Single-sideband modulation
From Freepedia
Single-sideband modulation (SSB) is a refinement of the technique of amplitude modulation designed to be more efficient in its use of electrical power and bandwidth. It is closely related to vestigial sideband modulation (VSB) (see below).
Amplitude modulation typically produces a modulated output signal that has twice the bandwidth of the modulating signal, with a significant power component at the center carrier frequency. Single-sideband modulation improves this, at the cost of extra complexity.
SSB was pioneered by telephone companies in the 1930s for use over long-distance lines, as part of a technique known as Frequency-division multiplexing. This enabled many voice channels to be sent down a single physical circuit. The use of SSB meant that the channels could be spaced (usually) just 4,000 Hz apart, while offering a speech bandwidth of nominally 300 – 3,400 Hz.
Radio amateurs began to experiment with the method seriously after World War II. It has become a de facto standard for long-distance voice radio transmissions since then.
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Signal generation
The best way of thinking of SSB modulation is to first consider an amplitude-modulated signal. This will have two frequency-shifted copies of the modulating signal (the lower one is frequency-inverted) on either side of the remaining carrier wave. These are known as sidebands: either upper sideband (USB) or less commonly lower sideband (LSB).
To produce an SSB signal, a filter removes one of the sidebands. Most often, the carrier is reduced (suppressed) or removed entirely. Assuming both sidebands are symmetric, no information is lost in the process. What remains still contains the entire information content of the AM signal, using substantially less bandwidth and power, but cannot now be demodulated by a simple envelope detector. 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.
An alternate method of signal generation has been gaining popularity recently in part due to the availability of low-cost digital signal processor (DSP) systems. To generate an SSB signal with this method, first two versions of the original signal are generated which are mutually 90° out of phase, usually by implementing a Hilbert transformer in a DSP. Each one of these signals are then mixed with carrier waves that are also 90° out of phase with each other. By either adding or subtracting the resulting signals, this can generate a lower or upper sideband signal.
Mathematical Highlights
Let <math>\hat s(t)\,</math> represent the Hilbert transform of the original signal: <math>s(t)\,</math>. Then <math>s_a(t) = s(t)+j \hat s(t)\,</math> is a useful mathematical concept, called the analytic signal. The Fourier transform of <math>s(t)\,</math> is symmetrical about the 0 Hz axis. So if we simply translate <math>s(t)\,</math> to a radio transmission frequency, <math>F_c\,</math>, its spectrum will be symmetrical about <math>F_c\,</math>, and the two halves are called sidebands. The Fourier transform of <math>s_a(t)\,</math> is the same as <math>2\cdot s(t)\,</math> above 0 Hz, but it has no negative frequency components. So when we translate it to a radio transmission frequency, it has just a single sideband. The product of <math>s_a(t)\,</math> with this complex sinusoid: <math>e^{j2\pi F_c\cdot t} = cos(2\pi F_c\cdot t)+j\cdot sin(2\pi F_c\cdot t)\,</math> accomplishes that translation. (Notice that <math>e^{j2\pi F_c\cdot t}\,</math> comprises the out-of-phase carrier waves mentioned earlier.)
Now here's the reward for your patience. The product: <math>s_a(t)\cdot e^{j2\pi F_c\cdot t}\,</math> has no negative frequency components. So it is the analytic representation of the single sideband signal we are trying to generate. As we have already seen, that means the signal we are trying to generate is just the real part of that product. I.e, <math>s_a(t)\cdot e^{j2\pi F_c\cdot t} = s_{ssb}(t) +j\hat s_{ssb}(t) \,</math>. Therefore we don't need to compute the entire complex product. (And how would we transmit & receive a complex-valued waveform anyway?) So here at last, is the SSB modulator: <math>s_{ssb}(t) = Re\big\{s_a(t)\cdot e^{j2\pi F_c\cdot t}\big\} = s(t)\cdot cos(2\pi F_c\cdot t) - \hat s(t)\cdot sin(2\pi F_c\cdot t)\,</math>, as described earlier.
Oh, you wanted the lower sideband? OK, just use the complex conjugate of <math>s_a(t)\,</math>: <math>s(t)-j \hat s(t)\,</math>. Its Fourier transform is the mirror image (about 0 Hz) of the analytic signal. Translate it up to <math>F_c\,</math>, keep just the real part, and voilà: <math>s_{lsb}(t) = s(t)\cdot cos(2\pi F_c\cdot t) + \hat s(t)\cdot sin(2\pi F_c\cdot t)\,</math>. The ease with which that was done explains how the analytic signal got its name.
Finally, notice that the sum of the two sideband signals is: <math>2s(t)\cdot cos(2\pi F_c\cdot t)\,</math>, which is the classic model of suppressed-carrier double-sideband AM.
SSB and VSB can also be regarded mathematically as special cases of quadrature amplitude modulation.
Demodulation
The front end of an SSB receiver is the same as 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).
For this to work, the BFO frequency must be accurately adjusted. If the BFO is mis-adjusted, the output signal will be frequency-shifted, making speech sound strange and "Donald Duck"-like... or unintelligible.
Example:
An IF SSB signal is centered at frequency <math>F_{if}\,</math> = 45000 Hz. And the baseband frequency it needs to be shifted to is <math>F_b\,</math> = 2000 Hz. Then the desired frequency shift is <math>F_{bfo}\,</math> = 43000 Hz, and the desired BFO output waveform is <math>cos(2\pi\cdot 43000\cdot t)\,</math>. When the signal at frequency <math>F_{if}\,</math> is multiplied by that waveform, it shifts the signal to two other frequencies: <math>(F_{if}-F_{bfo})\,</math> and <math>(F_{if}+F_{bfo})\,</math>. The difference frequency, <math>(F_{if}-F_{bfo})\,</math> = 2000 Hz, is also known as the beat frequency. The other frequency, <math>(F_{if}+F_{bfo})\,</math> = 88000 Hz, can be removed by a lowpass filter (such as your ear).
Note that if the BFO frequency <math>(F_{bfo})\,</math> is off by a small amount, then the beat frequency is not exactly <math>F_b\,</math>, which can lead to the speech distortion mentioned above.
SSB as a speech-scrambling technique
SSB techniques can also be adapted to frequency-shift and frequency-invert baseband waveforms. These effects were used, in conjunction with other filtering techniques, during World War II as a simple method for speech encryption. Radiotelephone conversations between the US and Britain were intercepted and "decrypted" by the Germans; they included some early conversations between Franklin D. Roosevelt and Churchill. In fact, the signals could be understood directly by trained operators. Largely to allow secure communications between Roosevelt and Churchill, the SIGSALY system of digital encryption was devised.
Today, such simple inversion-based speech encryption techniques are easily decrypted using simple techniques and are no longer regarded as secure.
Suppressed carrier SSB and VSB
Suppressed carrier SSB modulation is used by ATSC. DSL modems impliment suppressed carrier SSB modulation as well.
Vestigial sideband
A vestigial sideband (in radio communication) is a sideband that has been only partly cut off or suppressed. Television broadcasts (regardless of NTSC, PAL, or SECAM analog video format) use this method if the video is transmitted in AM, due to the enormous bandwidth used. It may also be used in digital transmission, such as the ATSC-standardized 8-VSB. The Milgo 4400/48 modem (circa 1967) used vesitigial sideband and phase-shift keying to provide 4800 bit/s transmission over a 1600 Hz channel.
See also
- modulation for other examples of modulation techniques
- Sideband for more general information about a sideband
- ACSB for Amplitude Compandored Sideband modulation
References
- partly from Federal Standard 1037C in support of MIL-STD-188
