4/15/10 1 MS in Telecommunications TCOM 500: Modern Telecommunications Dr. Bernd-Peter Paris George Mason University Spring 2009 MS in Telecommunications DISTORTION Paris 2 TCOM 500: Modern Telecommunications4/15/10 2 MS in Telecommunications Distortion • Distortion causes the shape of the transmitted signal to be altered during transmission. • Distortion can have different causes; • Non-linear distortion • Example: clipping of large amplitudes. • Amplitude distortion • Different parts of the spectrum of a signal experience different attenuation (see path loss tables for cables). • Delay distortion • Different parts of the spectrum of a signal experience different delays. • Multipath propagation • Multiple “echoes” of the signal are received (see multi-mode fibers) • Can also be described as amplitude and delay distortion. Paris 3 TCOM 500: Modern Telecommunications MS in Telecommunications Illustration: Wireless Multipath 450 500 550 600 650 700 750 800 850 900 9507508008509009501000105011001150120012501300x (m)y (m)ReceiverTransmitterParis 4 TCOM 500: Modern Telecommunications Propagation between transmitter and receiver will occur along many different paths.4/15/10 3 MS in Telecommunications Multipath: Impulse Response 0.8 1 1.2 1.4 1.6 1.8 201234x 10−5Delay (µs)Attenuation0.8 1 1.2 1.4 1.6 1.8 2−4−2024Delay (µs)Phase Shift/!Paris 5 TCOM 500: Modern Telecommunications Different propagation paths are characterized by different delays, attenuations, and phase shifts. Delay Spread ~ 2µs MS in Telecommunications Multipath: Frequency Response −5 −4 −3 −2 −1 0 1 2 3 4 5−98−96−94−92−90−88−86−84−82−80−78Frequency (MHz)|Frequency Response| (dB)Paris 6 TCOM 500: Modern Telecommunications • The attenuation of the channel around the carrier frequency (1GHz) varies significantly with frequency. • Different part of the signals spectrum will be attenuated differently.4/15/10 4 MS in Telecommunications Wideband PAM Signal Transmission 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5−2−1.5−1−0.500.511.52Time (µs)Amplitude TransmittedReal(Received)Imag(Received)Paris 7 TCOM 500: Modern Telecommunications Real = In-phase Imag = Quadrature • Transmitted signal has approximate bandwidth 6MHz. • symbol period 0.3µs. • Over this bandwidth, channel varies significantly. • Received signal is clearly distorted. • Need an equalizer in the receiver. MS in Telecommunications Wideband PAM Signal −5 −4 −3 −2 −1 0 1 2 3 4−100−95−90−85−80−75Frequency (MHz)|Frequency Response| (dB)Paris 8 TCOM 500: Modern Telecommunications Significant variation in attenuation over the band occupied by the signal.4/15/10 5 MS in Telecommunications Narrowband PAM Signal 0 50 100 150 200 250 300−2−1.5−1−0.500.511.52Time (µs)Amplitude TransmittedReal(Received)Imag(Received)−5 −4 −3 −2 −1 0 1 2 3 4−100−95−90−85−80−75Frequency (MHz)|Frequency Response| (dB)Paris 9 TCOM 500: Modern Telecommunications • Signal bandwidth approximately 60KHz. • No distortion MS in Telecommunications Summary • Distortion is a serious problem in high-rate communications systems. • Distortion occurs if the symbol period is as long or greater than the delay spread of the channel. • Equivalently, distortion occurs if the frequency response of the channel varies significantly over the bandwidth of the signal. • Distortion causes consecutive symbols to overlap at the receiver: intersymbol interference (ISI). • To overcome ISI, receiver must include an equalizer. Paris 10 TCOM 500: Modern Telecommunications4/15/10 6 MS in Telecommunications RECEIVERS FOR DIGITAL COMMUNICATIONS Paris 11 TCOM 500: Modern Telecommunications MS in Telecommunications Outline • Structure of receivers for digital communications: • Theory and practice. • Performance: probability of error. • Influence of imperfections modeled by channel: • Noise • Phase and frequency error • Multipath (distortion). Paris 12 TCOM 500: Modern Telecommunications4/15/10 7 MS in Telecommunications Context • Purpose of a digital communication system: • Replicate digital information available at the transmitter’s location at the receiver’s location. • Generally this implies connecting spatially separate locations. • Same principle applies for communicating over time – storage of information. • Receiver is responsible for reconstructing the transmitted signal from signal corrupted by channel. • Signal is noisy and possibly distorted. • Metric: probability of error. Paris 13 TCOM 500: Modern Telecommunications Transmitter Channel Receiver bits signal signal bits MS in Telecommunications OPTIMUM RECEIVER PRINCIPLES Paris 14 TCOM 500: Modern Telecommunications4/15/10 8 MS in Telecommunications Optimum Receiver • Receiver’s objective: reconstruct transmitted symbols. • For channels that add white Gaussian noise to the received signal, the best possible receivers are well known. • Best possible means: producing the fewest number of receivers. • These receivers consist of: • Analog frontend, called the matched filter, • Discrete-time decision circuit that selects the most likely transmitted symbol. Paris 15 TCOM 500: Modern Telecommunications s1(t) s2(t) Decision received signal reconstructed symbol matched filters samplers MS in Telecommunications Matched Filter • The optimum receiver uses one matched filter for each signal in the set of possibly transmitted signals. • The matched filter uses a replica of the signal that may have been transmitted like a template. • If the template signal appears in the received signal, then a strong response results. • The decision circuit will then look for the matched filter that produces the strongest response. Paris 16 TCOM 500: Modern Telecommunications s1(t) s2(t) Decision received signal reconstructed symbol matched filters samplers4/15/10 9 MS in Telecommunications Matched Filter Illustration 0 0.5 1 1.5 2 2.5 3ï1012Time/TAmplitude0 0.5 1 1.5 2 2.5 3ï0.500.51Time/TAmplitudeï3 ï2 ï1 0 1 2 3ï0.500.51Time/TAmplitudeParis 17 TCOM 500: Modern Telecommunications Received Signal Template Matched Filter Output: Slide template over received signal and integrate. sample here MS in Telecommunications Example: BPSK