Relation between C/N Ratio and S/N Ratio In our discussion in the past few lectures, we have coputed the C/N ratio of the received signals at different points of the satellite transission syste. The C/N generally is related to the quality of the received signal but it does not give an exact easure of how good the quality of the received signal has been preserved. What deterines this quality exactly is the Signal to Noise Ratio (S/N). The S/N ratio and C/N ratio are related to each other by a relationship that is deterined by the type of odulation that is used. While the carrier power (C) represents the total aount of power that is transitted, which includes the power carrying the inforation in addition to possibly other transitted power that ay carry no inforation at all, the signal power (S) represents only the power that carries the inforation. In the following discussion, we learn the relation between C/N and S/N for different types of odulations: S/N vs. C/N for DSBSC Modulation Double Side Band Suppressed Carrier (DSBSC) is characterized by transitting a frequency shifted version of the inforation signal obtained by ultiplying the inforation signal by a carrier signal. The transitted signal does not contain any unodulated coponent of the carrier, ion signal ultiplied by a carrier and no coponent of the unodulated carrier, hence the naing of suppressed carrier. Because the transitted signal is purely the inforation signal shifted in frequency to soe carrier frequency, the carrier power (C) is purely equal to the signal power (S). So, the C/N and S/N ratios are equal for that type of analog odulation: S C = DSBSC S/N vs. C/N for SSB Modulation Siilar to DSBSC, Single Side Band (Suppressed Carrier) (SSB) odulation transits one sideband of the DSBSC signal. Siilar to the DSBSC odulation, the transitted signal in SSB
odulation does not contain any unodulated coponent of the carrier (except a very sall pilot carrier that has power uch less than the inforation power and is used for extracting the phase of the carrier). Because of the lack of an unodulated carrier, the C/N and S/N ratios are equal for that type of analog odulation too: S C = SSB S/N vs. C/N for Full AM (DSB with Carrier) Modulation The case for the full AM odulation is different fro the DSBSC or SSB odulations. The reason is that a significantly large unodulated carrier is transitted in full AM odulation. In fact, the power of the unodulated carrier in the full AM is at least 2/3 the total power of the transitted signal (i.e., the inforation power is at ost 1/3 of the transitted signal power). So, S 1 C 3 Full AM S/N vs. C/N for Modulation Background of Modulation Let us have a very quick review of F odulation first. An signal has the for t g () t = A cos 2π f ct + 2 πk f ( α) dα where A is the aplitude of the signal, f c is the carrier frequency, k f is called the frequency sensitivity and has the units of Hz/Volt, and (t) the inforation signal in units of Volts. The frequency sensitivity deterines how any Hz the frequency of the signal changes as a result of increasing the input signal by 1 V. The instantaneous frequency f i (t) of the signal changes in the range
f k f () t f + k. c f p i c f p where p is aplitude (or axiu value of the inforation signal). This eans that the instantaneous frequency changes over a range of f = k f p on each side around the carrier frequency f c. The approxiate bandwidth of the of original signal g () t we use the Carson s rule, which states that the bandwidth of the signal is given by (we also use the fact that f = k f p ) BW = 2k + 2B Hz f p = 2 f + 2B Hz ( ) = 2 f + B Hz. where B is bandwidth of essage signal (t) in Hz. If we define the quantity β such that: f kf β = = B B p which is known as the odulation index of the signal, the bandwidth becoes f BW = 2 B + 1 Hz B = 2 B + 1 Hz ( β ) Relation between S/N and C/N Ratios for Modulation One iportant feature of is that it trades perforance (or quality of received signal in ters of S/N ratio) with bandwidth used for transission. That is, the higher the bandwidth of the transitted signal relative to the input signal, the higher the S/N ratio of the received signal. The relation between the S/N ratio and C/N ratio is given by
S C 3 BW f = N N 2 B B or in db for as where S C BW f db = db + 1.8 db + 10 log + 20 log 10 10 B B BW is the bandwidth of the signal obtained using Carson s rule f is the peak frequency deviation, which is equal to f = k f p 2 B is the bandwidth of the inforation signal. Therefore, the S/N ratio for can be written as S C = 3 + 1 ( β ) ( β ) 2 where β is the odulation index of the signal. It is clear fro the last relation that for large values of β, the S/N ratio becoes equal to 3 ties the C/N ratio ultiplied by the odulation index cubed, which indicates that the iproveent of the S/N ratio over the C/N ratio becoes huge. To show the perforance iproveent of, we can write the db relationship above as S C db = db + ( Iprovent ) db It is this iproveent that akes the use of attractive especially in applications where the C/N ratio of the received signal is relatively low and a reasonably higher S/N ratio is needed to deodulate the received signal properly. Often, the needed iproveent ay be around 20 db to 30 db. An iportant point that is worth entioning is that increasing the bandwidth of the signal iproves the S/N ratio over the C/N ratio but also reduces the C/N ratio of the received signal because a larger bandwidth of the transitted signal (the signal) results in a larger noise
power since the noise power is proportional to the transitted signal bandwidth and hence the added noise bandwidth. Pre-Ephasis and De-Ephasis One iportant feature of odulation that is not seen with other types of AM odulation is related to the noise that gets added the essage signal as it gets transitted. Although noise power that gets added to the transitted signal is alost flat in spectru (i.e., different frequencies of the transitted signal get equal aounts of noise power), the noise power that effectively gets added to the deodulated essage signal is not flat. This noise is low at low frequencies and increases as the frequency increases. This is illustrated in the following figure. In the above figure, the transitted signal is accopanied by theral noise at the receiver. Theral noise does not distinguish between different type of signal as they are transitted, and therefore, the power spectru of theral noise that gets added to the signal is alost flat. When deodulating the signal to get the original inforation signal, it is found that (because of the nature of the odulation), the power spectru density of theral noise in the deodulated signal is not flat but appears to be as shown below: The noise in the deodulated signal is found to be low at low frequencies and it increases as the frequency increases. Since low frequencies of the infoation signal are currepted by sall
aounts of noise while high frequencies are corrupted by large aounts of noise, the S/N ratio of the deodulated signal can be iproved by aplifying the frequency coponents of the inforation signal that will experience high aounts of noise power and reduce the power of the frequency coponents of the inforation signal that will experience low aounts of power. This process is known as PRE-EMPHASIS. Clearly, this process introduces soe controlled distortion to the inforation signal that would have to be reversed at the receiver side. At the receiver, the signal coponents that were aplified are attenuated and the signal coponents that were attenuated are aplified. This process is called DE-EMPHASIS. The process of pre-ephasis at the transitter and de-ephasis at the receiver can iprove the S/N ratio of the received signal by an aount of 5 to 10 db without the need to transit higher power or do any other odifications to the syste. Therefore, S C db = db + ( Iprovent ) db + ( Pre- & De-Ephasis Iprovent ) db