# digital modulation

Although based on the same concepts, the waveforms of the digital modulation seem very different from their analog counterparts.

Although it is not extinct, analog modulation is simply incompatible with a digital world. We do not focus more of our efforts on moving the analog waveforms from one place to another. Rather, we want to move data: reti wireless, digitized audio signals, measurements of sensors and so on. To transfer digital data, we use digital modulation.

We must be careful, But, with this terminology.”Analog” e “digital” in this context refers to the type of information being transferred, not to the basic characteristics of the waveforms actually transmitted. Both the analog modulation that utilize digital signals which vary smoothly; the difference is that a analogically modulated signal is demodulated in an analog waveform baseband, while a digitally modulated signal consists of discrete modulation unit, calls symbols , that are interpreted as digital data.

There are analogue and digital versions of the three types of modulation. Let's start with the amplitude and the frequency.

## amplitude digital modulation

This type of modulation is called amplitude shifting (ASK). The simplest case is “on-off keying” (ALSO), and it corresponds almost directly to the mathematical relationship discussed in the relevant page in [analog modulation]: If we use a digital signal as a waveform in the baseband, We multiply the baseband and the carrier producing a modulated waveform which is normal for the logic high and “extinguished” for the low logic. The logic high amplitude corresponds to the index modulation.

## Domain Time

The following graph shows OOK generated using a carrier at 10 MHz and a digital clock signal by 1 Mhz. Here we work in the mathematical realm, then the amplitude of the logic (and the amplitude of the carrier) it's simply “1” adimensionale; in a real circuit you might have a carrier waveform 1 V and a logic signal 3.3 V.

You may have noticed an inconsistency between this example and the mathematical relationship discussed on the page [Amplitude modulation]: we have not moved the baseband signal. If you have to do with a typical digital waveform coupled cc, it is not necessary a shift upwards because the signal remains in the positive part of the y-axis.

## Frequency Domain

Here is the corresponding spectrum:

Compared with the spectrum for the amplitude modulation with a sine wave to 1 MHz:

Most of the spectrum is the same: a peak at the carrier frequency (fC) and a peak at fC over the frequency baseband and fC less frequency in baseband. However, the ASK spectrum also has smaller peaks that correspond to the 3rd and 5th harmonic: the fundamental frequency (fF) is 1 MHz, which means that the 3rd harmonic (f3) is 3 MHz and the 5th harmonic (f5) is 5 Mhz. So we have more peaks at fC / less fF, f3 and f5. And actually, if you were to expand the plot, you would see that the peaks continue according to this scheme.

This makes perfect sense. A Fourier transform of a square wave it consists of a sine wave at the fundamental frequency together with sine waves to decreasing amplitude at odd harmonics, harmonic content and this is what we see in the spectrum shown above.

This discussion leads us to an important practical point: the abrupt transitions associated with digital modulation schemes produce unwanted content (higher frequencies). We must bear this in mind when we consider the effective bandwidth of the modulated signal and the presence of frequencies that may interfere with other devices.

## digital frequency modulation

This type of modulation is called frequency shift keying (FSK). For our purposes it is not necessary to consider a mathematical FSK; Rather, we can simply specify that we will have a frequency f1 when the baseband data are logical 0 and frequency f2 when the baseband data are logical 1.

## Domain Time

A method for generating the waveform FSK ready for transmission is to first create an analog baseband signal that switches between f1 and f2 on the basis of digital data. Here is an example of a waveform in base band FSK with f1 = 1 kHz e f2= 3 kHz. To ensure that a symbol has the same length for logic 0 and the logic 1, we use a cycle 1 kHz and the three cycles from 3 kHz.

The waveform of the baseband is then moved (using a mixer) until the carrier frequency and transmitted. This approach is particularly useful in systems software-defined radio: the waveform in analog base band is a low frequency signal, and therefore it can be generated mathematically and then introduced in the analog domain by a DAC. Using a DAC to create the signal transmitted at high frequency would be much harder.

A more conceptually simple way to implement the FSK is simply to have two carrier signals with different frequencies (f1e f2); one or the other is routed to the output based on the logic level of binary data. This results in a final waveform transmitted that abruptly changes between two frequencies, very similar to the waveform FSK base band above, except that the difference between the two frequencies is much smaller in relation to the average rate. In other words, if you observe a pattern in the time domain, It would be difficult to visually distinguish the sections from f1 f2 sections because the difference between f1 and f2 is only a small fraction of f1 (o f2).

## Frequency Domain

Let's look at FSK effects in the frequency domain. We will use our same carrier frequency 10 MHz (or carrier medium frequency in this case) and we will use ± 1 MHz as a deviation. (This is unrealistic, but it is convenient for our present purposes.) Then the transmitted signal will be 9 MHz for logic 0 e 11 MHz for logic 1. Here the spectrum:

Note that there is no energy to “carrier frequency”. This is not surprising, Whereas the modulated signal is never 10 Mhz. You always 10 MHz less 1 MHz o 10 MHz more 1 MHz, and this is exactly where we see the two dominant peaks: 9 MHz e 11 MHz.

But what about the other frequencies in this spectrum? Good, the FSK spectral analysis is not particularly simple. We know that there will be a further Fourier energy associated with the abrupt transitions between the frequencies. It turns out that the FSK produces a type of sinc-function spectrum for each frequency, that is, one is centered on f1 and the other is centered on f2. These explain the additional frequency peaks seen on both sides of the two dominant peaks.

digital phase modulation: BPSK, QPSK, DQPSK

The digital phase modulation method is a versatile and widely used for wireless digital data transfer.

So far we have seen that we can use discrete changes in amplitude or frequency of a carrier as a way of representing one and a zero. It should not be surprising that we can represent digital data using the phase; This technique is called phase shift keying (PSK).

### Binary Phase Shift Keying

The most direct form of PSK is called binary phase shifting (BPSK), dove “binary” It refers to the use of two phase offset (one for the high logic, one for low logic).

We can intuitively recognize that the system will be more robust if there is a greater separation between these two phases, of course it would be difficult for a receiver to distinguish between a symbol with a phase shift of 90 ° and a symbol with a phase lag 91 we have got only 360 ° phase with which to work, then the maximum difference between the logic high and logic low phases is 180 °. But we know that moving a sinewave 180 ° is invest; then, We can think of BPSK simply by reversing the carrier in response to a logic and leaving him only in response to the other logic state.

To take a step further, we know that multiplying a sine wave with a negative is the same thing as reverse it. This leads to the possibility to implement BPSK by using the following basic hardware configuration:

However, this scheme could easily lead to high slope transitions in the carrier waveform: if the transition between logic states occurs when the carrier is at its maximum value, the carrier voltage must move quickly to the minimum voltage.

high slope Events such as these are not desirable because they generate high frequency energy that might interfere with other RF signals. Furthermore, amplifiers have a limited ability to produce high slope variations in the output voltage.

If we perfect the implementation of the above with two additional features, we guarantee smooth transitions between symbols. First of all, It is necessary to ensure that the digital bit period is equal to one or more complete cycles of the modulating. Second, we need to synchronize the digital transitions with the waveform of the carrier. With these improvements, we could design the system in such a way that the phase change in 180 ° occurs when the carrier signal is located (or very close) zero-crossing.

### QPSK

BPSK moved one bit per symbol, that is what we are used to now. Everything we have discussed about the digital modulation has assumed that the carrier signal is changed depending on whether a digital voltage is low or high logic, and build the digital data receiver interpreting each symbol as 0 O 1.

Before discussing the quadrature for the phase shift (QPSK), It is necessary to introduce the following important concept: there is no reason why a symbol can only transfer one bit. It is true that the world of digital electronics is built around circuits in which the voltage is at one extreme or the other, in such a way that the voltage always represents a digital bit. But the RF is not digital; Rather, we are using waveforms analog for transferring data digital, and it is perfectly acceptable to design a system in which the analog waveforms are encoded and interpreted in such a way that a symbol can represent two (or more) bit.

QPSK is a modulation scheme that allows a symbol to transfer two data bits. There are four possible two-bit numbers (00, 01, 10, 11) and consequently it is required four phase offset. Once again, we want the maximum separation between the phase options, which in this case is 90 °.

The advantage is the high data rate: if we maintain the same period, we can double the rate at which the data is moved from the transmitter to the receiver. The disadvantage is the complexity of the system. (One might think that QPSK is also significantly more susceptible to bit errors than in BPSK, since there is less separation between the possible values ​​of fase.Questa it is a reasonable assumption, but if you go through the math it turns out that the chances of error are actually very similar.)

### variants

QPSK is, all in all, an efficient modulation scheme. But it can be improved.

#### Phase Jumps

QPSK standard guarantees the occurrence of transitions from symbol to symbol in high slope; since the phase jumps may be ± 90 °, we can not use the approach described for phase jumps 180 ° products from BPSK modulation.

This problem can be mitigated by using one of the two variants QPSK.

Offset QPSK, which provides for the addition of a delay in one of the two digital data streams used in the modulation process, It reduces the maximum phase jump in 90 °.

Another option is π / 4-QPSK, which reduces the maximum phase jump in 135 °. Offset QPSK is therefore higher than the reduction of the phase discontinuity, It is π / 4-QPSK is advantageous because it is compatible with the differential encoding in the next section.

Another way to handle the discontinuities from symbol to symbol is to implement a further signal processing which creates smoother transitions between the symbols. This approach is embedded in a modulation scheme called shifting keying minimum (MSK), and there is also an improvement of MSK MSK known as Gaussian.

#### differential Encoding

Another difficulty is that with PSK demodulation waveforms is more difficult compared to the waveforms FSK. Attendance is “absolute” in the sense that the frequency variations can always be interpreted by analyzing the variations of the signal with respect to time. The phase, however, It is relative in the sense that it does not have a universal reference: the transmitter generates the phase variations with respect to a point in time and the receiver may interpret the phase changes with reference to a separate point in time.

The practical manifestation of this is as follows: If there are differences between the phase (or frequency) the oscillators used for modulation and demodulation, PSK becomes unreliable. And we have to assume that there will be phase differences (unless the receiver incorporates the recovery circuits of the carrier).

differential QPSK (DQPSK) is a variant compatible with non-coherent receivers (or receivers that do not synchronize the oscillator of demodulation with the oscillator modulation). Differential QPSK encoding the data by producing a certain phase shift compared to the previous symbol. By using the phase of the previous symbol in this way, the demodulation circuitry analyzes the phase of a symbol using a common reference to the receiver and to the transmitter.

## As you compare the different modulation schemes in terms of performance and applications? Let's take a look.

It is important to understand the salient features of the three types of RF modulation. But this information does not exist in isolation: the real objective is to design systems that meet in an effective and efficient way to meet performance targets. Then, we need to have a general idea of ​​what modulation scheme is appropriate for a particular application.

## Amplitude Modulation

The amplitude modulation is simple in terms of implementation and analysis. Furthermore, AM of the waveforms are fairly easy to demodulate. All in all, then, AM can be seen as a simple low-cost modulation scheme. As always, however, the simplicity and low cost are accompanied by performance compromises, We will never expect that the simplest and cheapest solution is the best.

It might not be accurate to describe systems like AM “rare”, As countless vehicles worldwide include AM receivers. However, applications of analog modulation are currently very limited, because AM has two significant drawbacks.

## Amplitude Noise

Noise is a perpetual difficulty in wireless communication systems. In a sense, the quality of an RF design can be summed up by the signal ratio / noise of the demodulated signal: less noise in the received signal means higher quality output (for analog systems) or less bit errors (for digital systems ). The noise is always present and we must always recognize it as a fundamental threat to the overall system performance.

electrical noise, noise, interference, random electrical and mechanical transients affect the signal. In other words, the noise can create an amplitude modulation. This is a problem, since the amplitude modulation resulting from the random noise can not be distinguished from intentional amplitude modulation performed by the transmitter. Noise is a problem for any RF signal, but the AM systems are particularly sensitive.

## Linearity Amplifier

A major challenge in the design of RF power amplifiers is the linearity. (More in particular, it is difficult to achieve both high efficiency and high linearity.) A linear amplifier applies a certain fixed gain to the input signal; in graphic terms, the transfer function of a linear amplifier is simply a straight line, with the slope corresponding to the gain.

The real-life amplifiers always have a certain degree of non-linearity, which means that the gain applied to the input signal is influenced by the characteristics of the input signal. The non-linear amplification result is distortion, namely the creation of spectral energy at harmonic frequencies.

We can also say that the non-linear amplification is a form of amplitude modulation. If the gain of an amplifier varies depending on the frequency of the input signal or based on external factors such as temperature or power supply condition, the transmitted signal is experimenting with a modulation amplitude of unintentional (and unwanted). This is a problem in AM systems because the spurious amplitude modulation interferes with the modulation amplitude of intentional.

Any modulation scheme that incorporates amplitude variations is more susceptible to the effects of non-linearity. This includes both the ordinary analog amplitude modulation both widely used digital schemes collectively known as quadrature amplitude modulation (QAM).

## angle Modulation

The frequency and phase modulation encode information in the temporal characteristics of the transmitted signal and, Consequently, They are robust against noise amplitude and the non-linearity of the amplifier. The frequency of a signal can not be changed by noise or distortion. You can add additional frequency content, but the original frequency will still be present. The noise, naturally, It has negative effects on FM and PM systems, but the noise does not corrupt directly the signal characteristics that have been used to encode the data in baseband.

As mentioned earlier, the power amplifier design involves a compromise between efficiency and linearity. The angle modulation is compatible with the low linearity and these low linearity amplifiers amplifiers are more efficient in terms of energy consumption. Therefore, the angular modulation is a good choice for low-power RF systems.

## Bandwidth

The effects of the frequency domain of amplitude modulation are more direct than those of frequency and phase modulation. This can be considered an advantage AM: it is important to be able to predict the bandwidth occupied by the modulated signal.

However, the difficulty of predicting the spectral characteristics of FM and PM is more relevant for the theoretical part of the project. If we focus on practical considerations, the angle modulation could be considered advantageous because it can translate a slightly smaller bandwidth baseband date over a width of the transmission band (than AM).

## Frequency vs. phase

The frequency modulation and phase modulation are closely related; however, there are situations in which it is a better choice than the other. The differences between the two are more pronounced with digital modulation.

## Analog Frequency and phase modulation

As we have seen in the phase modulation, when the baseband signal is a sine wave, a PM waveform is simply a shifted version of a form corresponding FM wave. not surprisingly, then, that there are pros and cons in main AM vs. FM relative spectral characteristics or susceptibility to noise.

However, analog FM is much more common than analog AM, and the reason is that the modulation and demodulation circuitry is simpler FM. Eg, the frequency modulation can be performed with something as simple as an oscillator built around an inductor and a voltage-controlled capacitor (ie a capacitor having capacitance changes in response to a baseband signal voltage).

## digital frequency and phase modulation

The differences between AM and FM become quite significant when we enter the realm of digital modulation. The first consideration is the error rate in bits. Obviously the system of any bit error rate will depend on various factors, but if we compare mathematically a binary PSK system with a binary system FSK equivalent, we find that the FSK track needs a lot more transmission energy to achieve the same bit error rate. This is an advantage of the digital phase modulation.

But the common digital PM also has two significant drawbacks.

• As discussed in the digital phase modulation, ordinary PSK (ie non-differential) It is not compatible with non-coherent receivers. L'FSK, Unlike, It does not require coherent detection.
• The ordinary PSK schemes, in particular QPSK, involve abrupt phase changes that cause changes in the signal high slope and a high slope of the waveform sections are decreasing amplitude when the signal is processed by a low-pass filter. These amplitude variations combined with the non-linear amplification lead to a problem called spectral regrowth. To mitigate the spectral regrowth we can use a more linear power amplifier (and therefore less efficient) or implement a specialized version of PSK. Or we can go to FSK, requiring no abrupt changes of phase.
• The amplitude modulation is simple, but it is susceptible to noise and requires a high-linearity power amplifier.
• The frequency modulation is less susceptible to amplitude noise and can be used with high efficiency and low linearity amplifiers.
• The digital phase modulation offers the best theoretical performance in terms of bit error rate with respect to the digital frequency modulation, but the digital FM is advantageous in low power systems because it does not require a high-linearity amplifier.

##### Here you can see the variations of amplitude caused by the low-pass filtering of a PSK signal.

With this I consider the matter closed, if there are inquiries about I proceed with the explanation of demodulation and identify the transmitted signal.

Here's the direct link to the WIDTH MODULATION

Here's the direct link to the MODULATION FREQUENCY

Here's the direct link to the MODULATION PHASE

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