Channel Impairments BY Muhammad Uzair Rasheed 2009-CPE-03 UCE&T BZU MULTAN
Performance CriterionHow a “good” communication system can be differentiatedfrom a “sloppy” one?For analog communications ˆ – How close is m(t ) to m(t ) Fidelity! – SNR is typically used as a performance metricFor digital communications – Data rate and probability of error – No channel impairments, no error – With noise, error probability depends upon data rate, signal and noise powers, modulation scheme
NoiseNoise is unwanted signals generated by differentatmospheric conditions or other external and internalsources.These signals are added or combined with the transmittedsignal. This is denoted by: r(t) = s(t) + n(t).Noise signals are random and unpredictable in nature.There are various types of noise signals generated fromdifferent sources. One of the sources is thermal noisegenerated by the motion of the electrons movement duringtransmission. This is unavoidable noise. It is known asAdditive white Gaussian noise (AWGN).Noise has to be eliminated at the receiver end to recoverthe original signal.
Additive noise Internal noise generated by electronic components such as resistors and solid-state devices – thermal noise External noise: e.g. noise from another user in the same frequency band – co-channel/multi-user interference
Internal Noise• It is Due to Active and Passive Devices in receiver.• Random noise• Random noise power is proportional to the bandwidth over which it is measured.
Channels and their characteristicsWired and wireless channels. (freq. range,channel capacity and other factors).One problem in signal transmission is theadditive white Gaussian noise.It is the noise generated by the internalcomponents like resistors and capacitors.It is known as thermal noise.External noise.Amplitude and phase distortion and multi pathfading.
Modeling Transmission Channels Channel impulse response Channel transfer function Channel transfer function /linear/nonlinear + r (t ) = s(t ) ⊗ c(t ) + n(t ) s (t ) /linear/nonlinear c (t ) n(t ) (AWGN channel (usually transfer channel function is linear) and n(t) is Gaussian, white noise)Information is always transmitted in channels as radio path (wirelesscellular channel, microwave link, satellite link) or in wireline channels ascoaxial cable, fiber optic cable or wave guide. Note that informationstorage is also a transmission channelMost common channels we discuss are linear Additive, WhiteGaussian Noise (AWGN) channels or linear, fading channelsNote that the AWGN channel output is convolution of channel impulseresponse c(t) and channel input signal s(t) and has the noise term n(t)as additive component: r (t ) = s ⊗ c (t ) + n(t ) = ∫ s(t )c (τ − t )dt + n(t ) u 10 (u: where integrand exists)
Signal to noise ratio (SNR)It is defined as the ratio of signal power to noise power.During transmission, the power of noise decreases the power ofsignal.Lower SNR means poor performance.SNR decreases along the length of the channel.Solution for this is to pump more power to the signal so that at thereceiving end, the signal is received with better SNR.Increasing signal power reduces the effect of channel noise.Larger SNR allows transmission over a longer distance.Lower SNR means more error at the receiving end.Certain minimum SNR in necessary for transmission.SNR is usually given in decibel (dB): SNR(dB) = 10 log10(SNR).
Signal-to-Noise Ratio Signal Noise Signal + noiseHighSNR t t t No errors Signal Noise Signal + noiseLowSNR t t t Average signal power error SNR = Average noise power 12 SNR (dB) = 10 log10 SNR
SNRThe ratio of a signal power to the noise powercorrupting the signal.
Shannon Capacity Shannon Theory – It establishes that given a noisy channel with information capacity C and information transmitted at a rate R, then if R<C, there exists a coding technique which allows the probability of error at the receiver to be made arbitrarily small. This means that theoretically, it is possible to transmit information without error up to a limit, C. – The converse is also important. If R>C, the probability of error at the receiver increases without bound as the rate is increased. So no useful information can be transmitted beyond the channel capacity. The theorem does not address the rare situation in which rate and capacity are equal. Shannon Capacity C = B log 2 (1 + SNR ) bit / s EE 541/451 Fall 2006
Shannon Channel Capacity C = BT log2 (1 + SNR) bpsArbitrarily reliable communications is possible if the transmissionrate R < C.If R > C, then arbitrarily reliable communications is not possible.“Arbitrarily reliable” means the BER can be made arbitrarily smallthrough sufficiently complex coding.C can be used as a measure of how close a system design is to thebest achievable performance.Bandwidth BT & SNR determine C 15
Example Find the Shannon channel capacity for a telephone channel with BT = 3400 Hz and SNR = 10000C = 3400 log2 (1 + 10000) = 3400 log10 (10001)/log102 = 45200 bpsNote that SNR = 10000 corresponds to SNR (dB) = 10 log10(10000) = 40 dB 16
AttenuationAttenuation (in some contexts also called extinction) is thegradual loss in intensity of any kind of flux through amedium. For instance, sunlight is attenuated by darkglasses, and X-rays are attenuated by lead.Attenuation affects the propagation of waves and signals inelectrical circuits
Signal attenuationLarge scale – path loss, shadowingSmall scale – fadingAmplitude and phase distortionMultipath – Inter-symbol interference (ISI) (multipath is also the cause for fading)
FadingFading is the distortion that a carrier-modulated telecommunicationsignal experiences over certain propagation media. A fading channel isa communication channel that experiences fading. In wireless systems,fading is due to multipath propagation and is sometimes referred to asmultipath induced fading.
DistortionA distortion is the alteration of the original shape (or othercharacteristic) of an object, image, sound, waveform orother form of information or representation. Distortion isusually unwanted.
InterferenceInterference is anything which alters, modifies, or disruptsa signal as it travels along a channel between a source anda receiver.The term typically refers to the addition of unwantedsignals to a useful signal.Interference types•Constructive Interference.•Destructive Interference.Examples
Intersymbol Interference• Intersymbol interference (ISI) occurs when a pulse spreads out in such a way that it interferes with adjacent pulses at the sample instant.• Example: assume polar NRZ line code. The channel outputs are shown as spreaded (width Tb becomes 2Tb) pulses shown (Spreading due to band limited channel characteristics). Channel Input Channel Output Pulse width Tb Pulse width Tb Data 1 − Tb 0 Tb − Tb 0 Tb Data 0 − Tb 0 Tb − Tb 0 Tb Eeng 360 22
Reasons for ISI Multipath propagationOne of the causes of intersymbol interference is what is known as multipathpropagation in which a wireless signal from a transmitter reaches the receiver viamany different paths. The causes of this include reflection (for instance, the signalmay bounce off buildings), refraction (such as through the foliage of a tree) andatmospheric effects such as atmospheric ducting and ionospheric reflection. Since allof these paths are different lengths - plus some of these effects will also slow thesignal down - this results in the different versions of the signal arriving at differenttimes. This delay means that part or all of a given symbol will be spread into thesubsequent symbols, thereby interfering with the correct detection of those symbols.Additionally, the various paths often distort the amplitude and/or phase of the signalthereby causing further interference with the received signal.
Bandlimited channelsAnother cause of intersymbol interference is the transmission of a signalthrough a bandlimited channel, i.e., one where the frequency response iszero above a certain frequency (the cutoff frequency). Passing a signalthrough such a channel results in the removal of frequency componentsabove this cutoff frequency; in addition, the amplitude of the frequencycomponents below the cutoff frequency may also be attenuated by thechannel.This filtering of the transmitted signal affects the shape of the pulse thatarrives at the receiver. The effects of filtering a rectangular pulse; not onlychange the shape of the pulse within the first symbol period, but it is alsospread out over the subsequent symbol periods. When a message istransmitted through such a channel, the spread pulse of each individualsymbol will interfere with following symbols.