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

А_i

â_i


Figure: 5.1 Timing diagrams of signals in DSP devices


In the transmitter, special devices are usually provided for obtaining the desired shape of the modulating signal pulses, at which the stream of channel symbols has a permissible value of out-of-band emissions.
The main element of the receiver is a demodulator that estimates in the best way each received symbol. In this case, the important thing is not the form of the received channel symbol, which is known at the receiving point, but its number m. The delay of the recovered signal in relation to the transmitted one is due to both the propagation time of the radio waves themselves and the additional delays of electrical signals in the elements of the transmission system, which provide formation and processing of these signals.
Interference in the transmission channel is caused by thermal noise of the receiver elements and external sources of radiation of natural and artificial origin. It is especially necessary to note the radiation of transmitters operating on adjacent frequency channels, the out-of-band emissions of which fall into the frequency band of the transmission system. This interference is commonly referred to as adjacent channel interference.
In modern DSPs, quite strict limits are introduced on the level of out-of-band emissions, which can be performed using complex methods for generating channel symbols of a special form using digital devices. Interference from transmitters operating in the same frequency band but using different channel symbol shapes is also possible. Such interference is called internal - systemic.
The presence of noise and interference makes it difficult to make correct decisions in the receiver about which of the M channel symbols was transmitted on the next time interval. With a low level of interference and a large signal-to-noise ratio, the receiver demodulator is very rarely mistaken, i.e. the probability of an error when receiving one character is small and amounts to 10 - 3 or less. As a result, the DSP at large values ​​of the signal-to-noise ratio provides an almost accurate reproduction of the transmitted bit stream at the receiving point. This means an almost accurate reproduction of the original signal, which is impossible with analog transmission systems.
If the SNR is not very large, then the receiver demodulator makes mistakes more often, and incorrectly received symbols appear. A useful parameter, often used to characterize the quality of a digital transmission system, is the probability of error when receiving one symbol


р_с = Р { Symbol accepted s_n | Symbol transmitted s_m}, n ≠ т , (6.2)

or bit error probability


р_б = Р { Bit with value received d | Bit with value transmitted е},

d {0,1}, e {0,l} и d≠e. (6.3)

Modern wireless communication systems allow for one error per 1000 bits of transmitted information; it can be assumed that the permissible error probability when receiving one bit in this case is 10 - 3. At the same time, the human ear is still able to identify the subscriber's voice, i.e. the hearer recognizes the speaker's voice. At the same time, many information systems impose much more stringent requirements on the digital transmission system, allowing only one error when transmitting 100,000,000 bits, i.e.р_б = 10 ^{– 8}.
Depending on the number of levels M of the modulating (manipulating) signal, as noted above, two-level (binary) and multi-level manipulations are distinguished.
A generalized block diagram of a digital radio channel is shown in Fig. 5.2.

Fig.5.2 Generalized block diagram of a digital radio channel.

The following notation is used here:

U (t) - voltage of the transmitted digital signal;
KD - modulator encoder;
UM - modulation device;
D - detector;
Р - regenerator;
DC - demodulator decoder;
V (t) - recoded digital signal.

For many types of keying used in DSP, it is necessary to use keying signals V (t) that differ in structure from the original transmitted binary signal U (t). For such transcoding, a modulator encoder is used, and for an inverse transformation, a demodulator decoder is used. The purpose of the rest of the devices is self-explanatory.

Phase Shift Keying. In modern digital mobile radio communication systems, M-ary phase shift keying systems (binary, 4-level, etc.) are used.
With phase modulation, the instantaneous value of the phase of the radio signal deviates from the phase of the unmodulated carrier wave by an amount that depends on the instantaneous value of the modulating signal:


s[t, u(t)] = A∙cos{2nf₀ t + φ[u(t)]} = Re[A∙exp{jφ[u(t)]} exp{j2nf₀ t}]. (6.4)

It follows from this expression that the transmitted information contained in the modulating signal u (t) is encoded in a complex envelope


Á(t) = A∙exp{jφ [u(t)]} (6.5)
transmitted signal s[t, u(t)].
The concept of a complex envelope is very important for both the theory and technology of digital communication and plays an essential role.
With digital phase modulation, the carrier phase can differ from the current phase of the unmodulated carrier wave by a finite number of different values. In the case of binary phase shift keying (FM-2), 0 ° and 180 ° are usually chosen as such values. In modern communication systems, large sets of phase angles are often used to represent several bits of transmitted data in one channel symbol. For example, you can use four different phase angles: 45 °, 135 °, -45 °, -135 ° to represent the possible values ​​of a two-bit sequence (FM-4 system). Possible meanings of a three-bit word can be represented by a group of eight different phase angles (FM-8 system), a four-bit word - by a group of 16 phase angles (FM-16 system), etc.
Binary Phase Shift Keying. The simplest form of digital phase modulation is the FM-2 system. This method is often used in direct spreading systems in which the modulating signal is a pseudo-random binary sequence. With FM-2, depending on the value of the modulating signal, the deviation of the signal phase from the phase of the unmodulated carrier oscillation is equal to either 0o or 180 °. If for a phase-modulated signal (PM signal) we take the general description in the form of (6.4) and (6.5), then for the PM-2 signal the equalities should be fulfilled: