Manipulation in digital radio communication systems. Binary Phase Shift Keying. Quadrature phase and phase shift modulation

φ [u(t)] ≡ 0 при u(t) ≡ 1, φ[u(t)] ≡ π при u(t)≡ – 1; 0 ≤ t ≤ T_c.


The complex envelope of the signal does not change over this time interval and can take the following two values:


Á(t) = A при и(t) = 1, Á(t) = – A при и(t) = – 1; 0≤ t≤T_c. (6.6)

A graphical representation of the possible values of this envelope on the complex plane is useful and visual. For the signal under consideration, the complex envelope takes on only two values, shown in Fig. 5.3. Such an image is called a constellation signal

Figure 5.3 Signal constellation of the FM-2 signal

In fig. 5.4 shows the timing diagrams of binary phase modulation BPSK



Аsin(2πυτ) Аsin(2πυτ+π)


Figure: 5.4 BPSK timing diagrams
The main feature of this radio signal is that its current phase has discontinuities (jumps) when the polarity of the modulating signal changes. These 180 ° phase jumps are the main reason that the spectral power density of the FM-2 signal in the radio channel is significantly different from zero in a very wide frequency band. Therefore, in this form, FM-2 signals are practically not used. To reduce the frequency band occupied by them, they are filtered.
It is difficult to filter these signals after the modulator at a high frequency, since narrow-band high-Q filters would be required for each carrier frequency. The number of such frequencies in modern digital communication systems with mobile objects can reach several dozen. Therefore, the filtering operation is almost always performed on the baseband signal prior to modulation. The corresponding filter is low-pass, although quite complex. Modern advances in radio electronics ensure its implementation, and a large number of frequency channels in this case can be obtained by using a carrier vibration with a set of appropriate frequencies. Such a filter is called a baseband filter.
When reducing the frequency band occupied by the FM-2 radio signal, when filtering the signal, it is necessary to take into account the problem of intersymbol interference that arises in this case.
Figure 5.5 shows a functional diagram of a transmitter that forms an FM-2 radio signal. Here, after the modulator, a radio signal power amplifier and a narrow-band high-frequency filter are included. The main purpose of the filter is to attenuate the radiation of the transmitter at frequencies that are multiples of the fundamental frequency of the carrier wave. The danger of such emissions is due to non-linear effects in a power amplifier, which usually occur and are amplified as the gain of that amplifier is increased. Often this filter is used at the same time for the receiver, it suppresses strong extraneous signals outside the frequency band of the wanted radio signals before converting the frequency "down".

Figure: 5.5 Functional diagram of the forming device

FM-2 radio signal

During demodulation, the phase of the PM radio signal is compared with the phase of the reference waveform (carrier) recovered at the receiving end. Due to random distortion of the radio signal, there can be phase uncertainty of the recovered carrier, which is the reason for the so-called reverse operation, in which the binary messages are taken as "negative". To eliminate this phenomenon, difference coding of the phase of the transmitted radio pulses is used. This phase keying is called phase difference or relative phase keying OFM.

In digital RRL with OFM, when transmitting information, it is not the phase of the radio signal itself that is encoded, but the phase difference (phase shift) of two adjacent radio pulses.
The coding rule for OFM is shown in Figure 5.6.

Figure 5.6 Coded OFM signal

Here :	transition	1→1	- phase jump
		1→0	- no phase jump
		0→0	- no phase jump
		0→1	- phase jump.

With binary OFM, the duration of the radio pulse is τ = T. In the case of multilevel keying (M> 2), the original sequence of binary elements of duration T is transformed using the modulator encoder into a set of two (for M = 4) or three (for M = 8) sequences of binary elements with duration τ = 2T (for M = 4) or τ = 3Т (at М = 8).

There are two ways to demodulate the OFM radio signals. In the first, the carrier is first reconstructed and the OFM of the radio signal is coherently detected, then the received signals are decoded by difference (differential) in Fig. 5.7.



Figure 5.7 DPSK demodulation with carrier recovery

The second method assumes differential-coherent (autocorrelation) detection of the OFM radio signal, in which the previous radio pulse is used as a reference oscillation. In this case, the operation of detection and decoding are combined in Fig. 5.8

Figure 5.8 Differential-coherent detection of the OFM radio signal