
significant bit) and one synchronizing bit.  The two 32-bit
polynomials used for convolutional encoding have hexadecimal values
0xf2d05351 and 0xe4613c47, and the ordering of encoded bits is
scrambled by an interleaver.  The pseudo-random sync vector is the
following sequence (60 bits per line):

 000011000110110010100000001100000000000010110110101111101000
 100100111110001010001111011001000110101010101111101010110101
 011100101101111000011011000111011101110010001101100100011111
 10011000011000101101111010


[[JT9PRO]]
==== JT9

FEC in JT9 uses the same strong convolutional code as JT4: constraint
length K=32, rate r=1/2, and a zero tail, leading to an encoded
message length of (72+31) × 2 = 206 information-carrying
bits. Modulation is nine-tone frequency-shift keying, 9-FSK at
12000.0/6912 = 1.736 baud.  Eight tones are used for data, one for
synchronization. Eight data tones means that three data bits are
conveyed by each transmitted information symbol. Sixteen symbol
intervals are devoted to synchronization, so a transmission requires a
total of 206 / 3 + 16 = 85 (rounded up) channel symbols. The sync
symbols are those numbered 1, 2, 5, 10, 16, 23, 33, 35, 51, 52, 55,
60, 66, 73, 83, and 85 in the transmitted sequence.  Tone spacing of
the 9-FSK modulation for JT9A is equal to the keying rate, 1.736 Hz.
The total occupied bandwidth is 9 × 1.736 = 15.6 Hz.

[[JT65PRO]]
==== JT65

A detailed description of the JT65 protocol was published in
{jt65protocol} for September-October, 2005. A Reed Solomon (63,12)
error-control code converts 72-bit user messages into sequences of 63
six-bit information-carrying symbols.  These are interleaved with
another 63 symbols of synchronizing information according to the
following pseudo-random sequence:

 100110001111110101000101100100011100111101101111000110101011001
 101010100100000011000000011010010110101010011001001000011111111


The synchronizing tone is normally sent in each interval having a
"`1`" in the sequence. Modulation is 65-FSK at 11025/4096 = 2.692
baud.  Frequency spacing between tones is equal to the keying rate for
JT65A, and 2 and 4 times larger for JT65B and JT65C, respectively.
For EME QSOs the
signal report OOO is sometimes used instead of numerical signal
reports. It is conveyed by reversing sync and data positions in the
transmitted sequence.  Shorthand messages for RO, RRR, and 73 dispense
with the sync vector entirely and use time intervals of 16384/11025 =
1.486 s for pairs of alternating tones. The lower frequency is the
same as that of the sync tone used in long messages, and the frequency
separation is 110250/4096 = 26.92 Hz multiplied by n for JT65A, with n
= 2, 3, 4 used to convey the messages RO, RRR, and 73, respectively.

[[Q65_PROTOCOL]]
==== Q65

Q65 is intended for scatter, EME, and other extreme weak-signal
applications.  Forward error correction (FEC) uses a specially
designed (65,15) block code with six-bit symbols.  Two symbols are
“punctured” from the code and not transmitted, thereby yielding an
effective (63,13) code with a payload of k = 13 information symbols
conveyed by n = 63 channel symbols.  The punctured symbols consist of
a 12-bit CRC computed from the 13 information symbols.  The CRC is
used to reduce the false-decode rate to a very low value.  A 22-symbol
pseudorandom sequence spread throughout a transmission is sent as
“tone 0” and used for synchronization.  The total number of channel
symbols in a Q65 transmission is thus 63 + 22 = 85.  Q65 offers T/R
sequence lengths of 15, 30, 60, 120, and 300 s, and submodes A - E
have tone spacings 1, 2, 4, 8, and 16 times the symbol rate.  Submode
designations include a number for sequence length and a letter for
tone spacing, as in Q65-15A, Q65-120C, etc.  Occupied bandwidths are
65 times the tone spacing, ranging from 19 Hz (Q65-300A) to a maximum
of 1733 Hz (Q65-15C, Q65-30D, and Q65-60E).  

[[WSPR_PROTOCOL]]
==== WSPR

WSPR is designed for probing potential radio propagation paths using
low power beacon-like transmissions. WSPR signals convey a callsign,
Maidenhead grid locator, and power level using a compressed data
format with strong forward error correction and narrow-band 4-FSK
modulation. The protocol is effective at signal-to-noise ratios as low
as –31 dB in a 2500 Hz bandwidth.

WSPR messages can have one of three possible formats illustrated by
the following examples:

 - Type 1: K1ABC FN42 37
 - Type 2: PJ4/K1ABC 37
 - Type 3: <PJ4/K1ABC> FK52UD 37
 
Type 1 messages contain a standard callsign, a 4-character Maidenhead
grid locator, and power level in dBm. Type 2 messages omit the grid
locator but include a compound callsign, while type 3 messages replace
the callsign with a 15-bit hash code and include a 6-character locator
as well as the power level. Lossless compression techniques squeeze
all three message types into exactly 50 bits of user
information. Standard callsigns require 28 bits and 4-character grid
locators 15 bits.  In Type 1 messages, the remaining 7 bits convey the
power level. In message types 2 and 3 these 7 bits convey power level
along with an extension or re-definition of fields normally used for
callsign and locator. Together, these compression techniques amount to
“source encoding” the user message into the smallest possible number
of bits.

WSPR uses a convolutional code with constraint length K=32 and rate
r=1/2. Convolution extends the 50 user bits into a total of (50 + K –
1) × 2 = 162 one-bit symbols. Interleaving is applied to scramble the
order of these symbols, thereby minimizing the effect of short bursts
of errors in reception that might be caused by fading or interference.
The data symbols are combined with an equal number of synchronizing
symbols, a pseudo-random pattern of 0’s and 1’s.  The 2-bit
combination for each symbol is the quantity that determines which of
four possible tones to transmit in any particular symbol
interval. Data information is taken as the most significant bit, sync
information the least significant. Thus, on a 0 – 3 scale, the tone
for a given symbol is twice the value (0 or 1) of the data bit, plus
the sync bit.

[[FST4WPRO]]
==== FST4W

FST4W offers T/R sequence lengths of 120, 300, 900, and 1800 seconds.
Submodes are given names like FST4W-120, FST4W-300, etc., the appended
numbers indicating sequence length in seconds.  Message payloads
contain 50 bits, and a 24-bit cyclic redundancy check (CRC) appended
to create a 74-bit message-plus-CRC word.  Forward error correction
is accomplished using a (240,74) LDPC code.  Transmissions consist of
160 symbols: 120 information-carrying symbols of two bits each,
interspersed with five groups of eight predefined synchronization
symbols.  Modulation uses 4-tone frequency-shift keying (4-GFSK) with
Gaussian smoothing of frequency transitions.

[[SLOW_SUMMARY]]
==== Summary

Table 7 provides a brief summary of parameters for the slow modes in
_WSJT-X_.  Parameters K and r specify the constraint length and rate
of the convolutional codes; n and k specify the sizes of the
(equivalent) block codes; Q is the alphabet size for the
information-carrying channel symbols; Sync Energy is the fraction of
transmitted energy devoted to synchronizing symbols; and S/N Threshold
is the signal-to-noise ratio (in a 2500 Hz reference bandwidth) above
which the probability of decoding is 50% or higher.

[[SLOW_TAB]]
.Parameters of Slow Modes
[width="100%",cols="3h,^3,^2,^1,^2,^2,^2,^2,^2,^2",frame=topbot,options="header"]
|===============================================================================
|Mode |FEC Type |(n,k) | Q|Modulation type|Keying rate (Baud)|Bandwidth (Hz)
|Sync Energy|Tx Duration (s)|S/N Threshold (dB)
|FST4-15   |LDPC |  (240,101)| 4| 4-GFSK| 16.67 | 67.7 | 0.25| 9.6  | -20.7
|FST4-30   |LDPC |  (240,101)| 4| 4-GFSK|  7.14  | 28.6  | 0.25| 22.4  | -24.2
|FST4-60   |LDPC |  (240,101)| 4| 4-GFSK|  3.09  | 12.4  | 0.25| 51.8  | -28.1
|FST4-120  |LDPC |  (240,101)| 4| 4-GFSK|  1.46  |  5.9  | 0.25| 109.3 | -31.3
|FST4-300  |LDPC |  (240,101)| 4| 4-GFSK|  0.558  |  2.2  | 0.25| 286.7 | -35.3
|FST4-900  |LDPC |  (240,101)| 4| 4-GFSK|  0.180 |  0.72 | 0.25| 887.5 | -40.2
|FST4-1800 |LDPC |  (240,101)| 4| 4-GFSK|  0.089 |  0.36 | 0.25| 1792.0| -43.2
|FT4  |LDPC |(174,91)| 4| 4-GFSK| 20.83 | 83.3 | 0.15| 5.04 | -17.5
|FT8  |LDPC |(174,91)| 8| 8-GFSK| 6.25 | 50.0 | 0.27| 12.6 | -21
|JT4A |K=32, r=1/2|(206,72)| 2| 4-FSK| 4.375| 17.5 | 0.50| 47.1 | -23
|JT9A |K=32, r=1/2|(206,72)| 8| 9-FSK| 1.736| 15.6 | 0.19| 49.0 | -26
|JT65A |RS|(63,12) |64|65-FSK| 2.692| 177.6 | 0.50| 46.8 | -25
|Q65-15A |QRA|(63,13) |64|65-FSK|6.667|433|0.26| 12.8| -22.2
|Q65-30A |QRA|(63,13) |64|65-FSK|3.333|217|0.26| 25.5| -24.8
|Q65-60A |QRA|(63,13) |64|65-FSK|1.667|108|0.26| 51.0| -27.6
|Q65-120A|QRA|(63,13) |64|65-FSK|0.750| 49|0.26|113.3| -30.8
|Q65-300A|QRA|(63,13) |64|65-FSK|0.289| 19|0.26|293.8| -33.8
| WSPR |K=32, r=1/2|(162,50)| 2| 4-FSK| 1.465| 5.9 | 0.50|110.6 | -31
|FST4W-120  |LDPC |  (240,74)| 4| 4-GFSK|  1.46  |  5.9  | 0.25| 109.3 | -32.8
|FST4W-300  |LDPC |  (240,74)| 4| 4-GFSK|  0.558  |  2.2  | 0.25| 286.7 | -36.8
|FST4W-900  |LDPC |  (240,74)| 4| 4-GFSK|  0.180 |  0.72 | 0.25| 887.5 | -41.7
|FST4W-1800 |LDPC |  (240,74)| 4| 4-GFSK|  0.089 |  0.36 | 0.25| 1792.0| -44.8
|===============================================================================

 LDPC = Low Density Parity Check
 RS = Reed Solomon
 QRA = Q-ary Repeat Accumulate

Submodes of JT4, JT9, and JT65 offer wider tone spacings for
circumstances that may require them, such as significant Doppler spread.
Table 8 summarizes the tone spacings, bandwidths, and approximate
threshold sensitivities of the various submodes when spreading is
comparable to tone spacing.

[[SLOW_SUBMODES]]
.Parameters of Slow Submodes JT4, JT9, and JT65 with Selectable Tone Spacings
[width="50%",cols="h,3*^",frame=topbot,options="header"]
|=====================================
|Mode  |Tone Spacing  |BW (Hz)|S/N (dB)
|JT4A  |4.375|  17.5  |-23
|JT4B  |8.75 |  30.6  |-22
|JT4C  |17.5 |  56.9  |-21
|JT4D  |39.375| 122.5 |-20
|JT4E  |78.75|  240.6 |-19
|JT4F  |157.5|  476.9 |-18
|JT4G  |315.0|  949.4 |-17
|JT9A  |1.736|  15.6  |-26
|JT9B  |3.472|  29.5  |-26
|JT9C  |6.944|  57.3  |-25
|JT9D  |13.889| 112.8 |-24
|JT9E  |27.778| 224.0 |-23
|JT9F  |55.556| 446.2 |-22
|JT9G  |111.111|890.6 |-21
|JT9H  |222.222|1779.5|-20
|JT65A |2.692| 177.6  |-25
|JT65B |5.383| 352.6  |-25
|JT65C |10.767| 702.5 |-25
|=====================================

.Parameters of Q65 Submodes
[width="100%",cols="h,5*^",frame=topbot,options="header"]
|=====================================
|T/R Period (s)  |A Spacing Width (Hz)|B Spacing Width (Hz)|C Spacing Width (Hz)|D Spacing Width (Hz)|E Spacing Width (Hz)
|15|6.67 &#160; &#160; 4.33|13.33 &#160; &#160; 867|26.67 &#160; &#160; 1733|N/A|N/A
|30|3.33 &#160; &#160; 217|6.67 &#160; &#160; 433|13.33 &#160; &#160; 867| 26.67 &#160; &#160; 1733| N/A
|60|1.67 &#160; &#160; 108|3.33 &#160; &#160; 217|6.67 &#160; &#160; 433|13.33 &#160; &#160; 867|26.67 &#160; &#160; 1733
|120|0.75 &#160; &#160; 49|1.50 &#160; &#160; 98|3.00 &#160; &#160; 195|6.00 &#160; &#160; 390| 12.00 &#160; &#160; 780
|300|0.29 &#160; &#160; 19|0.58 &#160; &#160; 38|1.16 &#160; &#160; 75|2.31 &#160; &#160; 150|4.63 &#160; &#160; 301
|=====================================

[[FAST_MODES]]
=== Fast Modes

==== JT9

The JT9 slow modes all use keying rate 12000/6912 = 1.736 baud.  By contrast, with
the *Fast* setting submodes JT9E-H adjust the keying rate to match the
increased tone spacings.  Message durations are therefore much
shorter, and they are sent repeatedly throughout each Tx sequence.
For details see Table 9, below.

==== MSK144

Standard MSK144 messages are structured in the same way as in FT8,
with 77 bits of user information.  Forward error correction is
implemented by first augmenting the 77 message bits with a 13-bit
cyclic redundancy check (CRC) calculated from the message bits. The
CRC is used to detect and eliminate most false decodes at the
receiver. The resulting 90-bit augmented message is mapped to a
128-bit codeword using a (128,90) binary low-density-parity-check
(LDPC) code designed by K9AN specifically for this purpose.  Two 8-bit
synchronizing sequences are added to make a message frame 144 bits
long.  Modulation is Offset Quadrature Phase-Shift Keying (OQPSK) at
2000 baud. Even-numbered bits are conveyed over the in-phase channel,
odd-numbered bits on the quadrature channel.  Individual symbols are
shaped with half-sine profiles, thereby ensuring a generated waveform
with constant envelope, equivalent to a Minimum Shift Keying (MSK)
waveform.  Frame duration is 72 ms, so the effective character
transmission rate for standard messages is up to 250 cps.

MSK144 also supports short-form messages that can be used after QSO
partners have exchanged both callsigns.  Short messages consist of 4
bits encoding R+report, RRR, or 73, together with a 12-bit hash code
based on the ordered pair of "`to`" and "`from`" callsigns.  Another
specially designed LDPC (32,16) code provides error correction, and an
8-bit synchronizing vector is appended to make up a 40-bit frame.
Short-message duration is thus 20 ms, and short messages can be
decoded from very short meteor pings.

The 72 ms or 20 ms frames of MSK144 messages are repeated without gaps
for the full duration of a transmission cycle. For most purposes, a
cycle duration of 15 s is suitable and recommended for MSK144.

The modulated MSK144 signal occupies the full bandwidth of a SSB
transmitter, so transmissions are always centered at audio frequency
1500 Hz. For best results, transmitter and receiver filters should be
adjusted to provide the flattest possible response over the range
300Hz to 2700Hz. The maximum permissible frequency offset between you
and your QSO partner ± 200 Hz.

==== Summary

.Parameters of Fast Modes
[width="90%",cols="3h,^3,^2,^1,^2,^2,^2,^2,^2",frame="topbot",options="header"]
|=====================================================================
|Mode     |FEC Type   |(n,k)   | Q|Modulation Type|Keying rate (Baud)
|Bandwidth (Hz)|Sync Energy|Tx Duration (s)
|JT9E     |K=32, r=1/2|(206,72)| 8| 9-FSK| 25.0 |  225  | 0.19| 3.400 
|JT9F     |K=32, r=1/2|(206,72)| 8| 9-FSK| 50.0 |  450  | 0.19| 1.700 
|JT9G     |K=32, r=1/2|(206,72)| 8| 9-FSK|100.0 |  900  | 0.19| 0.850 
|JT9H     |K=32, r=1/2|(206,72)| 8| 9-FSK|200.0 | 1800  | 0.19| 0.425 
|MSK144   |LDPC       |(128,90)| 2| OQPSK| 2000 | 2400  | 0.11| 0.072 
|MSK144 Sh|LDPC       |(32,16) | 2| OQPSK| 2000 | 2400  | 0.20| 0.020 
|=====================================================================
