Selected Topics in DSP for Wireless

1. Selected Topics in DSP for Wireless Jean-Paul M.G. Linnartz Nat.Lab., Philips Research

2. DSP aspects • Source Coding (Speech coding) • Synchronization • Detection and matched filtering • Diversity and rake receivers • Multi-user detection • Equalization or subcarrier retrieval • Error Correction • Security & cryptographic algorithms

3. Outline • The Matched Filter Principle • Diversity • Diversity Techniques: The choice of the domain • Diversity Techniques: The signal processing • Performance • Space time coding • Code Division Multiple Access • Direct Sequence Basics • Rake receiver

4. The Matched Filter Principle • The optimum receiver for any signal • in Additive white Gaussian Noise • over a Linear Time-Invariant Channel • is ‘a matched filter’: Integrate Transmit Signal S Locally stored reference copy of transmit signal Channel Noise

5. The Matched Filter Principle Locally stored reference copy of transmit signal for “0” Transmit Signal, either S0(t) for “0” or S1(t) for “1” S0(t) Select largest Integrate S S Channel Noise Integrate S1(t) Locally stored reference copy of transmit signal for “1”

6. Fundamentals of Diversity Reception • What is diversity? • Diversity is a technique to combine several copies of the same message received over different channels. • Why diversity? • To improve link performance

7. Methods for obtaining multiple replicas • Antenna Diversity • Site Diversity • Frequency Diversity • Time Diversity • Polarization Diversity • AngleDiversity

8. Antenna (or micro) diversity. • - at the mobile • Covariance of received signal amplitude J02(2πfDτ) = J02(2πd/λ). • antenna spacing of λ/2 is enough • - at the base station • All signal come from approximately the same direction • received signals are highly correlated • Larger antenna separation needed • Relevant parameter: • distance between scattering objects antenna (typically, a is 10 .. 100 meters), and • distance between mobile and base station.

9. Site (or macro) diversity • Receiving antennas are located at different sites. • Example: at the different corners of hexagonal cell. • Advantage: multipath fading, shadowing, path loss and interference all become "independent"

10. Angle diversity • Waves from different angles of arrival are combined optimally, rather than with random phase • Directional antennas receive only a fraction of all scattered energy.

11. Frequency diversity • Each message is transmitted at different carrier frequencies simultaneously • Frequency separation >> coherence bandwidth

12. Time diversity • Each message is transmitted more than once. • Useful for moving terminals • Similar concept: Slow frequency hopping (SFH): • blocks of bits are transmitted at different carrier frequencies.

13. Selection Methods • Selection Diversity • Equal Gain Combining • Maximum Ratio Combining • Advanced filtering • if interference is present • wiener filtering (MMSE), smart antenna’s, adaptive beam steering, space-time coding • Post-detection combining: • Signals in all branches are detected separately • Baseband signals are combined.

14. Pure selection diversity • Select only the strongest signal • In practice: select the highest signal + interference + noise power. • Use delay and hysteresis to avoid ping-pong effects (excessive switching back and forth) • Simple implementation: Threshold Diversity • Switch when current power drops below a threshold • This avoids the necessity of separate receivers for each diversity branch.

15. Exercise: Selection Diversity • The fade margin of a Rayleigh-fading signal is h. • A receiver can choose the strongest signal from L antennas, each receiving an independent signal power. • What is the probability that the signal is x dB or more below the threshold?

16. Solution: Diversity • Diversity rule: • Select strongest signal. • Outage probability for selection diversity: • Pr(max(p) < pthr) = Pr(all(p) < pthr) = Pi Pr(pi < pthr) • For L-branch selection diversity in Rayleigh fading:

17. Outage Probability Versus Fade Margin • Performance improves very slowly with increased transmit power • Diversity Improves performance by orders of magnitude • Slope of the curve is proportional to order of diversity • Only if fading is independent for all antennas Better signal combining methods exist: Equal gain, Maximum ratio, Interference Rejection Combining

18. Performance of Diversity • In a fading channel, diversity helps to improve the slope of the BER curve. • Explain why coding can play the same role. • Diversity can be used to combat noise and fading, but also to separate different user signals.

19. Diversity Combining Methods • Each branch is • co-phased with the other branches • weighted by factor ai where ai depends on amplitude ri • Selection diversity • ai = 1 if ρi, > ρj, for all j  i and 0 otherwise. • Equal Gain Combining: ai =1 for all i. • Maximum Ratio Combining: ai = ρi.

20. Maximum ratio combining • Weigh signals proportional to their amplitude. MRC: ai = constant ri • This is the same as matched filter • After some math: SNR at the output is the sum of the SNRs at all the input branches

21. Comparison

22. Space-Time Coding (MIMO) • Multiple Input Multiple Output concept: • In a rich multipath environment, a system with N transmit antennas and M receive antennas can handle min(N,M) simultaneous communication streams.

23. Direct Sequence CDMA

24. EXOR User Bits Code Sequence Direct Sequence • User data stream is multiplied by a fast code sequence • Example: • User bits 101 (+ - +) • Code 1110100 (+ + + - + - -); spead factor = 7 User bit = 1 User bit = -1 User bit = 1 -1 0 +1 1 1 1 -1 1 -1 -1 -1 -1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1

25. St ci(t) cj(t) =M if i = j = “0” if i = j User separation in Direct Sequence • Different users have different (orthogonal ?) codes. Integrate User Data 1 S Code 1: c1(t) Code 1 User Data 2 Code 2: c2(t)

26. Multipath Separation in DS • Different delayed signals are orthogonal Integrate User Data 1 S Code 1: c1(t) Code 1 Delay T St ci(t) ci(t) =M St ci(t) ci(t+T) = “0” if T 0

27. D D D = EXOR addition mod 2 Popular Codes: m-sequences • Linear Feedback Shift Register Codes: • Maximal length: M = 2L - 1. Why? • Every bit combination occurs once (except 0L) • Autocorrelation is 2L - 1 or -1 • Maximum length occurs for specific polynomia only correlation: R(k) M k

28. R2 = [ ] R2i=[ ] R4=[ ] 1 1 1 -1 RiRi Ri -Ri 1 1 1 1 1 -1 1 -1 1 1 -1 -1 1 -1 -1 1 Popular Codes: Walsh-Hadamard • Basic Code (1,1) and (1,-1) • Recursive method to get a code twice as long • Length of code is 2l • Perfectly orthogonal • Poor auto correlation properties • Poor spectral spreading. E.g. all “1” code. One column is the code for one user

29. Cellular CDMA • IS-95: proposed by Qualcomm • W-CDMA: future UMTS standard • Advantages of CDMA • Soft handoff • Soft capacity • Multipath tolerance: lower fade margins needed • No need for frequency planning

30. Cellular CDMA • Problems • Self Interference • Dispersion causes shifted versions of the codes signal to interfere • Near-far effect and power control • CDMA performance is optimized if all signals are received with the same power • Frequent update needed • Performance is sensitive to imperfections of only a dB • Convergence problems may occur

31. Synchronous DS: Downlink • In the ‘forward’ or downlink (base-to-mobile): all signals originate at the base station and travel over the same path. • One can easily exploit orthogonality of user signals. It is fairly simple to reduce mutual interference from users within the same cell, by assigning orthogonal Walsh-Hadamard codes. BS MS 1 MS 2

32. IS-95 Forward link (‘Down’) • Logical channels for pilot, paging, sync and traffic. • Chip rate 1.2288 Mchip/s = 128 times 9600 bit/sec • Codes: • Length 64 Walsh-Hadamard (for orthogonality users) • maximum length code sequence (for effective spreading and multipath resistance • Transmit bandwidth 1.25 MHz • Convolutional coding with rate 1/2

33. EXOR (addition mod 2) IS-95 BS Transmitter W0 Pilot: DC-signal W0 Sync data Combining, weighting and quadrature modulation Wj User data Convol. Encoder Block interleaver PNI Long code PNQ

34. Asynchronous DS: uplink • In the ‘reverse’ or uplink (mobile-to-base), it is technically difficult to ensure that all signals arrive with perfect time alignment at the base station. • Different channels for different signals • power control needed BS MS 1 MS 2

35. IS-95 Reverse link (‘Up’) • Every user uses the same set of short sequences for modulation as in the forward link. • Length = 215 (modified 15 bit LFSR). • Each access channel and each traffic channel gets a different long PN sequence. Used to separate the signals from different users. • Walsh codes are used solely to provide m-ary orthogonal modulation waveform. • Rate 1/3 convolutional coding.

36. Rake receiver A rake receiver for Direct Sequence SS optimally combines energy from signals over various delayed propagation paths.

37. DS reception: Matched Filter Concept • The optimum receiver for any signal • in Additive white Gaussian Noise • over a Linear Time-Invariant Channel • is ‘a matched filter’: Integrate Transmit Signal S Locally stored reference copy of transmit signal Channel Noise

38. Integrate S H-1(f) Locally stored reference copy of transmit signal Transmit Signal H(f) Integrate Channel Noise S H(f) Locally stored reference copy of transmit signal Matched Filter with Dispersive Channel • What is an optimum receiver?

39. H(f) Channel estimate H(f) D D D D D D Channel estimate H*(f) Ref code sequence S Rake Receiver • 1956: Price & Green • Two implementations of the rake receiver: • Delayed reference • Delayed signal Integrate S Ref code sequence

40. Wireless BER LR = 1 LR = 2 LR = 3 Eb/N0 BER of Rake • Ignoring ISI, the local-mean BER is • where • with gi the local-mean • SNR in branch i. J. Proakis, “Digital Communications”, McGraw-Hill, Chapter 7.

41. Advanced user separation in DS • More advanced signal separation and multi-user detection receivers exist. • Matched filters • Successive subtraction • Decorrelating receiver • Minimum Mean-Square Error (MMSE) Spectrum efficiency bits/chip Optimum MMSE Decorrelator Matched F. Eb/N0 Source: Sergio Verdu

42. Software radio • Many functions are executed in software anyhow • There are many different radio standards, multi-mode is the way to go. • Can we share functions? • Can we realize a steep cost reduction on DSP platforms? • Architectural choices: • what to make in dedicated hardware? • what to do in programmable ‘filters’? • which operations are done by a general purpose processor?