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S-72.245 Transmission Methods in Telecommunication Systems (4 cr) Digital Baseband Transmission
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  • S-72.245 Transmission Methods in Telecommunication Systems (4 cr)Digital Baseband Transmission

    *Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen

    Digital Baseband TransmissionWhy to apply digital transmission?Symbols and bitsBaseband transmissionBinary error probabilities in baseband transmissionPulse shapingminimizing ISI and making bandwidth adaptation - cos roll-off signalingmaximizing SNR at the instant of sampling - matched filteringoptimal terminal filtersDetermination of transmission bandwidth as a function of pulse shapeSpectral density of Pulse Amplitude Modulation (PAM)Equalization - removing residual ISI - eye diagram

    *Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen

    Why to Apply Digital Transmission?Digital communication withstands channel noise, interference and distortion better than analog system. For instance in PSTN inter-exchange STP*-links NEXT (Near-End Cross-Talk) produces several interference. For analog systems interference must be below 50 dB whereas in digital system 20 dB is enough. With this respect digital systems can utilize lower quality cabling than analog systemsRegenerative repeaters are efficient. Note that cleaning of analog-signals by repeaters does not work as wellDigital HW/SW implementation is straightforwardCircuits can be easily reconfigured and preprogrammed by DSP techniques (an application: software radio)Digital signals can be coded to yield very low error ratesDigital communication enables efficient exchanging of SNR to BW-> easy adaptation into different channelsThe cost of digital HW continues to halve every two or three years

    STP: Shielded twisted pair

    *Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen

    Symbols and Bits

    110011111010For M=2 (binary signalling):

    For non-Inter-Symbolic Interference (ISI), p(t) mustsatisfy:

    This means that at the instant of decision Generally: (a PAM* signal)*Pulse Amplitude Modulationunipolar, 2-level pulses

    *Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen

    DigitalTransmissionBaseband means that no carrier wave modulation is used for transmission

    Information:- analog:BW & dynamic range- digital:bit rateMaximization of information transferredTransmitted power;bandpass/baseband signal BWMessage protection & channel adaptation;convolution, block codingM-PSK/FSK/ASK..., depends on channel BW & characteristicswireline/wirelessconstant/variablelinear/nonlinearNoiseInterferenceChannelModulatorChannelEncoderSource encoderChannel decoderSource decoderDemodulatorInformation sinkInformation sourceMessageMessage estimateReceived signal (may contain errors)Transmitted signalInterleavingFights against burst errorsDeinterleavingIn baseband systemsthese blocks are missing

    *Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen

    Baseband Digital Transmission Link

    message reconstruction at yieldsmessageISIGaussian bandpass noiseUnipolar PAMoriginal message bitsdecision instancesreceived wave y(t)

    *Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen

    Baseband Unipolar Binary Error Probability

    The sample-and-hold circuit yields:Establish H0 and H1 hypothesis:andpN(y): Noise spectral densityAssume binary & unipolar x(t)

    *Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen

    Determining Decision Threshold

    Choose Ho (ak=0) if YVThe comparator implements decision rule:Average error error probability:Assume Gaussian noise:Transmitted 0but detected as 1

    *Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen

    Determining Error Rate

    that can be expressed by using the Q-function, defined byand thereforeand also

    *Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen

    Baseband Binary Error Rate in Terms of Pulse Shape and gfor unipolar, rectangular NRZ [0,A] bitssetting V=A/2 yields thenfor polar, rectangular NRZ [-A/2,A/2] bitsand henceNote that(lower limit with sinc-pulses (see later))

    *Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen

    Pulse Shaping and Band-limited Transmission In digital transmission signaling pulse shape is chosen to satisfy the following requirements:yields maximum SNR at the time instance of decision (matched filtering)accommodates signal to channel bandwidth: rapid decrease of pulse energy outside the main lobe in frequency domain alleviates filter designlowers cross-talk in multiplexed systems

    *Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen

    Signaling With Cosine Roll-off SignalsMaximum transmission rate can be obtained with sinc-pulses

    However, they are not time-limited. A more practical choice is the cosine roll-off signaling:for raised cos-pulses b=r/2

    *Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen

    Example

    By using and polar signaling, the following waveform is obtained:

    Note that the zero crossing are spaced by D at (this could be seen easily also in eye-diagram)The zero crossing are easy to detect for clock recovery. Note that unipolar baseband signaling involves performance penalty of 3 dB compared to polar signaling:

    *Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen

    Matched FilteringShould be maximizedPost filter noisePeak amplitude to be maximized

    *Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen

    Matched Filtering SNR and Transfer Function

    Schwartzs inequality applies whenSNR at the moment ofsamplingConsidering righthand side yields max SNR impulse response is:pulse energy

    *Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen

    *Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen

    *Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen

    Determining Transmission Bandwidth for an Arbitrary Baseband Signaling WaveformDetermine the relation between r and B when p(t)=sinc2 atFirst note from time domain that hence this waveform is suitable for signalingThere exists a Fourier transform pair

    From the spectra we note that and hence it must be that for baseband

    *Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen

    PAM Power Spectral Density (PSD)PSD for PAM can be determined by using a general expression

    For uncorrelated message bits and therefore on the other hand andAmplitude autocorrelationTotal powerDC power

    *Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen

    Example

    For unipolar binary RZ signal:

    Assume source bits are equally alike and independent, thus

    *Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen

    Equalization: Removing Residual ISI

    Consider a tapped delay line equalizer with

    Search for the tap gains cN such that the output equals zero at sample intervals D except at the decision instant when it should be unity. The output is (think for instance paths c-N, cN or c0) that is sampled at yielding

    *Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen

    Tapped Delay Line: Matrix RepresentationAt the instant of decision:

    That leads into (2N+1)x(2N+1) matrix where (2N+1) tap coefficients can be solved:

    *Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen

    Example of EqualizationRead the distorted pulse values into matrix from fig. (a) and the solution isZero forced valuesQuestion: what does these zeros help because they dontexist at the sampling instant?

    *Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen

    Monitoring Transmission Quality by Eye DiagramRequired minimum bandwidth is Nyqvists sampling theorem:Given an ideal LPF with thebandwidth B it is possible totransmit independent symbols at the rate: