Single-sideband modulation

Illustration of the spectrum of AM and SSB signals. The lower side band (LSB) spectrum is inverted compared to the baseband. As an example, a 2 kHz audio baseband signal modulated onto a 5 MHz carrier will produce a frequency of 5.002 MHz if upper side band (USB) is used or 4.998 MHz if LSB is used.

In radio communications, single-sideband modulation (SSB) or single-sideband suppressed-carrier modulation (SSB-SC) 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

Radio transmitters work by mixing a radio frequency (RF) signal of a specific frequency, the carrier wave, with the audio signal to be broadcast. In AM transmitters this mixing usually takes place in the final RF amplifier (high level modulation). It is less common and much less efficient to do the mixing at low power and then amplify it in a linear amplifier. Either method produces a set of frequencies with a strong signal at the carrier frequency and with weaker signals at frequencies extending above and below the carrier frequency by the maximum frequency of the input signal. Thus the resulting signal has a spectrum whose bandwidth is twice the maximum frequency of the original input audio signal.

SSB takes advantage of the fact that the entire original signal is encoded in each of these "sidebands". Since a good receiver can extract the complete original signal from either the upper or lower sideband, it is not essential or efficient to transmit both sidebands plus the carrier - the full AM signal will occupy double the bandwidth of the original baseband signal, and transmitted RF power will be wasted in producing the carrier and redundant sideband. There are several methods for eliminating the carrier and one sideband from the transmitted signal. Producing this single sideband signal can be done at high level in the final amplifier stage as with AM but it is usually produced at a low power level and linearly amplified. The lower efficiency of linear amplification partially offsets the power advantage gained by eliminating the carrier and one sideband. Nevertheless, SSB transmissions use the available amplifier energy considerably more efficiently, providing longer-range transmission for the same power output. In addition, the occupied spectrum is less than half that of a full carrier AM signal.

SSB reception requires frequency stability and selectivity well beyond that of inexpensive AM receivers which is why broadcasters have seldom used it. In point-to-point communications, where expensive receivers are in common use already, they can successfully be adjusted to receive whichever sideband is being transmitted.

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). 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 (usually) 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.

Mathematical formulation

Frequency-domain depiction of the mathematical steps that convert a baseband function into a single-sideband radio signal

Single-sideband has the mathematical form of quadrature amplitude modulation (QAM) in the special case where one of the baseband waveforms is derived from the other, instead of being independent messages:

$s_{\text{usb}}(t)=s(t)\cdot \cos \left(2\pi f_{0}t\right)-{\widehat {s}}(t)\cdot \sin \left(2\pi f_{0}t\right),\,$ Eq.1

where $s(t)\,$ is the message (real-valued), ${\widehat {s}}(t)\,$ is its Hilbert transform, and $f_{0}\,$ is the radio carrier frequency.

To understand this formula, we may express $s(t)$ as the real part of a complex-valued function, with no loss of information:

$s(t)=\operatorname {Re} \left\{s_{\mathrm {a} }(t)\right\}=\operatorname {Re} \left\{s(t)+j\cdot {\widehat {s}}(t)\right\},$

where $j$ represents the imaginary unit.  $s_{\mathrm {a} }(t)$ is the analytic representation of $s(t),$  which means that it comprises only the positive-frequency components of $s(t)$:

${\frac {1}{2}}S_{\mathrm {a} }(f)={\begin{cases}S(f),&{\text{for}}\ f>0,\\0,&{\text{for}}\ f<0,\end{cases}}$

where $S_{\mathrm {a} }(f)$ and $S(f)$ are the respective Fourier transforms of $s_{\mathrm {a} }(t)$ and $s(t).$  Therefore, the frequency-translated function $S_{\mathrm {a} }\left(f-f_{0}\right)$ contains only one side of $S(f).$  Since it also has only positive-frequency components, its inverse Fourier transform is the analytic representation of $s_{\text{usb}}(t):$

$s_{\text{usb}}(t)+j\cdot {\widehat {s}}_{\text{ssb}}(t)={\mathcal {F}}^{-1}\{S_{\mathrm {a} }\left(f-f_{0}\right)\}=s_{\mathrm {a} }(t)\cdot e^{j2\pi f_{0}t},\,$

and again the real part of this expression causes no loss of information.  With Euler's formula to expand  $e^{j2\pi f_{0}t},\,$  we obtain Eq.1:

${\begin{aligned}s_{\text{usb}}(t)&=\operatorname {Re} \left\{s_{\mathrm {a} }(t)\cdot e^{j2\pi f_{0}t}\right\}\\&=\operatorname {Re} \left\{\,\left[s(t)+j\cdot {\widehat {s}}(t)\right]\cdot \left[\cos \left(2\pi f_{0}t\right)+j\cdot \sin \left(2\pi f_{0}t\right)\right]\,\right\}\\&=s(t)\cdot \cos \left(2\pi f_{0}t\right)-{\widehat {s}}(t)\cdot \sin \left(2\pi f_{0}t\right).\end{aligned}}$

Coherent demodulation of $s_{\text{ssb}}(t)$ to recover $s(t)$ is the same as AM: multiply by $\cos \left(2\pi f_{0}t\right),$  and lowpass to remove the "double-frequency" components around frequency $2f_{0}$. If the demodulating carrier is not in the correct phase (cosine phase here), then the demodulated signal will be some linear combination of $s(t)$ and ${\widehat {s}}(t)$, which is usually acceptable in voice communications (if the demodulation carrier frequency is not quite right, the phase will be drifting cyclically, which again is usually acceptable in voice communications if the frequency error is small enough, and amateur radio operators are sometimes tolerant of even larger frequency errors that cause unnatural-sounding pitch shifting effects).

Lower sideband

$s(t)$ can also be recovered as the real part of the complex-conjugate, $s_{\mathrm {a} }^{*}(t),$ which represents the negative frequency portion of $S(f).$ When $f_{0}\,$ is large enough that $S\left(f-f_{0}\right)$ has no negative frequencies, the product $s_{\mathrm {a} }^{*}(t)\cdot e^{j2\pi f_{0}t}$ is another analytic signal, whose real part is the actual lower-sideband transmission:

${\begin{aligned}s_{\mathrm {a} }^{*}(t)\cdot e^{j2\pi f_{0}t}&=s_{\text{lsb}}(t)+j\cdot {\widehat {s}}_{\text{lsb}}(t)\\\Rightarrow s_{\text{lsb}}(t)&=\operatorname {Re} \left\{s_{\mathrm {a} }^{*}(t)\cdot e^{j2\pi f_{0}t}\right\}\\&=s(t)\cdot \cos \left(2\pi f_{0}t\right)+{\widehat {s}}(t)\cdot \sin \left(2\pi f_{0}t\right).\end{aligned}}$

The sum of the two sideband signals is:

$s_{\text{usb}}(t)+s_{\text{lsb}}(t)=2s(t)\cdot \cos \left(2\pi f_{0}t\right),\,$

which is the classic model of suppressed-carrier double sideband AM.

Practical implementations

A Collins KWM-1, an early Amateur Radio transceiver that featured SSB voice capability

Bandpass filtering

One method of producing an SSB signal is to remove one of the sidebands via filtering, leaving only either the upper sideband (USB), the sideband with the higher frequency, or less commonly the lower sideband (LSB), the sideband with the lower frequency. Most often, the carrier is reduced or removed entirely (suppressed), being referred to in full as single sideband suppressed carrier (SSBSC). 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 (the carrier and redundant sideband account for well over half of the power output of an AM transmitter). Though SSB uses substantially less bandwidth and power, it cannot be demodulated by a simple envelope detector like standard AM.

Hartley modulator

An alternate method of generation known as a Hartley modulator, named after R. V. L. Hartley, uses phasing to suppress the unwanted sideband. To generate an SSB signal with this method, two versions of the original signal are generated, mutually 90° out of phase for any single frequency within the operating bandwidth. Each one of these signals then modulates carrier waves (of one frequency) that are also 90° out of phase with each other. By either adding or subtracting the resulting signals, a lower or upper sideband signal results. A benefit of this approach is to allow an analytical expression for SSB signals, which can be used to understand effects such as synchronous detection of SSB.

Shifting the baseband signal 90° out of phase cannot be done simply by delaying it, as it contains a large range of frequencies. In analog circuits, a wideband 90-degree phase-difference network is used. 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.

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, initially used only six resistors and six capacitors to generate equal amplitude signals with a 90° phase difference over the passband, as with the Hilbert Transformer. He later showed a method using low pass filters combined with four heterodyne operations.

In Weaver's method, the band of interest is first translated to be centered at zero, conceptually by modulating a complex exponential $\exp(j\omega t)$ with frequency in the middle of the voiceband, but implemented by a quadrature pair of sine and cosine modulators at that frequency (e.g. 2 kHz). This complex signal or pair of real signals is then lowpass filtered to remove the undesired sideband that is not centered at zero. Then, the single-sideband complex signal centered at zero is upconverted to a real signal, by another pair of quadrature mixers, to the desired center frequency.

Demodulation

Main article: 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 (RF) signal within a standard intermediate frequency (IF) 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 (BFO). 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 (up or down), making speech sound strange and "Donald Duck"-like.

As an example, consider an IF SSB signal centered at frequency $F_{\text{if}}\,$ = 45000 Hz. The baseband frequency it needs to be shifted to is $F_{b}\,$ = 2000 Hz. The BFO output waveform is $\cos \left(2\pi \cdot F_{\text{bfo}}\cdot t\right)$. When the signal is multiplied by (aka heterodyned with) the BFO waveform, it shifts the signal to  $\left(F_{\text{if}}+F_{\text{bfo}}\right)$, and to $\left|F_{\text{if}}-F_{\text{bfo}}\right|$, which is known as the beat frequency or image frequency. The objective is to choose an $F_{\text{bfo}}$ that results in  $\left|F_{\text{if}}-F_{\text{bfo}}\right|=F_{b}\,$ = 2000 Hz. (The unwanted components at $\left(F_{\text{if}}+F_{\text{bfo}}\right)\,$ can be removed by a lowpass filter; for which an output transducer or the human ear may serve).

There are two choices for $F_{\text{bfo}}$: 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 (43000 Hz) should be used.

SSB as a speech-scrambling technique

During WWII, SSB was the technique behind the radio/telephone link between Franklin D. Roosevelt, later Harry Truman, and Winston Churchill. Code name SIGSALY, it was developed by Bell Telephone Laboratories.

Suppressed carrier (SSB-SC), double-sideband suppressed carrier (DSB-SC), and vestigial sideband (VSB)

VSB modulation

Single sideband is also referred to as single sideband suppressed carrier, in which the carrier and one sideband are suppressed by frequency or phase (Hilbert Transform) discrimination. Though more complex and costly, it is used for two-point dedicated communications requiring less bandwidth and power. In double sideband suppressed carrier, only the carrier is suppressed, generating one hundred percent modulation efficiency, but with additional cost and complexity. It is used for television and FM stereo broadcasts. A vestigial sideband has been only partly suppressed, with only 25 to 30 percent of one bandwidth being used. It is used for television.

Compatible Single Side-band

A compatible transmission refers to one in which the receiver is capable of instantaneous amplitude demodulation. This could be a double sideband or a single sideband transmission. As an example, Leonard R. Kahn introduced an independent sideband (ISB) stereo scheme, in which the lower sideband transmitted the left channel, and the upper sideband the right. Kahn commercialized this AM stereo as the STR-77 and STR-84.

Frequencies for LSB and USB in amateur radio voice communication

When single-sideband is used in amateur radio voice communications, it is common practice that for frequencies below 10 MHz, lower sideband (LSB) is used and for frequencies of 10 MHz and above, upper sideband (USB) is used. For example, on the 40 m band, voice communications often take place around 7.100 MHz using LSB mode. On the 20 m band at 14.200 MHz, USB mode would be used.

An exception to this rule applies to the five discrete amateur channels on the 60-meter band (near 5.3 MHz) where FCC rules specifically require USB.

Extended single sideband (eSSB)

Extended single sideband is any J3E (SSB-SC) mode that exceeds the audio bandwidth of standard or traditional 2.9 kHz SSB J3E modes (ITU 2K90J3E) to support higher-quality sound.

Extended SSB modes	Bandwidth	Frequency response	ITU Designator
eSSB (Narrow-1a)	3 kHz	100 Hz ~ 3.10 kHz	3K00J3E
eSSB (Narrow-1b)	3 kHz	50 Hz ~ 3.05 kHz	3K00J3E
eSSB (Narrow-2)	3.5 kHz	50 Hz ~ 3.55 kHz	3K50J3E
eSSB (Medium-1)	4 kHz	50 Hz ~ 4.05 kHz	4K00J3E
eSSB (Medium-2)	4.5 kHz	50 Hz ~ 4.55 kHz	4K50J3E
eSSB (Wide-1)	5 kHz	50 Hz ~ 5.05 kHz	5K00J3E
eSSB (Wide-2)	6 kHz	50 Hz ~ 6.05 kHz	6K00J3E

Amplitude-companded single-sideband modulation (ACSSB)

Amplitude-companded single sideband (ACSSB) is a narrowband modulation method using a single sideband with a pilot tone, allowing an expander in the receiver to restore the amplitude that was severely compressed by the transmitter. It offers improved effective range over standard SSB modulation while simultaneously retaining backwards compatibility with standard SSB radios. ACSSB also offers reduced bandwidth and improved range for a given power level compared with narrow band FM modulation.

Controlled-envelope single-sideband modulation (CESSB)

The generation of standard SSB modulation results in large envelope overshoots well above the average envelope level for a sinusoidal tone (even when the audio signal is peak-limited). The standard SSB envelope peaks are due to truncation of the spectrum and nonlinear phase distortion from the approximation errors of the practical implementation of the required Hilbert transform. It was recently shown that suitable overshoot compensation (so-called controlled-envelope single-sideband modulation or CESSB) achieves about 3.8 dB of peak reduction for speech transmission. This results in an effective average power increase of about 140%. Although the generation of the CESSB signal can be integrated into the SSB modulator, it is feasible to separate the generation of the CESSB signal (e.g. in form of an external speech preprocessor) from a standard SSB radio. This requires that the standard SSB radio's modulator be linear-phase and have a sufficient bandwidth to pass the CESSB signal. If a standard SSB modulator meets these requirements, then the envelope control by the CESSB process is preserved.

ITU designations

In 1982, the International Telecommunication Union (ITU) designated the types of amplitude modulation:

Designation	Description
A3E	Double-sideband full-carrier – the basic amplitude-modulation scheme
R3E	Single-sideband reduced-carrier
H3E	Single-sideband full-carrier
J3E	Single-sideband suppressed-carrier
B8E	Independent-sideband emission
C3F	Vestigial-sideband
Lincompex	Linked compressor and expander

See also

• ACSSB, amplitude-companded single sideband
• Independent sideband
• Modulation for other examples of modulation techniques
• Sideband for more general information about a sideband

Sources

• Partly from Federal Standard 1037C in support of MIL-STD-188

Further reading

• Sgrignoli, G., W. Bretl, R. and Citta. (1995). "VSB modulation used for terrestrial and cable broadcasts." IEEE Transactions on Consumer Electronics. v. 41, issue 3, p. 367 - 382.
• J. Brittain, (1992). "Scanning the past: Ralph V.L. Hartley", Proc. IEEE, vol.80, p. 463.
• eSSB - Extended Single Sideband