Noise Immunity of Radio Receivers

Abstract

Free space as a medium for transmitting radio signals makes it possible to organize communications in any direction, both for an unlimited number of subscribers and with only a specific subscriber. This can be considered both its advantages and its disadvantages, depending on the structure and purpose of the network.

Thus, the organization of a large number of transmission directions increases the level of inter-channel and intra-channel interference at the point of reception of the radio signal, leading to nonlinear distortions and even blocking of the channel. When organizing a personal radio communication channel, it can also be accompanied by the occurrence of nonlinear distortions and inter-symbol interference caused by the phenomenon of signal multipath at the receiving point.

In this chapter, both the causes of interference and the ways to combat them are considered, based on the use of algorithmic and circuitry methods for increasing the noise immunity of signals in a radio channel: invariant reception, the construction of adaptive antenna systems based on space-time MIMO coding technology for fixed, mobile communication and radio access. As an example, we analyzed the influence of interference on the sensitivity and other parameters of the receiver.

Appendix: Interference Influence on the Main Receiver Indices

Application 4.1

Calculate the mean carrier power for the ideal QPSK system with the coherent demodulation and the linear amplification under conditions of Rayleigh fadings and a noise.

Analysis conditions:

• Error probability Р_е = 10⁻³

• Transmission rate f_b = 48 kbit/s

• Receiver noise factor NF = 7 dB

Only one transmitter signal acts in the receiver; the slow fading with the Rayleigh distribution acts in the channel. We can neglect the Doppler frequency shift and interferences from external sources; therefore, thermal noises (4.4) only act in the receiver input:

$$ N{F}_T= kT{B}_n NF,\left[\mathrm{dB}\right]. $$

For the room temperature t = 17 °C, which is equivalent to T = 290 °K and k = 1.38∙10⁻²³ J/Coul, the spectral density of thermal noises, which are created by the tuned antenna receiver input is kT =  − 174 dBm/Hz.

For the given error probability Р_е = 10⁻³, we obtain from the plot in Fig. 4.19: E_b/N₀ = 23 dB (the ratio of the energy per 1 bit to the power spectral density of thermal noises) from the ratio

$$ \frac{E_b}{N_0}=(SNR)\frac{B_n}{f_b}. $$

Fig. 4.19

Error probability graphs versus SNR for various types of manipulation

Taking into consideration that in the ideal QPSK system, the noise band B_n = f_b/2, we calculate the ratio of the carrier power to the thermal noise power in the receiver input:

$$ \frac{E_b}{N_0}=\left(\mathrm{SNR}\right)=\frac{24\cdotp {10}^3}{48\cdotp {10}^3}, $$

$$ \frac{E_b}{N_0}, dB=\left(\mathrm{SNR}\right), dB-3, dB,\kern0.62em \mathrm{then} $$

$$ \left(\mathrm{SNR}\right)=\frac{E_b}{N_0}+3=23+3=26\kern0.62em dB. $$

When there are no outside electromagnetic spurious impacts in the receiver input, the noise power in the frequency band of B_n= 24 kHz in the receiver input is:

$$ N{F}_T= kT{B}_n NF=-174,\frac{dBm}{Hz}+10\log \left(24\cdotp {10}^3\right)+7, dB=123.3\; dBm. $$

To satisfy the condition SNR = 26 dB, the carrier power in the receiver input is:

$$ C=N{F}_{T, dB m}+{\mathrm{SNR}}_{, dB}=-{123.2}_{, dB m}+{\mathrm{SNR}}_{, dB}=-97.2\; dBm. $$

The obtained value satisfies the requirement to the sensitivity of the subscriber mobile receiver of the IS-95 standard.

Application 4.2

Calculate the signal power in the input of the mobile station of the UMTS standard taking into account the inter-channel interference influence.

The examples given in the appendix can be divided into two types: when the initial information is from the standards of specific system, according to which the cascade structure is calculated, or when, based on the known characteristics of the device, the possibility of achieving the requirements of the standard is evaluated. The real power of signals, which act in the subscriber equipment input, is defined by many conditions: radio route characteristics, the network loading, the data transmission rate and subscriber displacements, and the input SNR . The speed of information transmission in the radio channel of a separate cell largely depends not only on its characteristics but also on reception conditions in neighboring cells, as well as the electromagnetic compatibility of UTRAN and GERAN radio access networks and a number of other factors that determine the bandwidth of the network as a whole. Due to the complexity of the mutual influence account of the mentioned reasons on the reception quality, we shall be limited by the impact of the following interferences in the consumer equipment input:

• Arising due to the noncoherent signal reception from the proper base station and caused by the multipath propagation

• Created by base stations of the adjacent cells

BS and AT transceivers of modern mobile communication systems, as follows from the open systems interconnection (OSI) of interaction at the physical level, at addition to the traffic channel, support the constant exchange of service information (synchronization channel, pilot-channel, broadcast channel, etc.) over dedicated or shared channels. At the formation of the group signal, they are multiplied by their channel-formation codes and are exposed by scrambling. Then, each of them is multiplied by the weight coefficient providing the maximum power of the transmitted control signals and pilot signals. Their resulting power should not be more than 15–20% of the maximal transmitter power. The smallest coefficients, which are inversely proportional to the speed of information transmission, are assigned to data transmitted through the traffic channel and control channels.

In the receiver input, the total interference power [114] should not exceed the ratio of the energy per 1 bit to the power spectral density of thermal noises E_b/N₀:

$$ \frac{E_b}{N_0}\le \frac{SP\cdotp {P}_j}{P_n+{P}_{\operatorname{int}. own}+{P}_{\operatorname{int}. adj}}, $$

(4.34)

where P_j is the signal power of the jth subscriber in the receiver input; Р_int.own is the interference in the receiver input created by the own base station due to the noncoherent reception; Р_int.adj. are interferences created by base stations of adjacent cells; and Р_n is the noise power in the receiver input.

Analysis conditions:

• The multipath property of radio wave propagation and also nonideal channel filtering, which are formed by the base station, leads to the appearance of the noncoherent noise in the input of consumer equipment. We can consider that the level of such interferences is 0.1–0.125 of the power of the useful receiving signal.

• The power of interferences produced by signals from adjacent base stations should not be more than 0.5 Р_s of the useful signal power.

• The ratio of the energy per 1 bit to the power spectral density of thermal noises in the receiver input should be E_b/N₀ = 7.4 dB [114].

• The receiver noise factor is NF = 5 dB.

• The radio signal transmission rate is R_bit = 12.2 kbit/s.

• The rate of the radio signal transfer is R_chip = 3.84 Mchip/s.

• The spread factor (SF ) is SF = R_chip/R_bit = 315.

The reliable reception of the synchronization signal is provided under the condition Р_s = 1.5 Р_n, where Р_n is the total noise power in the receiver input of the mobile station:

$$ {\mathrm{P}}_n=k{\mathrm{T}}_0{B}_n NF. $$

The power spectral density of thermal noises, which is created by the matched antenna for the room temperature Т = 290 К^о, is:

$$ k{T}_0=1.38\cdotp {10}^{-23}\cdotp 290=4\cdotp {10}^{-21}1\;\left[W\right]=>-174\frac{dBm}{Hz}. $$

The noise power in the consumer receiver input is:

$$ P=k{T}_0+10\lg {B}_n+ NF=-174{,}_{dB m/ Hz}+65.84{,}_{dB}+5{,}_{dB}=-103.2\; dBm. $$

The interference power of adjacent channels is:

$$ {P}_{\operatorname{int}. own}+{P}_{\operatorname{int}. adj.}=0.125\;{P}_{\mathrm{s}}+{P}_{\mathrm{s}}=0.125\;{P}_{\mathrm{n}}\cdotp 1.5+1.5\cdotp {P}_{\mathrm{n}}. $$

The inequality (4.34) takes a form:

$$ \frac{E_b}{N_0}=\frac{SF\cdotp {P}_j}{P_n+0.125\cdotp 1.5\cdotp {P}_n+1.5{P}_n}=\frac{SF\cdotp {P}_j}{2.7{P}_n}. $$

(4.35)

Then P_j is the signal power of j-th subscriber in the receiver input:

$$ {P}_j=-10\lg SF+10\lg \left(\frac{E_b}{N_0}\right)+10\lg \left(2,7{P}_n\right)=-10\lg 315+5-10\lg 2.7=-118.8\; dBm, $$

which satisfies to the standard requirements.

Application 4.3

Calculation of the power at the input of the receiver of a mobile station of the IS-95 standard.

Calculate the average power of the carrier (С) for the ideal QPSK system with coherent demodulation and the linear amplification under conditions of the Rayleigh fading and a noise.

Condition of an analysis:

• The error probability Р_еr = 10⁻³

• The transmission rate f_b = 48 kbit/s

• The noise factor of the receiver NF = 7 dB

Only one transmitter acts in the receiver input; the slow fading with Rayleigh distribution acts in the channel. We can neglect the Doppler frequency shift. We believe that in the UHF and microwave ranges, we can neglect interference from external sources due to large losses of the signal in free space in these frequency ranges and the absence of the effect of bending the Earth’s surface, as well as the difficulty of predicting them, so we will take into account only thermal noise at the receiver input.

For room temperature t = 17 °C, which is equivalent to T = 290 K and k = 1.38∙10⁻²³ J/Coul, the spectral density of thermal noises produced by the tuned antenna is kT = −174 dBm/Hz.

For specified error probability Р_еr = 10⁻³, we obtain E_b/N₀ = 23 dB (the ratio of the energy per 1 bit to the power spectral density of thermal noise from the plot in Fig. 4.19). Using the expression

$$ \frac{E_b}{N_0}=\frac{C}{N}\frac{B_n}{f_b}. $$

Taking into account that in the ideal QPSK system, the noise band B_n = f_b/2, we calculate the ratio of the carrier power to the thermal noise power in the receiver input:

$$ \frac{E_b}{N_0}=\frac{C}{N}\frac{24\cdotp {10}^3}{48\cdotp {10}^3}=\frac{C}{N}\frac{1}{2}, $$

$$ \frac{E_b}{N_0}, dB=\frac{C}{N}, dB-3, dB,\kern0.62em \mathrm{then} $$

$$ \frac{\mathtt{\mathrm{C}}}{N}=\frac{E_b}{N_0}+3=23+3=26\kern0.62em \mathrm{dB}. $$

When there are no external spurious electromagnetic influences in the receiver input, the thermal noise power, which is produced by an antenna in the band B_n = 24 kHz in the receiver input, is:

$$ {N}_{\mathtt{\mathrm{T}}}=k\mathtt{\mathrm{T}}{B}_n NF=-174, dB m/ Hz+10\log \left(24\cdotp {10}^3\right), dB+7, dB=123,2\kern0.62em dBm. $$

To fulfill the condition Р_s/Р_n = C/N = 26 dB, the carrier power in the receiver input is:

$$ \mathtt{\mathrm{C}}={N}_T{,}_{dB m}+C/N{,}_{dB}=-123.2{,}_{dB m}+26{,}_{dB}=-97.2\; dBm. $$

The obtained value satisfies the requirement to the sensitivity of the mobile receiver of the IS-95 standard systems.

Application 4.4

Calculation of the power at the input of the receiver of a UE of the standard UMTS with account of inter-channel interference influence.

Conditions of an analysis:

• The ratio of an energy per 1 bit to the power spectral density of thermal noises in the receiver input is E_b/N₀ = 7.4 dB.

• The receiver noise factor is NF = 5 dB.

• The speech transmission rate is R_bit = 12.2 kbit/s.

• The radio signal transmission rate is R_chip = 3.84 Mchip/s.

• The spread factor (SF ) is SF = R_chip/R_bit = 315.

Despite the fact that a system with CDMA technology at input of the UE receiver, in addition to the useful signal, there are many signals intended for the subscribers of cell, we will limit ourselves to the action at the input of only the useful signal. The real signal power acting in the UE input is determined by a series of conditions: characteristics of the radio routes, the network load, the data transmission rate and movement of a subscriber, and the SNR in the input.

The bandwidth in each cell is limited not only by the width of the allocated radio frequency band, it is also necessary to take into account the influence of reception conditions in other cells, electromagnetic compatibility of radio access networks UTRAN and GERAN, and other factors.

Due to the complexity of the mutual influence account of the mentioned reasons upon the reception quality, we are limited by the interference impact in the UE input:

• Arising due to the noncoherent reception of signals by the own base station caused by multipath properties at propagation

• Produced by base stations of the adjacent cells

Signals emitted by the base station, besides traffic channels, include also the control channels (the pilot channel, P-CCPCH, etc.). In the process of forming a group signal, it is subjected to channel coding and scrambling, which increase its noise immunity. Then, each of them is multiplied by the weight coefficient, which provides the maximal power to control signals and pilot signals. Their resulting power must be not more than 15–20% of the maximal transmitter power. The minimal coefficients, which are inversely proportional to the information transmission rate, are conferred to the traffic signals and control signals.

The multipath propagation of radio waves as well as the nonideal filtering of channels, which are formed by the base station, leads to the appearance of the noncoherent noise in the UE input. We assume that the level of such interferences is 0.1–0.125 of the power of the useful receiving signal.

The interference power, which is produced by signals of adjacent base stations, should not be more than 0.5 Р_s of the useful signal power.

The total power of interference acting at the receiver input must not exceed (E_b/N₀) the ratio energy per 1 bit to the spectral power density of thermal noise determined by the standards:

$$ \frac{E_b}{N_0}\le \frac{SP\cdotp {P}_j}{P_n+{P}_{inter\kern0.6em own}+{P}_{inter, ad}}, $$

(4.36)

where P_j is the signal power of the jth subscriber in the receiver input; Р_inter,own are interferences in the receiver input, which are created by the own base station owing to the noncoherent reception; Р_inter,adj are interferences created by base stations of the adjacent cells; and Р_n is the noise power in the receiver input.

The reliable reception of the synchronization signal is provided under the condition P_s = 1.5 P_n, where Р_n is the total noise power in the receiver input of the mobile station:

$$ {\mathrm{P}}_n=k{\mathrm{T}}_0{B}_n NF. $$

The power spectral density of thermal noises, which are produced by the matched antenna for the room temperature Т = 290 К, is:

$$ k{T}_0=1.38\cdotp {10}^{-23}\cdotp 290=4\cdotp {10}^{-21}{,}_W\Rightarrow -174\; dBm/ Hz. $$

The thermal noise power created by an antenna in the receiver input is:

$$ {P}_n=k{T}_0+101\mathrm{g}{B}_n+ NF=-174{,}_{dB m/ Hz}+65.84{,}_{dB}+5{,}_{dB}=-103.2 dBm. $$

The interference power of adjacent channels is:

$$ {\mathtt{\mathrm{P}}}_{inter. own}+{\mathtt{\mathrm{P}}}_{inter, ad.}={\mathtt{\mathrm{P}}}_s+0.125\;{\mathtt{\mathrm{P}}}_s=1.5\;{\mathtt{\mathrm{P}}}_n+0.125\;{\mathtt{\mathrm{P}}}_n\;1.5. $$

Replacing the inequality (4.36)with the equation (a sticker condition), we obtain (4.37):

$$ \frac{E_b}{N_0}=\frac{SF\cdotp {P}_j}{P_n+0.125\cdotp 1.5\cdotp {P}_n+1.5\cdotp {P}_n}=\frac{SF\cdotp {P}_j}{2.7\;{P}_n}. $$

(4.37)

The inequality (4.37) resolved with respect to P_j permits to calculate the power of the jth subscriber in the receiver input:

$$ {P}_j=-10\log SF+10\log \left(\frac{E_b}{N_0}\right)+10\log \left(2.7{P}_n\right)=-10\lg 315+5-10\lg 2.7=-118.8\;\mathrm{dBm}, $$

which satisfied to standard requirements UMTS [114].