9.2
RADIO SYSTEMS
207
We round 1.995 to 2; thus
2
- 1 = T
e
/290,
T
e
= 290 K.
The thermal noise power level of a device operating at room temperature is
P
n
= -204 dBW/Hz + NF
dB
+ 10 log BW
Hz
,
(9.11)
where BW is the bandwidth of the device in Hz.
Example. A microwave receiver has a noise figure of 8 dB and its bandwidth is 10 MHz.
What is the thermal noise level (sometimes called the thermal noise threshold)?
P
n
= -204 dBW/Hz + 8 dB + 10 log(10 × 10
6
)
= -204 dBW/Hz + 8 dB + 70 dB
= -126 dBW.
Calculation of E
b
/N
0
in Digital Radio Systems. In Section 3.2.1 signal-to-noise ratio
(S/N) was introduced. S/N is widely used in analog transmission systems as one measure
of signal quality. In digital systems the basic measure of transmission quality is BER.
With digital radio links, we will introduce and employ the ratio
E
b
/N
0
as a measure of
signal quality. Given a certain modulation type, we can derive BER from an
E
b
/N
0
curve.
In words,
E
b
/N
0
means energy per bit per noise spectral density ratio.
N
0
is simply
the thermal noise in 1 Hz of bandwidth or
N
0
= -204 dBW/Hz + NF
dB
.
(9.12)
NF, as defined above, is the noise figure of the receiver in question. The noise figure tells
us the amount of thermal noise a device injects into a radio system.
Example. Suppose a receiver has a noise figure of 2.1 dB, what is its thermal noise level
in 1 Hz of bandwidth. In other words, what is
N
0
?
N
0
= -204 dBW + 2.1 dB
= -201.9 dBW/Hz.
E
b
is the signal energy per bit. We apply this to the receive signal level (RSL). The RSL
represents the total power (in dBm or dBW) entering the receiver front end, during, let's
say, 1-sec duration. (energy). We want the power carried by just 1 bit. For example, if
the RSL were 1 W and the signal were at 1000 bps, the energy per bit would be 1/1000
or 1 mW per bit. However, it will be more convenient here to use logarithms and decibel
values (which are logarithmic). Then we define
E
b
as
E
b
= RSL
dBm or dBW
- 10 log(bit rate)
(9.13)
Here is an example using typical values. The RSL into a certain receiver was
-89 dBW
and bit rate was 2.048 Mbps. What is the value of
E
b
?