DIGITAL MODULATION ; FILTERING

4. Filtering

Filtering allows the transmitted bandwidth to be significantly reduced without losing the content of the digital data. This improves the spectral efficiency of the signal.
There are many different varieties of filtering. The most common are
• raised cosine
• square-root raised cosine
• Gaussian filters
Any fast transition in a signal, whether it be amplitude, phase or frequency will require a wide occupied bandwidth. Any technique that helps to slow down these transitions will narrow the occupied bandwidth.
Filtering serves to smooth these transitions (in I and Q). Filtering reduces interference because it reduces the tendency of one signal or one transmitter to interfere with another in a Frequency-Division-Multiple-
Access (FDMA) system. On the receiver end, reduced bandwidth improves sensitivity because more noise and interference are rejected.
Some tradeoffs must be made. One is that some types of filtering cause the trajectory of the signal (the path of transitions between the states) to overshoot in many cases. This overshoot can occur in certain types of filters such as Nyquist. This overshoot path represents carrier power and phase.
For the carrier to take on these values it requires more output power from the transmitter amplifiers. It requires more power than would be necessary to transmit the actual symbol itself. Carrier power cannot be
clipped or limited (to reduce or eliminate the overshoot) without causing the spectrum to spread out again. Since narrowing the spectral occupancy was the reason the filtering was inserted in the first place, it becomes a very fine balancing act.
Other tradeoffs are that filtering makes the radios more complex and can make them larger, especially if performed in an analog fashion. Filtering can also create Inter-Symbol Interference (ISI). This occurs when the signal is filtered enough so that the symbols blur together and each symbol affects those around it. This is determined by the time-domain response, or impulse response of the filter.
4.1 Nyquist or raised cosine filter
This graph shows the impulse or time-domain response of a raised cosine filter, one class of Nyquist filter. Nyquist filters have the property that their impulse response rings at the symbol rate. The filter is chosen to ring, or have the impulse response of the filter cross through zero, at the symbol clock frequency.

Figure 18. Nyquit or Raised Cosine Filter

The time response of the filter goes through zero with a period that exactly corresponds to the symbol spacing. Adjacent symbols do not interfere with each other at the symbol times because the response equals zero at all symbol times except the center (desired) one. Nyquist filters heavily filter the signal without blurring the symbols together at the symbol times.
This is important for transmitting information without errors caused by Inter-Symbol Interference. Note that Inter-Symbol Interference does exist at all times except the symbol (decision) times. Usually the filter is split,
half being in the transmit path and half in the receiver path. In this case root Nyquist filters (commonly called root raised cosine) are used in each part, so that their combined response is that of a Nyquist filter.
4.2 Transmitter-receiver matched filters
Sometimes filtering is desired at both the transmitter and receiver. Filtering in the transmitter reduces the adjacent-channel-power radiation of the transmitter, and thus its potential for interfering with other transmitters.

Figure 19.Transmitter-Receiver Matched Filters

Filtering at the receiver reduces the effects of broadband noise and also interference from other transmitters in nearby channels.
To get zero Inter-Symbol Interference (ISI), both filters are designed until the combined result of the filters and the rest of the system is a full Nyquist filter. Potential differences can cause problems in manufacturing because the transmitter and receiver are often manufactured by different companies.
The receiver may be a small hand-held model and the transmitter may be a large cellular base station. If the design is performed correctly the results are the best data rate, the most efficient radio, and reduced effects of interference and noise. This is why root-Nyquist filters are used in receivers and transmitters as à Nyquist x à Nyquist = Nyquist. Matched filters are not used in Gaussian filtering.
4.3 Gaussian filter
In contrast, a GSM signal will have a small blurring of symbols on each of the four states because the Gaussian filter used in GSM does not have zero Inter-Symbol Interference. The phase states vary somewhat causing a blurring of the symbols as shown in figure 17. Wireless system architects must decide just how much of the Inter-Symbol Interference can be tolerated in a system and combine that with noise and interference.

Figure 20. Gaussian Filter

Gaussian filters are used in GSM because of their advantages in carrier power, occupied bandwidth and symbol-clock recovery. The Gaussian filter is a Gaussian shape in both the time and frequency domains, and it does not ring like the raised cosine filters do. Its effects in the time domain are relatively short and each symbol interacts significantly (or causes ISI) with only the preceding and succeeding symbols. This reduces the tendency for particular sequences of symbols to interact which makes amplifiers easier
to build and more efficient.
4.4 Filter bandwidth parameter alpha

The sharpness of a raised cosine filter is described by alpha (a). Alpha gives a direct measure of the occupied bandwidth of the system and is calculated as

occupied bandwidth = symbol rate X (1 + a).

If the filter had a perfect (brick wall) characteristic with sharp transitions and an alpha of zero, the occupied bandwidth would be

for a = 0, occupied bandwidth = symbol rate X (1 + 0) = symbol rate.

Figure 21. Filter Bandwidth Parameters “a”

In a perfect world, the occupied bandwidth would be the same as the symbol rate, but this is not practical. An alpha of zero is impossible to implement.

Alpha is sometimes called the “excess bandwidth factor” as it indicates the amount of occupied bandwidth that will be required in excess of the ideal occupied bandwidth (which would be the same as the symbol rate).

At the other extreme, take a broader filter with an alpha of one, which is easier to implement. The occupied bandwidth will be

for a = 1, occupied bandwidth = symbol rate X (1 + 1) = 2 X symbol rate.

An alpha of one uses twice as much bandwidth as an alpha of zero. In practice, it is possible to implement an alpha below 0.2 and make good, compact, practical radios. Typical values range from 0.35 to 0.5, though

some video systems use an alpha as low as 0.11. The corresponding term for a Gaussian filter is BT (bandwidth time product). Occupied bandwidth cannot be stated in terms of BT because a Gaussian filter’s frequency response does not go identically to zero, as does a raised cosine. Common values for BT are 0.3 to 0.5.

4.5 Filter bandwidth effects

Different filter bandwidths show different effects. For example, look at a QPSK signal and examine how different values of alpha effect the vector diagram. If the radio has no transmitter filter as shown on the left of the graph, the transitions between states are instantaneous. No filtering means an alpha of infinity.

Figure 22. Effect of Different Filter Bandwidth

Transmitting this signal would require infinite bandwidth. The center figure is an example of a signal at an alpha of 0.75. The figure on the right shows the signal at an alpha of 0.375. The filters with alphas of 0.75 and 0.375 smooth the transitions and narrow the frequency spectrum required.
Different filter alphas also affect transmitted power. In the case of the unfiltered signal, with an alpha of infinity, the maximum or peak power of the carrier is the same as the nominal power at the symbol states. No extra power is required due to the filtering.

Take an example of a ^π/₄ DQPSK signal as used in NADC (IS-54). If an alpha of 1.0 is used, the transitions between the states are more gradual than for an alpha of infinity. Less power is needed to handle those

transitions. Using an alpha of 0.5, the transmitted bandwidth decreases from 2 times the symbol rate to 1.5 times the symbol rate. This results in a 25% improvement in occupied bandwidth. The smaller alpha takes

more peak power because of the overshoot in the filter’s step response.

This produces trajectories which loop beyond the outer limits of the constellation.

At an alpha of 0.2, about the minimum of most radios today, there is a need for significant excess power beyond that needed to transmit the symbol values themselves. A typical value of excess power needed at an alpha of 0.2 for QPSK with Nyquist filtering would be approximately 5dB. This is more than three times as much peak power because of the filter used to limit the occupied bandwidth.

These principles apply to QPSK, offset QPSK, DQPSK, and the varieties of QAM such as 16QAM, 32QAM, 64QAM, and 256QAM. Not all signals will behave in exactly the same way, and exceptions include FSK, MSK and any others with constant-envelope modulation. The power of these signals

is not affected by the filter shape.

4.6 Chebyshev equiripple FIR (finite impulse respone) filter

A Chebyshev equiripple FIR (finite impulse response) filter is used for baseband filtering in IS-95 CDMA. With a channel spacing of 1.25 MHz and a symbol rate of 1.2288 MHz in IS-95 CDMA, it is vital to reduce

leakage to adjacent RF channels. This is accomplished by using a filter with a very sharp shape factor using an alpha value of only 0.113. A FIR filter means that the filter’s impulse response exists for only a finite

number of samples. Equiripple means that there is a “rippled” magnitude frequency-respone envelope of equal maxima and minima in the pass- and stopbands. This FIR filter uses a much lower order than a Nyquist filter to implement the required shape factor. The IS-95 FIR filter does not have zero Inter Symbol Interference (ISI). However, ISI in CDMA is not as important as in other formats since the correlation of 64 chips at a time is  used to make a symbol decision. This “coding gain” tends to average out the ISI and minimize its effect.

Figure 23. Chebyshev Equiripple FIR Filter

4.7 Competing goals of spectral efficiency and power consumption
As with any natural resource, it makes no sense to waste the RF spectrum by using channel bands that are too wide. Therefore narrower filters are used to reduce the occupied bandwidth of the transmission. Narrower filters with sufficient accuracy and repeatability are more difficult to build.
Smaller values of alpha increase ISI because more symbols can contribute.
This tightens the requirements on clock accuracy. These narrower filters also result in more overshoot and therefore more peak carrier power. The power amplifier must then accommodate the higher peak power without distortion. The bigger amplifier causes more heat and electrical interference to be produced since the RF current in the power amplifier will interfere with other circuits. Larger, heavier batteries will be required. The alternative is to have shorter talk time and smaller batteries. Constant envelope modulation, as used in GMSK, can use class-C amplifiers which are the most efficient. In summary, spectral efficiency is highly desirable, but there are penalties in cost, size, weight, complexity, talk time, and reliability.


Lihat juga

DIGITAL MODULATION; INTRODUCTION
DIGITAL MODULATION ; WHY DIGITAL MODULATION
DIGITAL MODULATION ; USING I/Q MODULATION TO CONVEY INFORMATION 
DIGITAL MODULATION ; DIGITAL MODULATION TYPES AND RELATIVE EFFICIENCIES 
DIGITAL MODULATION ; FILTERING 
DIGITAL MODULATION ; DIFFERENT WAYS OF LOOKING AT A DIGITAL MODULATED SIGNAL TIME AND FREQUENCT DOMAIN VIEW 
DIGITAL MODULATION ; SHARING THE CHANNEL 
DIGITAL MODULATION ; HOW DIGITAL TRANSMITTER AND RECEIVER WORK 
DIGITAL MODULATION ; MEASUREMENT ON DIGITAL RF COMMINICATION SYSTEMS 
DIGITAL MODULATION ; SUMMARY 
DIGITAL MODULATION ; OVERVIEW OF COMMUNICATION SYSTEM 
DIGITAL MODULATION ; GLOSSARY OF TERM