Digital Communication
5.5 Digital Link Specifications
5.5.2 Link Margin
The link margin is the amount that the received signal power exceeds the receiver sensitivity.
M = PR − S
where M is link margin (in decibels), PR is signal strength at the receiver system input (dBm), and S is receiver system sensitivity at output of receiving antenna, including the effects of any cable losses from the antenna (dBm).
The received signal power is a function of the ERP, propagation losses, and receiving antenna gain.
PR = ERP − L + GR
Figure 5.21 The received power in a data link receiver is a function of all of the gains and losses between the
transmitter and receiver.
where ERP is the effective radiated power from the transmitting antenna (dBm) including adjustments for transmitting antenna pointing error gain reduction and radome loss; L is
the propagation loss between the transmitting and receiving antennas, including line-of- sight or two-ray propagation loss, diffraction loss, atmospheric loss, and rain loss (all in decibels); and GR is the receiving antenna gain including radome loss and antenna and gain reduction caused by pointing error. Table 5.2 Typical Link Specifications Specification Definition Maximum range Maximum operating range of link Data rate Transmission data bit or symbol rate Bit error rate Ratio of bits incorrectly received Angular tracking rate Maximum angular tracking rate and angular acceleration of transmit or receive antennas Weather Rain conditions under which the link will meet its other specifications Antijam capability The jamming to received signal ratio under which the link will meet full performance specifications Antispoof capability The authentication measures of the system to prevent hostile insertion of false data
The three important propagation loss models used to predict general future performance of systems in dynamic conditions are discussed in Chapter 6.
Figure 5.22 shows the antenna pointing error in the transmitting antenna. This same geometry applies to the receiving antenna not perfectly pointed at the transmitter. In our previous radio propagation discussions related to intercept and jamming situations, we discussed transmitting antenna gain toward the receiver and receiving antenna gain toward the transmitter. This gain has been used in jamming and intercept equations. In that case, we were typically talking about jamming or intercepting into or out of radar main beam versus side lobes. In this case, we are generally in the main lobe of the link antennas, but away from the antenna boresight by a small angle. The gain reduction relative to boresight can be calculated with reasonable accuracy, but it is normally more practical to get the gain patterns of the antennas from the manufacturers and determine the gain reduction at the angle from boresight equal to the specified maximum antenna pointing error.
5.5.3 Sensitivity
The receiver system sensitivity, as discussed in Chapter 6 is:
S(dBm) = kTB(dBm) + NF(dB) + RFSNR(dB)
Figure 5.22 The transmit antenna gain in the direction of the receiver is reduced from the boresight gain by a factor determined from the offset angle.
Within the atmosphere, a common expression for kTB is –114 dBm + 10 log(bandwidth/1 MHz). This assumes that the receiver is at 290K. NF, the system noise figure, is the amount of noise above kTB added by the receiver system, referred back to the receiver input. RFSNR is the predetection SNR. In some literature, this is called the CNR (the carrier- to-noise ratio) to differentiate it from the output SNR. Note that the signal power used in the calculation is the total predetection signal power, not just the carrier power, which is why we use RFSNR in the EW 101 series. In digital links, the RFSNR is related to the bit error rate as a function of a ratio called
Eb/N0 as shown in Figure 5.23. There are two typical curves shown in this figure; however, the actual curve for a specific link is determined by the digital modulation used to carry the data.
5.5.4 E
b/N
0Versus RFSNR
Eb/N0 is the energy per bit divided by the noise density (i.e., the noise per hertz of noise equivalent bandwidth). Eb = S/Rbwhere S is the received signal power (PR in Figure 5.1) and Rb is the bit rate (bits per second). Note that this refers to the data bits rather than all of the bits sent (i.e., not the synchronization and error correction bits).
Figure 5.23 The bit error rate in a demodulated digital signal is a function of Eb/No. where N is the noise in the receiver (i.e., kTB + Noise figure) and B is the noise equivalent bandwidth that can be approximated as equal to the symbol rate. Thus, Eb/N0 is related to RFSNR by the equation: Eb/N0 = SB/NRb In decibel form, this equation is: Eb/N0(dB) = RFSNR(dB) + [B/Rb](dB)
5.5.5 Maximum Range
The maximum range is the distance at which the received signal is equal to the sensitivity plus the specified operating margin. Note that there is a trade-off between margin and maximum range and that, for the moment, we are ignoring any weather related losses. To determine the maximum range, start with the received power formula in Section 5.5.1. Then expand the loss term (L) for the appropriate propagation model. In most data link cases, this will be the line-ofsight model, making the received power formula:PR = ERP − 32 − 20log(d) − 20log(F) + GR
where PR is the signal strength into the link receiver (in dBm), d is the link distance (in kilometers), F is the operating frequency (in megahertz), and GR is the receiving antenna gain (decibels).
losses. Then set PR equal to the sensitivity (S) in dBm + the required link margin (M) in decibels. The above equation is now: S + M = ERP − 32 − 20log(d) − 20log(F) + GR Solving for the range term: 20log(d) = ERP − 32 − 20log(F) + GR − S − M Then solve the 20 log(d) term for distance, which is the maximum range in kilometers: d = antilog{[20log(d)]/20} or 10{[20log(d)]/20}