Single-sideband modulation

In radio communications, single-sideband modulation or single-sideband suppressed-carrier modulation is a type of signal modulation used to transmit information, such as an audio signal, by radio waves. A refinement of amplitude modulation, it uses transmitter power and bandwidth more efficiently. Amplitude modulation produces an output signal the bandwidth of which is twice the maximum frequency of the original baseband signal. Single-sideband modulation avoids this bandwidth increase, and the power wasted on a carrier, at the cost of increased device complexity and more difficult tuning at the receiver.

Basic concept

In conventional amplitude modulation, an audio signal controls the amplitude of a radio-frequency carrier, producing a carrier plus two mirror-image sidebands. Each sideband contains a complete copy of the original information, while the carrier itself conveys none. Consequently, an AM signal occupies a bandwidth equal to twice the highest audio frequency and expends a large fraction of the transmitted power on the carrier and redundant sideband. This spectral structure of AM is described in classic radio texts, including Everitt's treatments of modulation theory.
Single-sideband modulation is derived directly from AM by removing this redundancy. Since either sideband alone contains the entire modulating signal, SSB transmits only one sideband and usually suppresses the carrier. Compared with AM, SSB requires approximately half the bandwidth and uses transmitter power more efficiently. SSB signals are typically generated at low power using filtering or phase-cancellation techniques and then amplified linearly.
Because the carrier is suppressed, SSB reception requires reinsertion of a locally generated carrier and greater frequency stability than AM. AM can be generated and received with relatively simple equipment, while SSB is used primarily where efficiency and range are important. In amateur radio, prior to widespread digital voice, most HF voice operation moved from AM to SSB.

History

The first U.S. patent application for SSB modulation was filed on December 1, 1915, by John Renshaw Carson. The U.S. Navy experimented with SSB over its radio circuits before World War I. SSB first entered commercial service on January 7, 1927, on the longwave transatlantic public radiotelephone circuit between New York and London. The high power SSB transmitters were located at Rocky Point, New York, and Rugby, England. The receivers were in very quiet locations in Houlton, Maine, and Cupar, Scotland.
SSB was also used over long-distance telephone lines, as part of a technique known as frequency-division multiplexing. FDM was pioneered by telephone companies in the 1930s. With this technology, many simultaneous voice channels could be transmitted on a single physical circuit, for example in L-carrier. With SSB, channels could be spaced only 4,000 Hz apart, while offering a speech bandwidth of nominally 300 Hz to 3,400 Hz.
Amateur radio operators began serious experimentation with SSB after World War II. The Strategic Air Command established SSB as the radio standard for its aircraft in 1957. It has become a de facto standard for long-distance voice radio transmissions since then.
In December 1956, the Proceedings of the IRE devoted a full issue to single-sideband transmission, covering its history, theory, and practical implementation across spectrum management, transmitters, receivers, filtering, power amplifiers, and military, commercial, and amateur applications, including Oswald's historical review and Weaver's third method of SSB generation and detection.

Mathematical formulation

Single-sideband has the mathematical form of quadrature amplitude modulation in the special case where one of the baseband waveforms is derived from the other, instead of being independent messages:
where is the message, is its Hilbert transform, and is the radio carrier frequency.
To understand this formula, we may express as the real part of a complex-valued function, with no loss of information:
where represents the imaginary unit. is the analytic representation of which means that it comprises only the positive-frequency components of :
where and are the respective Fourier transforms of and Therefore, the frequency-translated function contains only one side of Since it also has only positive-frequency components, its inverse Fourier transform is the analytic representation of
and again the real part of this expression causes no loss of information. With Euler's formula to expand we obtain :
Coherent demodulation of to recover is the same as AM: multiply by and lowpass to remove the "double-frequency" components around frequency. If the demodulating carrier is not in the correct phase, then the demodulated signal will be some linear combination of and, which is usually acceptable in voice communications.

Lower sideband

can also be recovered as the real part of the complex-conjugate, which represents the negative frequency portion of When is large enough that has no negative frequencies, the product is another analytic signal, whose real part is the actual lower-sideband transmission:
The sum of the two sideband signals is:
which is the classic model of suppressed-carrier double sideband AM.

Practical implementations

Bandpass filtering

One method of producing an SSB signal is to remove one of the sidebands via filtering, leaving only either the upper sideband, the sideband with the higher frequency, or less commonly the lower sideband, the sideband with the lower frequency. Most often, the carrier is reduced or removed entirely, being referred to in full as single sideband suppressed carrier. Assuming both sidebands are symmetric, which is the case for a normal AM signal, no information is lost in the process. Since the final RF amplification is now concentrated in a single sideband, the effective power output is greater than in normal AM. Though SSB uses substantially less bandwidth and power, it cannot be demodulated by a simple envelope detector like standard AM.

Hartley modulator

In addition to filter-based approaches, single-sideband signals can be generated by the phasing method, which uses phase relationships to cancel one sideband. The approach was described in Ralph V. L. Hartley's 1928 patent, which outlined generating single-sideband suppressed-carrier signals by combining two paths of the modulating signal with a 90° phase difference and carrier signals in quadrature, so that one sideband reinforces and the other cancels. In practice, the audio is split into two channels with a 90° phase difference, each channel driving a balanced modulator fed by one of two quadrature carrier signals. When the two modulator outputs are summed or differenced, the unwanted sideband is cancelled, producing a single-sideband signal without the need for sharp RF filtering. The method was popular in the days of vacuum tube radios, but later gained a bad reputation due to poorly adjusted commercial implementations. Modulation using this method is again gaining popularity in the homebrew and DSP fields.
In 1946, R. B. Dome published low-component-count all-pass RC phase-shift networks in Electronics magazine, including a six-resistor, six-capacitor circuit suitable for voice communications using the Hartley phasing method. Experimental amateur implementations soon followed, with QST reporting phasing-based SSB transmitters and receivers in the late 1940s. In 1954, Stanford University student Donald K. Weaver published in IRE Transactions network-synthesis techniques for designing arbitrary all-pass phase-shift networks, including Chebyshev-optimized realizations. He presented a mathematical derivation of the 6R–6C network and showed that the approach could be extended to wider bandwidths, including full audio bandwidth if desired. This work formalized the design of audio phase networks; Weaver's later modulation method, which avoids audio quadrature networks entirely, is described separately.
This method, utilizing the Hilbert transform to phase shift the baseband audio, can be done at low cost with digital circuitry.

Weaver modulator

Another variation, the Weaver modulator, uses low-pass filtering combined with two stages of quadrature frequency translation. Weaver described this approach in “A Third Method of Generation and Detection of Single-Sideband Signals”, published two years after his early phasing paper.
In Weaver's method, the band of interest is prefiltered, removing low frequencies. The signal is then translated upward by quadrature modulation at a convenient offset. This produces a complex signal in which the desired sideband appears at lower frequencies while the unwanted sideband appears at higher frequency.
This initial translation creates a spectral gap, which simplifies low-pass filter design. A matched pair of low-pass filters removes the undesired sideband. Finally, the resulting single-sideband signal is translated a second time, using another pair of quadrature mixers, to the desired radio-frequency.

Demodulation

The front end of an SSB receiver is similar to that of an AM or FM receiver, consisting of a superheterodyne RF front end that produces a frequency-shifted version of the radio frequency signal within a standard intermediate frequency band.
To recover the original signal from the IF SSB signal, the single sideband must be frequency-shifted down to its original range of baseband frequencies, by using a product detector which mixes it with the output of a beat frequency oscillator. In other words, it is just another stage of heterodyning. For this to work, the BFO frequency must be exactly adjusted.
If the BFO frequency is off by more than 30 Hz, the output signal will be frequency-shifted, making speech sound strange and "Donald Duck"-like.
As an example, consider an IF SSB signal centered at frequency = 45000 Hz. The baseband frequency it needs to be shifted to is = 2000 Hz. The BFO output waveform is. When the signal is multiplied by the BFO waveform, it shifts the signal to , and to , which is known as the beat frequency or image frequency. The objective is to choose an that results in = 2000 Hz..
There are two choices for : 43000 Hz and 47000 Hz, called low-side and high-side injection. With high-side injection, the spectral components that were distributed around 45000 Hz will be distributed around 2000 Hz in the reverse order, also known as an inverted spectrum. That is in fact desirable when the IF spectrum is also inverted, because the BFO inversion restores the proper relationships. One reason for that is when the IF spectrum is the output of an inverting stage in the receiver. Another reason is when the SSB signal is actually a lower sideband, instead of an upper sideband. But if both reasons are true, then the IF spectrum is not inverted, and the non-inverting BFO should be used.