Mobile Radio Channel
5.6 Receiver Noise Factor (Noise Figure)
The impact of noise on the system needs to be calculated to determine the system per- formance. The major noise contributions in mobile wireless systems usually come from the receiver itself. In any case, the total noise associated with the system can be calcu- lated by assuming that the system consists of a two-port network, with a single input and a single output as shown in Figure 5.16. The network is characterized by a gainG, being the ratio of the signal power at the output to the signal power at its input, and by a noise factorF. The noise factor is the ratio between the output noise power of the element divided by gainG(i.e. referred to the input) and the input noise.
The noise in the input of the receiver may consist of several components, such as man-made industrial noise, spurious emission of electrical and electronic devices and thermal noise. Thermal noise is non-avoidable, it is always present. Thermal noise imposes the fundamental limit on radio communications; that is, thermal noise floor.
Figure 5.16 Noisy two-port network. Gain, G
Noise Factor, F
The power spectral density of thermal noise is given by
N0=kBT (5.22)
wherekB is Boltzmann’s constant,kB=1.38•10−23J∕K=1.38•10−23W•Hz−1•K−1,Tis an environmental temperature of the noise source in Kelvin, and the noise power (noise floor) is
N=N0B (5.23)
whereBis a receiver bandwidth (in units of Hz). It is common to write equation (5.23) using logarithmic units (power P expressed in units of dBm is 10 log10(P∕1mW)).
Assuming room temperature, the noise spectral power density has the value:
N0= −174 dBm (5.24)
This means that the noise power contained in a 1-Hz bandwidth is−174 dBm. The noise power contained in bandwidth B is
N= −174+10 log10B,dB (5.25)
Noise power densityN0can also be normalized to MHz bandwidth and then approx- imated to 114 dBm/MHz as an easier figure to work with. Any physically realizable system introduces additional noise on the top of the thermal noise floor. That additional noise component defines the noise figureFof network element of receiver system. The noise figure is defined as ratio of SNR at the input to SNR at the output of the receiver
F=
Sin∕Nin
Sout∕Nout
=
Sin∕kBT•B G•Sin∕Nout
= Nout∕G
kBT•B (5.26)
We assume that the network in Figure 5.16 is impedance matched to resistance. The noise figure is then
F= Nout
Nin = Nout
kBT•B (5.27)
whereNout is the output noise power of the network element referred to input; that is, the actual noise output power divided byG.Noise figureFdepends on the design and physical construction of the network. Its value in decibels is the noise figure of the network,
FdB=10 log10F (5.28)
The numerical value of the noise power [dBW] can be expressed approximately as
Nout=FdB−204+10 log10B (5.29)
and, respectively, in dBm:
Nout=FdB−174+10 log10B. (5.30)
The value of noise power given by equations (5.29) or (5.30) is known as areceiver noise floor, please note that it differs from thermal noise floor at noise figureFdB. For successful recovery of the received data the signal level must exceed the noise floor with sufficient margin, at least, for non-CDMA systems. This margin is given by the signal-to-noise ratio required for decoding/demodulation of the received data stream with performance
Mobile Radio Channel 47
G1, F1 G2, F2 Gk, Fk GN, FN
Figure 5.17 Cascade network.
levels specified in terms of Bit-Error Rate (BER) or other parameters such as SINAD, MOS and so on.
The receiver sensitivity level is determined by addition of required SNR on the top of receiver noise floor:
Rxsens=receiver noise floor+SNR=Nout+SNR (5.31) Receiver sensitivity level varies according to modulation scheme and desired level of performance, often quoted in terms of bit-error-rate (BER). If this value is, say, 9 dB above noise (or noise and distortion), then the minimum receiver sensitivity for a 270-kHz system with a 8 dB noise figure would be:
−114−5.68+8+9= −102.68 dBm
In general, a complete system can be characterized by a cascade of two-port elements, where theith element has gainGkand noise factorFk(Figure 5.17). Each element could consist of an individual module within a receiver, such as an amplifier or filter, or one of the elements within the channel such as the antenna, feeder or some source of external noise.
The gainGof the complete network is then simply given by
G=G1•G2· · ·GN, (5.32)
while the overall noise factor is given by the Friis formula:
F=F1+F2−1
G1 + F3−1
G1•G2 + · · · + FN−1
G1•G2· · ·GN (5.33) where noise figures and gains in (5.33) are in absolute units, not in dB. As observed from (5.33), the noise from the first element adds directly to the noise of the complete network, while subsequent contributions are divided by the gains of the earlier elements.
It is therefore important that the first element in the series has a low noise factor and a high gain, since this will dominate the noise in the whole system. As a result, receiver systems often have a separatelow noise amplifier(LNA) placed close to the antenna, often at the top of the mast and sometimes directly attached to the feed of a dish antenna in order to overcome the impact of feeder loss.