Multiple frequency-shift keying (MFSK) is a variation of frequency-shift keying (FSK) that uses more than two frequencies. MFSK is a form of M-ary orthogonal modulation, where each symbol consists of one element from an alphabet of orthogonal waveforms. M, the size of the alphabet, is usually a power of two so that each symbol represents log2 M bits.
Fundamentals In a M-ary signaling system like MFSK, an "alphabet" of M tones is established and the transmitter selects one tone at a time from the alphabet for transmission. M is often a power of 2, so each tone transmission from the alphabet represents log2 M data bits. MFSK is classed as an M-ary orthogonal signaling scheme because each of the M tone detection filters at the receiver responds only to its tone and not at all to the others; this independence provides the orthogonality. Like other M-ary orthogonal schemes, the required Eb/N0 ratio for a given probability of error decreases as M increases without the need for multisymbol coherent detection. In fact, as M approaches infinity the required Eb/N0 ratio decreases asymptotically to the Shannon limit of −1.6 dB. However this decrease is slow with increasing M, and large values are impractical because of the exponential increase in required bandwidth. Typical values in practice range from 4 to 64, and MFSK is combined with another forward error correction scheme to provide additional (systematic) coding gain. Spectral efficiency of MFSK modulation schemes decreases with increasing of modulation order M:
ρ = 2 log 2 M M {\displaystyle \rho ={\frac {2\log _{2}M}{M}}}
Like any other form of angle modulation that transmits a single RF tone that varies only in phase or frequency, MFSK produces a constant envelope. This significantly relaxes the design of the RF power amplifier, allowing it to achieve greater conversion efficiencies than linear amplifiers.
2-tone MFSK It is possible to combine two MFSK systems to increase the throughput of the link. Perhaps the most widely used 2-tone MFSK system is dual-tone multi-frequency (DTMF), better known by its AT&T trademark of "Touch Tone". Another is the Multi-frequency (MF) scheme used during the 20th century for in-band signalling on trunks between telephone exchanges. Both are examples of in-band signaling schemes, i.e., they share the user's communication channel. Symbols in the DTMF and MF alphabets are sent as tone pairs; DTMF selects one tone from a "high" group and one from a "low" group, while MF selects its two tones from a common set. DTMF and MF use different tone frequencies largely to keep end users from interfering with inter-office signaling. In the 1970s, MF began to be replaced by digital out-of-band signaling, a conversion motivated in part by the widespread fraudulent use of MF signals by end users known as phone phreaks. These signals are distinctive when received aurally as a rapid succession of tone pairs with almost musical quality. The simultaneous transmission of two tones directly at RF loses the constant-envelope property of the single tone system. Two simultaneous RF tones is in fact the classic "stress test" of an RF power amplifier for measuring linearity and intermodulation distortion. However, two audio tones can be sent simultaneously on a conventional, constant-envelope FM RF carrier, but the noncoherent detection of the FM signal at the receiver would destroy any signal-to-noise ratio advantage the multitone scheme might have.
MFSK in HF communications Skywave propagation on the high frequency bands introduces random distortions that generally vary with both time and frequency.
Delay spread and coherence bandwidth When several separate paths from transmitter to receiver exist, a condition known as multipath, they almost never have exactly the same length so they almost never exhibit the same propagation delay. Small delay differences, or delay spread, smear adjacent modulation symbols together and cause unwanted intersymbol interference. Delay spread is inversely proportional to its frequency-domain counterpart, coherence bandwidth. This is the frequency range over which the channel gain is relatively constant. This is because summing two or more paths with different delays creates a comb filter even when the individual paths have a flat frequency response.
Coherence time and Doppler spread Fading is a (usually random and undesired) change in path gain with time. The maximum fade rate is limited by the physics of the channel, such as the rate at which free electrons form and are recombined in the ionosphere and charged particle cloud velocities within the ionosphere. The maximum interval over which the channel gain does not appreciably change is the coherence time. A fading channel effectively imposes an unwanted random amplitude modulation on the signal. Just as the bandwidth of intentional AM increases with the modulation rate, fading spreads a signal over a frequency range that increases with the fading rate. This is Doppler spreading, the frequency domain counterpart of coherence time. The shorter the coherence time, the greater the Doppler spread and vice versa.
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