Biblio5

a For 99.9% to 99.99% time availability.

where F is the frequency (the microwave transmitter operating frequency) in GHz, and d1, d2, and D are in now kilometers with R in meters.

The three basic increment factors that must be added to obstacle heights are now available—earth curvature (earth bulge), Fresnel zone clearance, and trees and growth (T&G). These are marked on the path profile chart. On the chart a straight line is drawn from right to left just clearing the obstacle points as corrected for the three factors. Another similar line is drawn from left to right. A sample profile is shown in Figure 9.5. The profile now gives us two choices, the first based on the right-to-left line and the second based on the left-to-right line. However, keep in mind that some balance is desirable so that at one end we do not have a very tall tower and at the other a small, stubby tower. Nevertheless, an imbalance may be desirable when a reflection point exists at an inconvenient spot along the path so we can steer the reflection point off the reflecting medium such as smooth desert or body of water.

9.2.3.4 Path Analysis or Link Budget

9.2.3.4.1 Introduction. A path analysis or link budget is carried out to dimension the link. What is meant here is to establish operating parameters such as transmitter power output, parabolic antenna aperture (diameter), and receiver noise figure, among others. The link is assumed to be digitally based on one of the formats discussed in Chapter 6 or possibly some of the lower bit rate formats covered in Chapter 17. The type of modulation, desired BER, and modulation rate (i.e., the number of transitions per second) are also important parameters.

Table 9.2 shows basic LOS microwave equipment/ system parameters in two columns. The first we call “normal” and would be the most economic; the second column is titled “special,” giving improved performance parameters, but at an increased price.

Diversity reception is another option to be considered. It entails greater expense. The options in Table 9.2 and diversity reception will be addressed further on in our discussion.

9.2.3.4.2 Approach. We can directly relate the desired performance to the receive signal level (RSL) at the first active stage of the far-end receiver and that receiver’s noise characteristics. To explain: The RSL is the level or power of the received signal in dBW or dBm, as measured at the input of the receiver’s mixer, or, if the receiver has an LNA (low-noise amplifier) at the LNA’s input. This is illustrated in the block diagram of a typical LOS microwave receiver shown in Figure 9.6.

Table 9.2 Digital LOS Microwave Basic Equipment Parameters

214 CONCEPTS IN TRANSMISSION TRANSPORT

Figure 9.9 Calculation of isotropic receive level (IRL).

Calculation of isotropic receive level (IRL). The IRL is the RF power level impinging on the receive antenna. It would be the power we would measure at the base of an isotropic receive antenna.

This calculation is shown graphically in Figure 9.9.

Calculation of receive signal level (RSL). The RSL is the power level at the input port of the first active stage in the receiver. The power level is conventionally measured in dBm or dBW.

(Note: Power levels can be in dBm as well, but we must be consistent.)

Example. Suppose the IRL was −121 dBW, the receive antenna gain was 31 dB, and the line losses were 5.6 dB. What would the RSL be?

RSL c −121 dBW + 31 dB − 5.6 dB

c−95.6 dBW.

Calculation of receiver noise level. The thermal noise level of a receiver is a function of the receiver noise figure and its bandwidth. For analog radio systems, receiver thermal noise level is calculated using the bandwidth of the intermediate frequency (IF). For digital systems, the noise level of interest is in only 1 Hz of bandwidth using the notation N0, the noise level in a 1-Hz bandwidth.

The noise that a device self-generates is given by its noise figure (dB) or a noise temperature value. Any device, even passive devices, above absolute zero generates thermal noise. We know the thermal noise power level in a 1-Hz bandwidth of a perfect receiver operating at absolute zero. It is:

where Pn is the noise power level. Many will recognize this as Boltzmann’s constant expressed in dBW.

We can calculate the thermal noise level of a perfect receiver operating at room temperature using the following formula:

The value, 290 K (kelvins), is room temperature, or about 178C or 688F.

Noise figure simply tells us how much noise has been added to a signal while passing through a device in question. Noise figure (dB) is the difference in signal-to-noise ratio between the input to the device and the output of that same device.

We can convert noise figure to noise temperature in kelvins with the following formula:

where Te is the effective noise temperature of a device. Suppose the noise figure of a device is 3 dB. What is the noise temperature?

3dB c 10 log(1 + Te/ 290) 0.3 c log(1 + Te/ 290)

1.995 c 1 + Te/ 290.

We round 1.995 to 2; thus

2 − 1 c Te/ 290 Te c 290K.

The thermal noise power level of a device operating at room temperature is:

where BW is the bandwidth of the device in Hz.

Example. A microwave receiver has a noise figure of 8 dB and its bandwidth is 10 MHz. What is the thermal noise level (sometimes called the thermal noise threshold)?

Pn c −204 dBW/ Hz + 8 dB + 10 log(10 × 106)

c−204 dBW/ Hz + 8 dB + 70 dB

c−126 dBW.

Calculation of Eb/ N0 in digital radio systems. In Section 3.2.1 signal-to-noise ratio (S/ N) was introduced. S/ N is widely used in analog transmission systems as one measure of signal quality. In digital systems the basic measure of transmission quality is BER. With digital radio links, we will introduce and employ the ratio Eb/ N0 as a mea-

NF, as used above, is the noise figure of the receiver in question. The noise figure tells us the amount of thermal noise a device injects into a radio system.

216 CONCEPTS IN TRANSMISSION TRANSPORT

Example. Suppose a receiver has a noise figure (NF) of 2.1 dB. What is its thermal noise level in 1 Hz of bandwidth? In other words, what is N0?

N0 c −204 dBW + 2.1 dB

c−201.9 dBW/ Hz.

Eb is the signal energy per bit. We apply this to the receive signal level (RSL). The RSL represents the total power (in dBm or dBW) entering the receiver front end, during, let’s say, 1-sec duration (energy). We want the power carried by just 1 bit. For example, if the RSL were 1 W, and the signal was at 1000 bps, the energy per bit would be 1/ 1000 or 1 mW per bit. However, it will be more convenient here to use logarithms and decibel values (which are logarithmic). Then we define Eb as:

Here’s an example using typical values. The RSL into a certain receiver was −89 dBW and bit rate was 2.048 Mbps. What is the value of Eb?

Some notes on Eb/ N0 and its use. Eb/ N0, for a given BER, will be different for different types of modulation (e.g., FSK, PSK, QAM, etc.). When working with Eb, we divide RSL by the bit rate, not the symbol rate nor the baud rate. There is a theoretical Eb/ N0 and a practical Eb/ N0. The practical is always a greater value than the theoretical, greater by the modulation implementation loss in dB, which compensates for system imperfections.

Figure 9.10 is an example of where BER is related to Eb/ N0. There are two curves in the figure. The first from the left is for BPSK/ QPSK (binary phase shift keying/ quadrature phase shift keying), and the second is for 8-ary PSK (an eight-level PSK modulation scheme). The values are for coherent detection. Coherent detection means that the receiver has a built-in phase reference as a basis to make its binary or higher-level decisions.

9.2.3.5 Digital Modulation of LOS Microwave Radios. Digital systems, typically standard PCM, as discussed in Chapter 6, are notoriously wasteful of bandwidth compared with their analog counterparts.6 For example, the analog voice channel is

6A cogent example is FDM using frequency modulation; another is single sideband modulation.

Figure 9.10 Bit error probability (BER) versus Eb/ N0 performance for BPSK/ QPSK and 8-ary PSK (octal PSK).

nominally of 4 kHz bandwidth, whereas the digital voice channel requires a 64-kHz bandwidth, assuming 1 bit per Hz occupancy. This is a 16-to-1 difference in required bandwidth. Thus national regulatory authorities such as the FCC require that digital systems be bandwidth conservative. One means that is used to achieve bandwidth conservation is bit packing. This means packing more bits into 1 Hz of bandwidth. Another driving factor for bit packing is the need to transmit such higher bit rate formats such as SONET and SDH (Chapter 17). Some radio systems can transmit as much as 622 Mbps using advanced bit packing techniques.

How does bit packing work? In the binary domain we can estimate bandwidth to approximately equate to 1 bit/ Hz. For example, if we were transmitting at 1.544 Mbps, following this premise, we’d need 1.544 MHz of bandwidth. Suppose now that we turn

218 CONCEPTS IN TRANSMISSION TRANSPORT

Figure 9.11 Conceptual block diagram of a QPSK modulator. Note that these are two BPSK modulators working jointly, and one modulator is 90 degrees out of phase with the other. The first bit in the bit stream is directed to the upper modulator, the second to the lower, the third to the upper, and so on.

to higher levels of modulation. Quadrature phase shift (QPSK) keying is one example. In this case we achieve a theoretical packing of 2 bits/ Hz. Again, if we are transmitting 1.544 Mbps, with QPSK we would need 1.544 MHz/ 2 or 0.772 MHz. QPSK is one of a family of modulation schemes that are based on phase-shift keying (PSK). With binary PSK (BPSK) we might assign a binary 1 to the 08 position (i.e., no phase retardation) and a binary 0 to the 1808 phase retardation point. For QPSK, the phase-circle is broken up into 908 segments, rather than 1808 segments as we did with binary PSK. In this case, for every transition we transmit 2 bits at a time. Figure 9.11 is a functional block diagram of a QPSK modulator. It really only consists of two BPSK modulators where one is out of phase with the other by 908.

Eight-ary PSK modulation is not uncommon. In this case the phase circle is broken up into 458 phase segments. Now for every transition, 3 bits at a time are transmitted. The bit packing in this case as 3 bits per Hz theoretical.

Now add two amplitude levels to this making a hybrid waveform covering both amplitude modulation as well as phase modulation. This family of waveforms is called quadrature amplitude modulation (QAM). For example, 16-QAM has 16 different state possibilities: eight are derived for 8-ary PSK and two are derived from the two amplitude levels. We call this 16-QAM, where for each state transition, 4 bits are transmitted at once. The bit packing in this case is theoretically 4 bits/ Hz. Certain digital LOS microwave system used 256-QAM and 512-QAM, theoretically achieving 8 bits/ Hz and 9 bits/ Hz of bit packing. The difference between theoretical bit packing and the practical deals with filter design. For QAM-type waveforms, depending on design, practical bit packing may vary, from 1.25 to 1.5, the baud-rate-bandwidth. The extra bandwidth required provides a filter with spectral space to roll-off. In other words, a filter’s skirts are not perfectly vertical. Figure 9.12 is a space diagram for 16-QAM. The binary values for each of the 16 states are illustrated.

Suppose we are using a 48-Mbps bit stream to input to our transmitter which was using 16-QAM modulation. Its baud rate, which measures transitions per second, would be 48/ 4 megabauds/ sec. If we allowed 1 baud/ Hz, then 12 MHz bandwidth would be required. If we used a roll-off factor of 1.5, then the practical bandwidth required would be 18 MHz. Carry this one step further to 64-QAM. Here the theoretical bit packing is 6 bits/ Hz and for the 48-Mbps bit stream, a 12-MHz bandwidth would be required (practical).

Figure 9.12 A 16-QAM state diagram. I c in-phase; Q c quadrature.

There are no free lunches. As M increases (e.g., M c 64), for a given error rate, Eb/ N0 increases. Figure 9.13 illustrates a family of Eb/ N0 curves for various M-QAM modulation schemes plotted against BER.

In summary, to meet these bandwidth requirements, digital LOS microwave will commonly use some form of QAM, and as a minimum at the 64-QAM level, or 128QAM, 256-QAM, or 512-QAM. The theoretical bit packing capabilities are 6 bits/ Hz, 7 bits/ Hz, 8 bits/ Hz, and 9 bits/ Hz, respectively. Figure 9.13 compares BER performance versus Eb/ N0 for various QAM schemes.

9.2.3.6 Parabolic Dish Antenna Gain. At a given frequency the gain of a parabolic antenna is a function of its effective area and may be expressed by the formula:

where G is the gain in decibels relative to an isotropic antenna, A is the area of antenna aperture, h is the aperture efficiency, and l is the wavelength at the operating frequency. Commercially available parabolic antennas with a conventional horn feed at their focus usually display a 55% efficiency or somewhat better. With such an efficiency, gain (G, in dB) is then

where F is the frequency in GHz, and D is the diameter of the parabolic reflector in feet. In metric units we have:

where D is in meters and F is in GHz.

9.2.3.7 Running a Path/ Site Survey. This can turn out to be the most important step in the design of an LOS microwave link (or hop). We have found through expe-