Microwave Radio System Gain

* Gs is the difference between the nominal output power of a transmitter (Pt) and the minimum input power to a receiver (Cmin) necessary to achieve satisfactory performance; * Must be greater than or equal to the sum of all gains and losses incurred by a signal as it propagates from a transmitter to a receiver * In essence, system gain represents the net loss of a radio system, which is used to predict the reliability of a system for a given set of system parameters.

* Ironically, system gain is actually a loss.
* Losses are much higher than the gains.
* Therefore, the net system gain always equates to a negative dB value (i.e., a loss)
* Because system gain is defined as a net loss
* individual losses are represented with positive dB
* individual gains are represented with negative dB
* Mathematically, system gain in its simplest form is
* Gs = Pt – Cmin

where
Gs = system gain (dB)
Pt = transmitter output power (dBm or dBW)
Cmin = minimum receiver input power necessary to achieve a given reliability and quality objective

* Gs = Pt – Cmin > = losses – gains
* Pt – Cmin >= FM(dB) + Lp(dB) + Lf(dB) + Lb(dB)- At(dB)- Ar(dB) Gains:
* At= transmit antenna gain relative to an isotropic radiator (dB) * Ar = receive antenna gain relative to an isotropic radiator (dB) Losses
* FM = fade margin for a given reliability objective (dB) * Lp = free-space path loss in (dB)
* Lf= transmission line loss in (dB)
* Lf= total coupling or branching loss in (dB)
*
FADE MARGINS
(Link Margin)
Fading
* The reduction in receive signal level;
* Reduction in signal strength at the input to a receiver; * It applies to propagation variables in the physical radio path that affect changes in the path loss between transmit and receive antennas

What Is Fade Margin?
* Considers the non-ideal and less predictable characteristics of radiowave propagation, such as multipath propagation and terrain sensitivity; these characteristics cause temporary, abnormal atmospheric conditions * Under interference-free conditions, the fade margin is defined as the difference between the received signal level under ”normal” wave propagation conditions (fade-free time) and the receiver’s threshold level at a given bit-error level * The fade margin in the absence of frequency selective fading within the bandwidth of the receiver

Types of Fade Margin
* Flat Fade Margin
* Interference Fade Margin
* Dispersive Fade Margin
* Composite Fade Margin

Flat Fade Margin
* In flat fading, the coherence bandwidth of the channel is larger than the bandwidth of the signal. Therefore, all frequency components of the signal will experience the same magnitude of fading.

Interference Fade Margin
* Based on congestion of systems within the path using the same band of frequencies. Taken from graphs from a specific location and varies over time.

Dispersive Fade Margin
* Dependent on the type of equipment and modulation used. * These are gains in the equipment which are factored in because of technical improvements on the system and how they improve the information signal itself * It is defined to be the fade depth exceeded for the same number of seconds at a threshold error rate (the threshold error rate is defined to residue at the value of interest for which the dispersion signatures were created).

Dispersive Fade Margin
* DFM is calculated based on the W-curves using computation * DFM = 17.6 – log10 (Sw/158.4)

Composite Fade Margin
* This is the total of all fade margins

RECEIVER THRESHOLD (Receiver Sensitivity)
What is Receiver Threshold?
* Receiver threshold means the lowest signal your receiver will pick up and still operate. When nearing threshold, radio will sound noisy with static, TV will show snow and your cell phone will show only one bar or drop out * The receiver threshold is the minimum signal required for the demodulator to work at a specific error rate. Two thresholds are normally defined, one at a BER of 10^−6 and the other at a BER of 10^−3. * The reason for this is the original cutoff for audio applications was 10^−3, whereas it is generally considered data requires at least 10^−6 for an acceptable throughput rate. * Explaining the value 10^−3 ,or the loss of frame synchronization point (2×^10−5 for SDH/SONET), is the correct threshold to use from a performance objective perspective as it is related to the severely eroded second ratio (SESR) but the industry tends to use 10^−6 due to the data concerns. * The receiver threshold is dependent on the minimum S/N required at the receiver input, the noise figure of the receiver’s front-end, and the background thermal noise (Pn) * Pn = kTB

where
k – Boltzmann’s constant (1.38×10^−23)
T – temperature in Kelvin
B – bandwidth of the receiver.

* In general, the receiver threshold considered depends both on the required output performance at base- band, and on the type of interference * For linear modulation, such as AM and SSB, and any Gaussian interference, the relation between the SNR at the detector output and the (RF) C/I-ratio is linear * In non-linear modulation, such as phase modulation (PM) or frequency modulation (FM), the post-detection signal-to-noise ratio can be greatly enhanced as compared to baseband transmission or compared to linear modulation * Typically, for FM signals, the threshold is in the range of 3 to 10 dB. This threshold fundamentally limits the noise immunity of various types of non-linear modulation techniques * Typically, for FM signals, the threshold is in the range of 3 to 10 dB. This threshold fundamentally limits the noise immunity of various types of non-linear modulation techniques CARRIER-TO-NOISE

VS
SIGNAL-TO-NOISE
RATIO
Carrier-to-Noise Ratio
* In communications, the carrier-to-noise ratio, often written CNR or C/N, is a measure of the received carrier strength relative to the strength of the received noise. High C/N ratios provide better quality of reception, and generally higher communications accuracy and reliability, than low C/N ratios. * Carrier to noise ratio is the ratio of the carrier signal power to the noise power in some specified channel, usually expressed in decibels (dB). For the analog channels the noise is assumed flat and the result of thermal and amplifier noises.

Carrier-to-Noise Ratio
(mathematical definition)
* Engineers specify the C/N ratio in decibels (dB) between the power in the carrier of the desired signal and the total received noise power. If the incoming carrier strength in microwatts is Pc and the noise level, also in microwatts, is Pn, then the carrier-to-noise ratio, C/N, in decibels is given by the formula: * C/N = 10 log10(Pc/Pn)

* Engineers specify the C/N ratio in decibels (dB) between the power in the carrier of the desired signal and the total received noise power. If the incoming carrier strength in microwatts is Pc and the noise level, also in microwatts, is Pn, then the carrier-to-noise ratio, C/N, in decibels is given by the formula: C/N = 10 log10(Pc/Pn)

* The C/N ratio is measured in a manner similar to the way the signal-to noise ratio (S/N) is measured, and both specifications give an indication of the quality of a communications channel. However, the S/N ratio specification is more meaningful in practical situations. The C/N ratio is commonly used in satellite communications systems to point or align the receiving dish; the best dish alignment is indicated by the maximum C/N ratio. * Graphical representaion of C/N ratio

Signal-to-Noise Ratio
* In analog and digital communications, signal-to-noise ratio, often written S/N or SNR, is a measure of signal strength relative to background noise. The ratio is usually measured in decibels (dB). * Signal-to-noise ratio, or SNR, is a measurement that describes how much noise is in the output of a device, in relation to the signal level. * SNR is actually two level measurements, followed by a simple calculation. First, we measure the output level of the device under test with no input signal. Then we apply a signal to the device and take another level measurement. Then we divide.

Signal-to-Noise Ratio
(mathematical approach)
* If the incoming signal strength in microvolts is Vs, and the noise level, also in microvolts, is Vn, then the signal-to-noise ratio, S/N, in decibels is given by the formula: S/N = 20 log10(Vs/Vn)

CNR vs. SNR Recap
* CNR is a predetection measurement performed on RF signals. * Raw carrier power to raw noise power in the RF transport path only – say, a coaxial cable distribution network or a standalone device such as a converter or headend hetrodyne processor; Ideal for characterizing network impairments * SNR is a pre modulation or post-detection measurement performed on baseband signals. * Includes noise in original signal, transmitter or modulator, transport path, and reciever and demodulator * Ideal for characterizing end-to-end performance – the overall signal quality seen by the end user NOISE FACTOR AND

NOISE FIGURE
What is Noise Factor?
* Simply a ratio of input signal-to-noise ratio tooutput signal-to-noise ratio
* “Any unwanted input”
* Limits systems ability to process weak signals
* Sources:
* Random noise in resistors and transistors
* Mixer noise
* Undesired cross-coupling noise
* Power supply noise
* Dynamic range – capability of detecting weak signals in presence of large-amplitude signals

Noise Factor
* IEEE Standards: “The noise factor, at a specified input frequency, is defined as the ratio of (1) the total noise power per unit bandwidth available at the output port when noise temperature of the input termination is standard (290 K) to (2) that portion of (1) engendered at the input frequency by the input termination.” * “noisiness” of the signal measure = signal-to-noise ratio (frequency dependant) * The noise factor F of a system is defined as:

F = (SNRin)/(SNRout)
* where
* SNRin= input signal-to-noise power ratio
* SNRout = output signal-to-noise power ratio

What is Noise Figure?
* Indicates how much the signal-to-noise ratio deteriorates as a waveform propagates from the input of a circuit * It is a measure of the degradation of SNR due to the noise added * Implies that SNR gets worse as we process the signal

* Spot noise factor
* The answer is the bandwidth

Noise Figure
* The noise figure NF is defined as:
* Noise figure in temperature(k)