# Receiver Designs for the Radio Channel

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1 Receiver Designs for the Radio Channel COS 463: Wireless Networks Lecture 15 Kyle Jamieson [Parts adapted from C. Sodini, W. Ozan, J. Tan]

2 Today 1. Delay Spread and Frequency-Selective Fading 2. Time-Domain Equalization 3. Orthogonal Frequency Division Multiplexing 2

3 Last Time: Power Delay Profile, Delay Spread, Excess Delay a 2,d 2,τ 2 Transmitter a 1,d 1,τ 1 Receiver a 1 Power Delay Profile P(t) a 1 τ 1 a 2 τ 2 RMS delay spread t 3

4 Last Time: Multipath causes Frequency Selectivity Interference between reflected and line-of-sight radio waves results in frequency dependent fading 35 Received Power (dbm) Frequency (khz)

5 Problem: Inter-symbol interference (ISI) Transmitted signal Received signal with ISI 5

6 Problem: Inter-symbol interference (ISI) Transmitted signal Received signal with ISI ISI at one symbol depends on the value of other symbols 6

7 Today 1. Delay Spread and Frequency-Selective Fading 2. Time-Domain Equalization 3. Orthogonal Frequency Division Multiplexing 7

8 Wideband System Design Transmitter Data d k p(t) Transmit filter h(t) Channel y t Receiver y[n] p*( t) Matched filter h eq (t) Equalizer!" # \$ % = ' ) % ' ( %) Composite channel f (made up of pulse shape, radio channel, and matched filter) 8

9 Zero-Forcing Equalizer Receiver: Receiver front-end noise: n k y t y[n] + p*( t) h eq (t)!" # Matched filter \$ %& ' = 1 *(') Equalizer 9

10 Physical Layer Preamble Preamble Packet body Sequence of symbols known to both transmitter & receiver 10

11 Minimal Mean-Squared Error Equalizer Goal: h eq that minimizes mean-squared error (MSE) between received and transmitted symbols from preamble )!"# = % + & -+. / &'( Assumes packet has a preamble, channel stays same over a packet time 11

12 Decision-feedback Equalizer Idea: Subtract the interference caused by already detected data (symbols) Noise: n k y t y[n] + + p*(-t) w (t) Matched filter Forward filter - + Decision device!" # This part shapes the signal to work well with the decision feedback. This part removes ISI on future symbols from the currently detected symbols. d(t) Feedback filter 12

13 Decision-feedback Equalizer Forward filter w(t) is a linear equalizer e.g., zero-forcing, MSE Noise: n k y t y[n] + + p*(-t) Matched filter w (t) Forward filter error Decision device!" # d(t) Feedback filter The DFE has access to the symbol decisions, computes error signal to update feedback filter (complex!) 13

14 Today 1. The Culprits: Delay Spread and Frequency-Selective Fading 2. Time-Domain Equalization 3. Orthogonal Frequency Division Multiplexing 14

15 Problem: Inter-symbol interference (ISI) Transmitted signal Received signal with ISI 15

16 Symbol time determines frequency bandwidth Symbol time T W 2T t W/2 f t f Slowing down by a factor of two halves the frequency bandwidth of the sender s signal 16

17 A narrowband signal fits into the coherence bandwidth Over what frequency range is the channel approximately the same? This is the coherence bandwidth! " \$ %& ' 35 Coherence bandwidth W c Received Power (dbm) Frequency (khz)

18 Simple Solution: Slow down 1 (double) T s No ISI Transmitted signal Received signal 18

19 Wideband versus OFDM Frequency Wideband Signal Frequency selective fading distorts wideband signals Multipath causes ISI Time Frequency OFDM Signal Narrowband signals Longer OFDM symbol time Time 9

20 Subcarriers are Orthogonal Peaks of each subcarrier coincide in frequency with zeros of other subcarriers Carriers can be packed very densely with minimal interference Requires very good control over frequencies 3

21 One OFDM symbol in time New OFDM symbol time T s 21

22 Difference between FDM and OFDM 10

23 Orthogonality of Subcarriers 13

24 OFDM: System Design Transmitter: Receiver: 11

25 Problem: Inter-OFDM Symbol Interference

26 Problem: Receiver synchronization Receiver: Receiver s view of Symbol 1 contains actual Symbols 1 and 2

27 Interference solution: Inter-symbol guard interval Guard interval between adjacent symbols mitigates adjacent symbol interference

28 Synchronization solution: Cyclic prefix N fft, T fft N s, T s Receiver: Symbol OK!

29 OFDM signal: Frequency-Domain view Uniform power in the frequency domain over the OFDM signal bandwidth 5

30 OFDM signal: Time Domain View Re(x[n]) Large Peak Time Sample Index n Many low-frequency sinusoids in the time domain Occasionally in time, many will all constructively interfere Result: High ratio of peak power / average power 30

31 Peak to Average Power & Transmit Amplifiers Transmit power amplifier sits just before the transmit antenna Peak power in non-linear region causes signal distortion So lower input signal level so that peak input power falls in linear region Typical Transmit Power Amplifier Response (V out / V in ) Put peak power here High peak to average power ratio (PAPR) à Low average power level à Signal mostly uses fewer levels in discrete representation, so high quantization error (another form of distortion) 31

32 An OFDM Modem N subchannels N complex samples Bits S/P quadrature amplitude modulation (QAM) encoder N-IFFT add cyclic prefix P/S D/A + transmit filter TRANSMITTER P/S RECEIVER QAM decoder N subchannels invert channe l = frequency domain equalizer N-FFT N complex samples S/P remove cyclic prefix multipath channel Receive filter + A/D

33 Estimating the Channel Transmit known OFDM preamble symbol x In frequency domain on frequency i, denote preamble X i After FFT, hears frequency domain value Y i 3

34 Packet detection OFDM uses two identical, repeated symbols s 1, s 2 in the preamble for packet detection: s 1 s 2 Preamble Packet body Receiver radio is always listening, receiving samples Call this received sample stream r[n] 34

35 Searching for the preamble in noise Suppose each preamble symbol is of length L Receiver computes c n = ()* %&' +, +. + [, ] Computing c[0]: L r[n]: background noise s 1 s 2 Packet body Angle of each term in the sum is random Sum of complex numbers with random angle 0 c[0] 0 35

36 Search window encounters preamble Suppose preamble at position n 0 Receiver computes c n = ()* %&' +, +. + [, ] Computing c[n 0 ]: L r[n]: background noise s 1 s 2 Packet body (zz*) = 0, so angle of each term in the sum is 0 Sum of complex numbers with 0 angle is large c[n 0 ] is large n 0 36

37 Schmidl-Cox Packet Detection c n = ()* %&' +, +. + [, ] Normalize power fluctuations in r[n], by measuring power: p n = ()* %&' +, +. 4 Schmidl-Cox Packet Detection signal: m[n] = c[n] / p[n] Packet detection metric m[n] Time samples n 37

38 A Closer Look at Carrier Frequency Offset Impact of Frequency Offset z(t) w(t) Lowpass Filter H(j2πf) r(t) y(t) = 2cos(2π(f o +ε)t) Limited precision of frequency oscillators Up-convert baseband signal s n to passband signal y n :! " = \$ " % &'() *+", - Down-convert passband signal y n back to baseband:. " = \$ " % &'() *+", - % &'() /+", - = \$ " % &'( )", - ( 1 = ) 26

39 Estimating Carrier Frequency Offset Because of carrier frequency offset,! " =! \$ % &"' )*+, c. / = 34\$ 12/ 5. / [. / :] Computing c[n 0 ]: L r[n]: background noise s 1 s 2 Packet body n 0 Consider the k th term in sum: 5. / / + 7 % &"' )*+, This is equal to % &"' )*+, 5[. / + 7] " So all terms have the same angle 2= A So, carrier frequency offset estimator B C = E[F G] HIJK L 39

40 Sample Clock Offset The transmitter and receiver may sample the signal at slightly different rates, leading to a sample time offset ζ All subcarriers experience the same sampling delay, but travel over different frequencies 28

41 Correcting Sample Clock Offset in the Frequency Domain H "#\$ % & % ''( f Sample clock offset : slope Residual CFO: intersection with y-axis 30

42 Per-subcarrier Bit Rate Choice SNR(dB) SNR vs Freq 256QAM 64QAM 16QAM 4QAM BPSK NULL Freq (MHz) Figure 1-4: Measurement: Frequency Adaptive Modulation In Action erence bandwidth of the channel. 42

43 Example: IEEE a, g OFDM with up to 48 subcarriers Subcarrier spacing is KHz Subcarriers modulated: BPSK, QPSK, 16-QAM, or 64- QAM Uses a convolutional code at a rate of ½, 2/3, ¾, or 5/6 to provide forward error correction Results in data rates of 6, 9, 12, 18, 24, 36, 48, and 54 MBps Cyclic prefix is 25% of a symbol time (16 vs 64)

44 Friday Precept: Lab 4: Single-carrier transceiver on the HackRF hardware 44

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