Quadrature-carrier multiplexing
A quadrature-carrier multiplexing, or quadrature-amplitude modulation (QAM), system enables two DSB-SC modulated waves, it results from the application of two independent message signals and occupies the same transmission bandwidth, and yet it allows for their separation at the receiver output. It is therefore a bandwidth-conservation scheme.
The multiplexed signal s(t) consists of the sum of two product modulator outputs; that is:
s(t) = Am1(t) cos(wt) + Am2(t) sin(wt),
where m1(t) and m2(t) denote the two different message signals applied to the product modulators. Since each term in the above-mentioned equation has a transmission bandwidth of 2wm and is centered on w, we see that the multiplexed signal occupies a transmission bandwidth of 2wm, centered on the carrier frequency w, where 2wm is the common message bandwidth of and m1(t) and m2(t).
For the quadrature-carrier multiplexing system to operate satisfactorily, it is important to maintain the correct phase and frequency relationships between the local oscillators used in the transmitter and receiver parts of the system, which can be achieved by using the Costas receiver. This increase in system complexity is the price that must be paid for the practical benefit gained from bandwidth conservation.
Other variants of amplitude modulation.
The full AM and DSB-SC forms of the modulation are wasteful of bandwidth because they both require a transmission bandwidth equal to twice the message bandwidth. In either case, one-half the transmission bandwidth is occupied by the lower sideband. Indeed, the upper and lower sidebands are uniquely related to each other by virtue of their symmetry about the carrier valued signals. That is, given the amplitude and phase spectra of either sideband =, we can uniquely determine the other. This means that so far as the transmission of information is concerned, only one sideband is necessary, and if both the carrier and the other sideband are suppressed at the transmitter, no information is lost. In this way, the channel needs to provide only the same bandwidth as the message signal, a conclusion that is intuitively satisfying. When only one sideband is transmitted, the modulation is referred to as single sideband (SSB) modulation.
Frequency-domain description of SSB modulation.
The precise frequency-domain description of an SSB modulated wave depends on which sideband is transmitted. To investigate this issue, consider a message signal m(t) with a spectrum m(jw) limited to the band ws <= |w| <= wb. The spectrum of the DSB-SC modulated wave, obtained by multiplying m(t) by the carrier wave A cos(wt). The upper sideband is represented in duplicate by the frequencies above wi and those below -wc; when only the upper sideband is transmitted, the resulting SSB modulated wave has the spectrum shown in the figure below. Likewise, the lower sideband is represented in duplicate by the frequencies below wi (for positive frequencies) and those above -wc (for negative frequencies); when only the lower sideband is transmitted, the spectrum of the corresponding SSB modulated wave is as shown below, numbered as 2. Thus, the essential function of SSB modulation is to translate the spectrum of the modulating wave, either with or without inversion, to a new location in the frequency domain. Moreover, the transmission bandwidth requirement of an SSB modulation system is one-half that of a full AM or DSB-SC modulation system. The benefit of using SSB modulation is therefore derived principally from the reduced bandwidth requirement and the elimination of the high-power carrier wave, two features that make SSB modulation the optimum form of linear CW modulation. The principal disadvantage of SSB modulation is the cost and complexity of implementing both the transmitter and the receiver. Here again, we have a trade-off between increased system complexity and improved system performance.
Time-domain description or SSB modulation.
Unlike the situation with DSB-SC modulation, the time-domain description of SSB modulation is not as straightforward. To develop the time-domain description of SSB modulation, we need a mathematical tool known as the Hilbert transform. The device used to perform this transformation is known as the Hilbert transformer, the frequency response of which is characterized as follows:
The magnitude response is unity for all frequencies, both positive and negative. The phase response is – 90 degrees for positive frequencies and 90 degrees for negative frequencies.
The Hilbert transformer may therefore be viewed as a wideband – 90 degrees phase shifter, wide hand in the sense that its frequency response occupies a band of frequencies that, in theory, is infinite in extent.
Vestigial Sideband Modulation
Single sideband modulation is well suited for the transmission of speech because of the energy gap that exists in the spectrum of speech signals between zero and a few hundred hertz for positive frequencies. When the message signal contains significant components at extremely low frequencies (as in the case of television signals and wideband data), the upper and lower sidebands meet at the carrier frequency. This means that the use of SSB modulation is inappropriate for the transmission of such message signals, owing to the practical difficulty of building a filter to isolate one sideband completely. This difficulty suggests another scheme known as vestigial sideband (VSB) modulation, which is a compromise between SSB and DSB-SC forms of modulation. In VSB modulation, one sideband is passed almost completely, whereas just a trace, or vestige, of the other sideband, is retained.
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