RECEIVER SENSITIVITY / NOISE

1 SENSITIVITY / NOISERECEIVER SENSITIVITYS ensitivity in a RECEIVER is normally taken as the minimum input signal (S) required to produce a specified outputminsignal having a specified signal-to- NOISE (S/N) ratio and is defined as the minimum signal-to- NOISE ratio times the meannoise power, see equation [1]. For a signal impinging on the antenna (system level) SENSITIVITY is known as minimumoperational SENSITIVITY (MOS), see equation [2]. Since MOS includes antenna gain, it may be expressed in dBLi (dBreferenced to a linear isotropic antenna). When specifying the SENSITIVITY of receivers intended to intercept and process pulsesignals, the minimum pulse width at which the specified SENSITIVITY applies must also be stated.

2 See the discussion of post-detection bandwidth (B) in Section 5-2 for significance of minimum pulsewidth in the RECEIVER S = (S/N)kTB(NF) RECEIVER SENSITIVITY ("black box" performance parameter)[1]min minoor MOS = (S/N)kTB(NF)/G system SENSITIVITY the RECEIVER is connected to an antenna [2]mino(transmission line loss included with antenna gain)where:S/N=Minimum signal-to- NOISE ratio needed to process (vice just detect) a signalminNF= NOISE figure/factork=Boltzmann's Constant = x 10 Joule/EK-23 T=Absolute temperature of the RECEIVER input (EKelvin) = 290 EKoB= RECEIVER Bandwidth (Hz)G=Antenna/system gainWe have a lower MOS if temperature, bandwidth, NF, or S/N decreases, or if antenna gain increases.

3 For radar,minmissile, and EW receivers, SENSITIVITY is usually stated in dBm. For communications and commercial broadcasting receivers, SENSITIVITY is usually stated in micro-volts or dB v. See Section is no standard definition of SENSITIVITY level. The term minimum operational SENSITIVITY (MOS) can be usedin place of S at the system level where aircraft installation characteristics are included. The "black box" term minimummindetectable signal (MDS) is often used for S but can cause confusion because a RECEIVER may be able to detect a signal,minbut not properly process it. MDS can also be confused with minimum discernable signal, which is frequently used whena human operator is used to interpret the reception results.

4 A human interpretation is also required with minimum visiblesignal (MVS) and tangential SENSITIVITY (discussed later). To avoid confusion, the terms S for "black box" minimumminsensitivity and MOS for system minimum SENSITIVITY are used in this section. All receivers are designed for a certainsensitivity level based on requirements. One would not design a RECEIVER with more SENSITIVITY than required because itlimits the RECEIVER bandwidth and will require the RECEIVER to process signals it is not interested in. In general, whileprocessing signals, the higher the power level at which the SENSITIVITY is set, the fewer the number of false alarms which willbe processed.

5 Simultaneously, the probability of detection of a "good" (low- NOISE ) signal will be can be defined in two opposite ways, so discussions can frequently be confusing. It can be the ratio ofresponse to input or input to response. In using the first method (most common in RECEIVER discussions and used herein),it will be a negative number (in dBm), with the more negative being "better" SENSITIVITY , -60 dBm is "better" than -50dBm SENSITIVITY . If the second method is used, the result will be a positive number, with higher being "better." Thereforethe terms low SENSITIVITY or high SENSITIVITY can be very confusing.

6 The terms S and MOS avoid (S/N) RATIOThe Signal-to- NOISE Ratio (S/N) ( SNR) in a RECEIVER is the signal power in the RECEIVER divided by the meannoise power of the RECEIVER . All receivers require the signal to exceed the NOISE by some amount. Usually if the signalpower is less than or just equals the NOISE power it is not detectable. For a signal to be detected, the signal energy plus theB Bandwidth (Hz)THRESHOLDAVERAGENOISE POWERABCk Boltzman's Constant x 10 Joules / EK-23To Temperature (EK) 290 EKPN -114 dBm for a 1 MHz bandwidth! PN k To B!Distribution isGaussianTIMES/NPN -174 dBm for a 1 Hz bandwidthDETECTIONF alse alarm due to 1.

7 RECEIVER NOISE Power at Room Temperaturenoise energy must exceed some threshold value. Therefore, just because N is in the denominator doesn't mean it can beincreased to lower the MOS. S/N is a required minimum ratio, if N is increased, then S must also be increased to maintainthat threshold. The threshold value is chosen high enough above the mean NOISE level so that the probability of randomnoise peaks exceeding the threshold, and causing false alarms, is acceptably 1 depicts the concept of required S/N. It can be seen that the signal at time A exceeds the S/N ratio andindicates a false alarm or target.

8 The signal at time B is just at the threshold, and the signal at time C is clearly below the sample, if the temperature is taken as room temperature (T = 290EK), the NOISE power input is -114 dBm for a oneoMHz bandwidth. Normally S/N may be set higher than S/N shown in Figure 1 to meet false alarm acceptable minimum Signal-to- NOISE ratio (or think of it as Signal above NOISE ) for a RECEIVER depends on theintended use of the RECEIVER . For instance, a RECEIVER that had to detect a single radar pulse would probably need a higherminimum S/N than a RECEIVER that could integrate a large number of radar pulses (increasing the total signal energy) fordetection with the same probability of false alarms.

9 Receivers with human operators using a video display may functionsatisfactorily with low minimum S/N because a skilled operator can be very proficient at picking signals out of a noisebackground. As shown in Table 1, the setting of an acceptable minimum S/N is highly dependant on the requiredcharacteristics of the RECEIVER and of the signal. Table 1. Typical Minimum S/N RequiredTOA, and Frequency MeasurementsInterferometerComparisonSkil led OperatorAuto-DetectionAuto-detection with Amplitude,AOA PhaseAOA Amplitude3 to 8 dB10 to 14 dB14 to 18 dB14 to 18 dB16 to 24 dBA complete discussion of the subject would require a lengthy dissertation of the probability and statistics of signaldetection, which is beyond the scope of this handbook, however a simplified introduction follows.

10 Let's assume that wehave a RECEIVER that we want a certain probability of detecting a single pulse with a specified false alarm probability. Wecan use Figure 2 to determine the required signal-to- NOISE ratio. S/N EXAMPLEIf we are given that the desired probability of detecting a single pulse (P) is 98%, and we want the false alarm rated(P) to be no more than 10, then we can see that S/N must be 12 dB (see Figure 2). (S/N) Ratio - ( dB )ExampleS(orPR)PtGtGr82(4B)2R2 PtGtGr82(4B)2(S/N)minkToB(NF)orPtGtGrc2( 4Bf)2(S/N)minkToB(NF)orPtGtAe4B(S/N)mink ToB(NF) 2. Nomograph of Signal-to- NOISE (S/N) Ratio as a Function of Probability of Detection (P) and dProbability of False Alarm Rate (P)nMAXIMUM DETECTION RANGE (ONE-WAY)From Section 4-3, the one way signal strength from a transmitter to a RECEIVER is: For calculations involving RECEIVER SENSITIVITY the "S" can be replaced by S.