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 digital based on one of the formats discussed in Chapter 6 or possibly some of the lower bit rate formats covered in Chapter 19. 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 that may wish 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) of the first active stage of the far-end receiver and that receiver's noise characteristics. Let us 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 its input. This is illustrated in the block diagram of a typical LOS microwave receiver shown in Figure 9.6.

In Figure 9.6, the incoming signal from the antenna (RF) is amplified by the LNA and then fed to the downconverter, which translates the signal to the intermediate frequency (IF), often 70 MHz. The IF is amplified and then inputs the demodulator. The demodulator output is the serial bit stream, replicating the input serial bit stream at the far-end transmitter.

The next step in the path analysis (link budget) is to calculate the free-space loss between the transmit antenna and the receive antenna. This is a function of distance and

Table 9.2 Digital LOS Microwave Basic Equipment Parameters

Parameter

Normal

Special

Comments

Transmitter power

1 W

10W

500 mW common

above 10 GHz

Receiver noise figure

4-8 dB

1-2.5 dB

Use of low-noise

amplifier

Antenna

Parabolic, 2- to

Same

Antennas over 12 ft not

12-ft diameter

recommended

Modulation

64-256 QAM

Up to 512 QAM,

Based on bandwidth

Note: Bit packing

or QPR, or

bit rate constraints,

requirements

QAM/trellis

or bandwidth desired

in case of

SONET/SDH

Bpsk Transmitter Receiver Block Diagram

Figure 9.6 Simplified block diagram of an LOS microwave receiver. RF is radio frequency; IF is intermediate frequency; LNA is low-noise amplifier. Point A is used to measure RSL when and LNA is employed, which is optional. Otherwise, the measurement point is point B, at the input of the downconverter.

Figure 9.6 Simplified block diagram of an LOS microwave receiver. RF is radio frequency; IF is intermediate frequency; LNA is low-noise amplifier. Point A is used to measure RSL when and LNA is employed, which is optional. Otherwise, the measurement point is point B, at the input of the downconverter.

frequency (i.e., the microwave transmitter operational frequency). We then calculate the EIRP (effective isotropically radiated power) at the transmit antenna. The EIRP (in dBm or dBW, Appendix C) is the sum of the transmitter power output, minus the transmission line losses plus the antenna gain, all in decibel units. The units of power must be consistent, either in dBm or dBW. If the transmitter power is in dBW, the EIRP will be in dBW and the distant-end RSL must also be in dBW.

We then algebraically add the EIRP to the free-space loss in dB (often called path loss), the result is the isotropic4 receive level (IRL). When we add the receive antenna gain to the IRL and subtract the receive transmission line losses, we get the receive signal level (RSL). This relationship of path losses and gains is illustrated in Figure 9.7.

Antenna

M I M I I II I

gain

\ /V EIRP = +27.5 dBW

Line loss (each endl = 2.5 dB

Antenna gain (each end) = 30 dB

0 dBW 7

N Line losses \

^ Free-space path loss = 140 dB

Line losses

Antenna gain d

7 GHZ

-100 dBW

/ Receiver

input

I I I I I I I I I

I I I I I I I I I I "85dBW

Figure 9.7 LOS microwave link gains and losses (simplified). Transmitter power output is 1 W or 0 dBW.

4An isotropic antenna is an antenna that is uniformly omnidirectional and thus, by definition, it has a 0-dB gain. It is a hypothetical reference antenna. The isotropic receive level (IRL) is the power level we would expect to achieve at that point using an isotropic antenna.

Path Loss. For operating frequencies up to about 10 GHz, path loss is synonymous with free-space loss. This represents the steady decrease of power flow as the wave expands out in space in three dimensions. The formula for free-space loss is

where L is the free-space loss between isotropic antennas, F is measured in GHz, and D is in statute miles. In the metric system

where D is in kilometers.

Calculation of EIRP. Effective isotropically radiated power is calculated by adding decibel units: transmitter power (in dBm or dBW), the transmission line losses in dB (a negative value because it is a loss), and the antenna gain in dBi.5

EIRPdBW = trans. output powerdBW — trans. line lossesdB + ant.gaindB. Figure 9.8 shows this concept graphically.

Example. If a microwave transmitter has 1 W (0 dBW) of power output, the waveguide loss is 3 dB and the antenna gain is 34 dBi, what is the EIRP in dBW?

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 receive signal level (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.

RSLdBW = IRLdBW + rec. ant. gain (dB) — rec. trans. line losses (dB). (Note: Power levels can be in dBm as well, but we must be consistent.)

EIRP = Trans, output (dBW) - Trans, line loss {dB) + Ant. gain (dB)

Figure 9.8 Elements in the calculation of EIRP.

5 dBi stands for decibels referenced to an isotropic (antenna).

EIRP = Trans, output (dBW) - Trans, line loss {dB) + Ant. gain (dB)

Figure 9.8 Elements in the calculation of EIRP.

5 dBi stands for decibels referenced to an isotropic (antenna).

Figure 9.9 Calculation of isotropic receive level (IRL).

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?

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 17°C or 68°F.

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?

We round 1.995 to 2; thus

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)?

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 measure of signal quality. Given a certain modulation type, we can derive BER from an Eb/N0 curve.

In words, Eb/N0 means energy per bit per noise spectral density ratio. N0 is simply the thermal noise in 1 Hz of bandwidth or

NF, as defined 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.

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

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 were 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

Pn = -204 dBW/Hz + 8 dB + 10 log(10 x 106) = -204 dBW/Hz + 8 dB + 70 dB = -126 dBW.

Here is 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?

Eb = -89 dBW - 10 log(2.048 x 106) = -89 dBW - 63.11 dB = -152.11 dBW

We can now develop a formula for Eb/N0:

Eb/N0 = RSLdBw - 10 log (bit rate) - (-204 dBW + NFdB). (9.14)

Simplifying, we obtain

Eb/N0 = RSLdBW - 10 log (bit rate) + 204 dBW - NFdB. (9.15)

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 decibels, 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 to their analog counterparts.6 For example, the analog voice channel is nominally of 4kHz bandwidth, whereas the digital voice channel requires a 64-kHz bandwidth, assuming 1-bit/Hz occupancy. This is a 16-to-1 difference in required bandwidth. Thus national regulatory authorities, such as the U.S. 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 19). 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 to higher levels of modulation. Quadrature phase shift 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, we might assign a binary 1 to the 0° position (i.e., no phase retardation) and a binary 0 to the 180° phase retardation point. For QPSK, the phase circle is broken up into 90° segments, rather than 180° 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 90°.

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

Ary Psk Probability Error

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

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

Eight-ary PSK modulation is not uncommon. In this case the phase circle is broken up into 45° phase segments. Now for every transition, 3 bits at a time are transmitted. The bit packing in this case is 3 bits/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'd 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 use 256-QAM and 512-QAM, theoretically achieving 8 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

Bpsk Receiver Simple Block Diagram
Figure 9.11 Conceptual block diagram of aQPSK modulator. Note that these are two BPSK modulators working jointly, and one modulator is 90° 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.
Q

0000

0001

0011

0010

0100

0101

0111

0110

1100

1101

1111

1110

»

1000

1001

1011

1010

Figure 9.12 A 16-QAM state diagram. I stands for in-phase, Q stands for quadrature.

Figure 9.12 A 16-QAM state diagram. I stands for in-phase, Q stands for quadrature.

the baud-rate bandwidth from 1.25 to 1.5. 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 a 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).

There are no free lunches. As M increases (e.g., M = 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 bit rate/bandwidth requirements, digital LOS microwave commonly uses some form of QAM; as a minimum, it uses 64-QAM, 128-QAM, 256-QAM, or 512-QAM. The theoretical bit packing capabilities of these QAM waveforms

Curve For Qam
Energy-per-bit/Noise-density in dB (Eb/No) Figure 9.13 BER performance for several modulation types.

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, n is the aperture efficiency, and X 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 decibels) is then

where F is the frequency in gigahertz 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 gigahertz.

9.2.3.7 Running a Path/Site Survey. This exercise can turn out to be the most important step in the design of an LOS microwave link (or hop). We have found through experience that mountains move (i.e., map error), buildings grow, grain elevators appear where none were before, east of Madrid a whole high-rise community goes up, and so forth.

Another point from experience: If someone says "line-of-sight" conditions exist on a certain path, don't believe it! Line of sight must be precisely defined. We reiterate that for each obstacle in the LOS microwave path, earth curvature with proper K-factor must be added to obstacle height, 0.6 of the first Fresnel zone must be added on top of that, and then 50 ft for trees and 10 ft more for growth must be added if in a vegetated area (to avoid foliage-loss penalties).7

Much of the survey is to verify findings and conclusions of the path profile. Of course, each site must be visited to determine the location of the radio equipment shelter, the location of the tower, whether site improvement is required, the nearest prime power lines, and site access, among other items to be investigated.

Site/path survey personnel must personally inspect the sites in question, walking/driving the path or flying the path in a helicopter, or a combination thereof. The use of GPS receivers are helpful to verify geographical positions along the path, including altitudes.8

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    What does IRL and RSL stands for in radio system?
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