Quadrature Amplitude Modulation (QAM) ReceiverOutlineIntroductionBaseband QAMAutomatic Gain ControlCarrier DetectionSymbol Clock RecoveryChannel EqualizerSlide 9Adaptive FIR Channel EqualizerBaseband QAM DemodulationSlide 12EE445S Real-Time Digital Signal Processing Lab Fall 2014 Lecture 16 http://www.ece.utexas.edu/~bevans/courses/realtimeQuadrature Amplitude Modulation (QAM) ReceiverProf. Brian L. EvansDept. of Electrical and Computer EngineeringThe University of Texas at Austin16 - 2Outline•Introduction•Automatic gain control•Carrier detection•Symbol clock recovery•Channel equalization•QAM demodulation16 - 3Introduction•Channel impairmentsLinear and nonlinear distortion of transmitted signalAdditive noise (often assumed to be Gaussian)•Mismatch in transmitter/receiver analog front ends•Receiver subsystems to compensate for impairmentsFading Automatic gain control (AGC)Additive noise Matched filtersLinear distortion Channel equalizerCarrier mismatch Carrier recoverySymbol timing mismatch Symbol clock recovery16 - 4Baseband QAMReceive FilterA/DSymbolClockRecoveryLPFLPFCarrier DetectAGCXXr0(t)r1(t)r(t)r[m]ChannelEqualizerLLL samples/symbolm sample indexn symbol indexQAM Demodulationc(t)2 cos(c m)-2 sin(c m)Receiveri[n]gT[m] L+cos(c m)q[n]gT[m] Lsin(c m)Serial/parallelconverter1BitsMap to 2-D constellationJPulse shapers(FIR filters)Indexs[m]D/As(t)TransmitterfsCarrier recovery is not shown][ˆmi][ˆmq][ˆni][ˆnqi[m]q[m]Automatic Gain Control•Scales input voltage to A/D converterIncrease gain for low signal levelDecrease gain for high signal level•Consider A/D converter with 8-bit signed outputWhen c(t) is zero, A/D output is 0When c(t) is infinity, A/D output is -128 or 127Let f-128, f0 and f127 represent how frequently outputs -128, 0 and 127 occur over a window of previous samplesEach frequency value is between 0 and 1, inclusiveUpdate: c(t) = (1 + 2 f0 – f-128 – f127) c(t – )Initial values: f-128 = f0 = f127 = 1 / 256. Zero also works.16 - 5A/DAGCr1(t)r(t) r[m]c(t)16 - 6Carrier Detection•Detect energy of received signal (always running)c is a constant where 0 < c < 1 and r[m] is received signalLet x[m] = r2[m]. What is the transfer function?What values of c to use?•If receiver is not currently receiving a signalIf energy detector output is larger than a large threshold, assume receiving transmission•If receiver is currently receiving signal, then it detects when transmission has stoppedIf energy detector output is smaller than a smaller threshold, assume transmission has stopped][ )1(]1[ ][2mrcmpcmp 16 - 7Symbol Clock Recovery•Two single-pole bandpass filters in parallelOne tuned to upper Nyquist frequency u = c + 0.5 sym Other tuned to lower Nyquist frequency l = c – 0.5 symBandwidth is B/2 (100 Hz for 2400 baud modem)•A recovery methodMultiply upper bandpass filter output with conjugate of lower bandpass filter output and take the imaginary valueSample at symbol rate to estimate timing error Smooth timing error estimate to compute phase advancement ) sin(][symsymnv 1 symwhen][ ]1[ ][ nvnpnpLowpass IIR filterPole locations?See Reader handout MChannel Equalizer•Mitigates linear distortion in channel•When placed after A/D converterTime domain: shortens channel impulse responseFrequency domain: compensates channel distortion over entire discrete-time frequency band instead of transmission band•Ideal channelCascade of delay  and gain gImpulse response: impulse delayed by with amplitude gFrequency response: allpass and linear phase (no distortion)Undo effects by discarding  samples and scaling by 1/g16 - 8z- gChannel Equalizer•IIR equalizerIgnore noise nmSet error em to zeroH(z) W(z) = g z-W(z) = g z-/ H(z)Issues?•FIR equalizerAdapt equalizer coefficients when transmitter sends training sequence to reduce measure of error, e.g. square of em16 - 9Discrete-Time Baseband Systemz- h+w-xmymemrmnm+EqualizerChannelgIdeal Channel+Receiver generatesxm Training sequenceAdaptive FIR Channel Equalizer•Simplest case: w[m] = [m] + w1 [m-1]Two real-valued coefficients w/ first coefficient fixed at one•Derive update equation for w1 during trainingUsing least mean squares (LMS)Step size 0 <  < 1]1[ ][ ][]1[][21][][][]1[112][11111mymemwmwmemJwmJmwmwLMSmwwLMS]1[ ][][][ ][][][][1mywmymrmxgmsmsmrmez- h+w-xmymemrmnm+EqualizerChannelgIdeal Channel+Receiver generatesxm Training sequencesmBaseband QAM Demodulation•Recovers baseband in-phase/quadrature signals•Assumes perfect AGC, equalizer, symbol recovery•QAM modulation followed by lowpass filteringReceiver fmax = 2 fc + B and fs > 2 fmax•Lowpass filter has other rolesMatched filterAnti-aliasing filter•Matched filtersMaximize SNR at downsampler outputHence minimize symbol error at downsampler output16 - 11LPFLPFXX2 cos(c m)-2 sin(c m)x[m]][ˆmi][ˆmq16 - 12Baseband QAM Demodulation•QAM baseband signal•QAM demodulationModulate and lowpass filter to obtain baseband signals) sin( ][) cos( ][][ mmqmmimxcc)cos(][2][ˆmmxmic)cos()sin(][2)(cos][22mmmqtmiccc)2sin(][)2cos(][][ mmqmmimicc)sin(][2][ˆmmxmqc)(sin][2)sin()cos(][22mmqmmmiccc)2cos(][)2sin(][][ mmqmmimqcc)2cos1(21cos22sinsincos2 )2cos1(21sin2baseband high frequency component centered at 2 cbaseband high frequency component centered at 2