Signal Fading

Destructive interference due to multiple reflective paths of varying distances. This is a rare and transient phenomena, but it happens.

Frequency Diversity - Use two signals at slightly different wavelengths. The probability that destructive interference will occur simultaneously at both wavelengths is extremely low.

Tx

Rx

Space Diversity: Use multiple antennas separated by at least six wavelengths. The probability that destructive interference will occur simultaneously for both paths is extremely low.

Additional Losses in Multi-Link Systems

Tx1

Rx

TxN. . . P1

PN

GT GRLS

LF

EIRP = P1 + GT - LbT - LfT

LfT(Feeder)

LbT (Branching)

Rx1

RxN

.

.

.LfR(Feeder)

LbR

(Branching)

Pr = EIRP – LS + GR - LF - LbR - LfR

Since Fading is a transient phenomena, we usually provide a Fade Margin to account for LF in a statistical sense, e.g., 95%.

System GainGSYS,i(dB) = PT,i(dBw) – PR,i(dBw)

= PT,i - ( PT,i – LbT – LfT + GT – LS – FM + GR – LfR – LbR)

= LbT + LfT - GT + LS + FM - GR + LfR + LbR

System ThresholdSystem threshold is the input power required to achieve a specified S/N or C/N or EB/N0

Effective noise power at the Receiver input is N0B or kTRB, where TR is the Receiver Noise Temperature = 290(NRR-1). For a specified S/NREQ,

PR > S/NREQ(kTRB) (not dB)

Using the convention we have adopted for use of the terms “Gain” and “Loss”, it would be more appropriate to call the above “Transmission Loss”.

G/TFor Digital systems, we are interested in achieving a specified EB/N0 , therefore

PR > S/NREQ(kTRB) = {(EB/N0)(fB/B)}(kTRB) = (EB/N0)fBkTR

Neglecting Branching, feeder, and fading losses, the received power is

PR = (EIRP/LS)(GR) > (EB/N0)fBkTR

Rewriting,

(EIRP/LS)(GR /TR)/(fBk) > (EB/N0)REQ

Note that the term (GR /TR) captures the two important parameters of the receiving system in one number. This number, G/T, is usually published to characterize receiving systems rather than giving the two values separately. The above relation , expressed in dB is therefore:

(EB/N0)REQ < EB/N0 = EIRP(dBw) - LS (dB) + G/T(dB) – k(dB) - fB (dB)

Note that eq. 17-26 in the text is totally wrong.