Selected Topics in DSP for Wireless Jean-Paul M.G. Linnartz Nat.Lab., Philips Research This section covers the basic principles of mobile propagation. Random fluctuations of the channel play an important role in the performance of wireless systems, and many countermeasure are known and used to improve the reliability of a radio system and make it less vulnerable to random channel fluctuations. Some effects, such as path loss and shadow attenuation are mostly addressed in the layout of the cell structure, whereas other effects, such as multipath fading are mostly addressed by the choice of the transmission and modulation method, our by other measure in the receiver. It is generally accepted that a sound understanding of the wireless channel is essential to design good systems. Jean-Paul Linnartz is Senior Scientist with the Natuurkundig Laboratories of Philips Research in Eindhoven, The Netherlands. He leads of team of researchers working on conditional access, copy control, security and electronic watermarking. He joined Philips Research in 1995. From 1994-1998, he also was Assistant Adjunct Professor at the University of California at Berkeley. 1988-1991 and in 1994, he worked at T.U. Delft as Assistant and Associate Professor, respectively. In 1992-1994, he was Assistant Professor with the University of California at Berkeley. His research interests include wireless networks, communication over multipath and fading channels, Random Access and Intelligent Transport Systems (ITS). He was involved in the INFOPAD and PATH research projects. He was the first to use the term (Orthogonal) Multi-Carrier CDMA (MC-CDMA) for a spread spectrum transmission method which combines Direct-Sequence CDMA with Orthogonal Frequency Division Multiplexing (OFDM). During his M.Sc. and PhD project he worked on mathematical methods to evaluate the performance of wireless data and cellular phone networks. At Philips Research, his research mainly is on Electronic Watermarks, Conditional Access and Information Security. He developed the ticket concept for copy generation control, which plays an important role in CPTWG and SDMI standardization, and he invented the sensitivity attack on public watermarking.

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

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

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

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) Integrate Select largest S S Channel Noise Integrate S1(t) Locally stored reference copy of transmit signal for “1”

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

Methods for obtaining multiple replicas Antenna Diversity Site Diversity Frequency Diversity Time Diversity Polarization Diversity Angle Diversity

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.

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"

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.

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

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.

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.

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.

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?

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:

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 A signal transmitted at a particular carrier frequency and at a particular instant of time may be received in a multipath null. Diversity reception reduces the probability of occurrence of communication failures (outages) caused by fades by combining several copies of the same message received over different channels. In general, the efficiency of the diversity techniques reduces if the signal fading is correlated at different branches. In antenna (or micro) diversity the signal from antennas mounted at separate locations are combined. Typically these antennas are located on the vehicle or at the same base station tower and their spacing is a few wavelengths. The received signal amplitude is correlated, depending on the antennas separation d relative to the wavelength. The received multipath signal becomes practically uncorrelated if antennas at the mobile are spaced by more than, say, half a wavelength. In the analysis of this correlation, it was assumed that the mobile antenna is mounted at low height and close to all kinds of reflecting and scattering objects. The base station antenna however, is mostly located well above such obstacles. Hence at the base station all multipath waves arrive from approximately the same direction. If the antenna is moved over a certain small distance d, the phase shift is almost identical for all arriving waves. This is in sharp contrast to the situation at the mobile where motion over half a wavelength leads to almost uncorrelated signal phases. To ensure effective antenna diversity at the base station, antennas must be separated much farther than the fraction of the wavelength required for diversity at the mobile. Better signal combining methods exist: Equal gain, Maximum ratio, Interference Rejection Combining

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.

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.

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

Comparison

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.

Direct Sequence CDMA

Direct Sequence User data stream is multiplied by a fast code sequence Example: User bits 101 (+ - +) Code 1110100 (+ + + - + - -); spead factor = 7 EXOR User Bits Code Sequence In Direct Sequence Spread Spectrum transmission, the user data signal is multiplied by a fast code sequence. Mostly, binary sequences are used. The duration of an element in the code is called the "chip time". The ratio between the user symbol time and the chip time is called the spread factor. The transmit signal occupies a bandwidth that equals the spread factor times the bandwidth of the user data. Different CDMA users use different codes. In this example the receiver sees the signal from user 1, while the signal from user 2 is heavily attenuated by the correlator (multiplier and integrator) in the receiver. Despreading the signal requires knowledge of the user's code. In military systems these codes are kept secret, so it is very difficult for an unauthorized attacker to tap into or transmit on another user's channel. Often it is even difficult to detect the presence of a spread-spectrum signal because it is below the noise that is present in the transmit bandwidth. Note that in cellular systems, the codes are fully described in publicly available standards. In digital systems, security against eavesdropping (confidentiality) is obtained through encryption. This is a highly desirable alternative to the analog FDMA cellular phone system in wide use today, where with an inexpensive scanner one can tune in to the private conversations of unwary neighbors. User bit = 1 User bit = -1 User bit = 1 -1 +1 1 1 1 -1 1 -1 -1 -1 -1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1

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) St ci(t) cj(t) = M if i = j = “0” if i = j

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

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 D = EXOR addition mod 2 correlation: R(k) M k

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. 1 1 1 -1 R2 = [ ] R2i=[ ] R4=[ ] Ri Ri Ri -Ri 1 1 1 1 1 -1 1 -1 1 1 -1 -1 1 -1 -1 1 One column is the code for one user

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 There are many attributes of CDMA which are beneficial to cellular systems Soft handoff. Since every cell uses the same radio frequency band, the only difference between user channels is the spreading code sequences. Therefore, there is no jump from one frequency to another frequency when a user moves between cells. The mobile terminal receives the same signal in one cell as it does in the next, and thus there is no harsh transition from one receiving mode to another. Two or more neighboring base stations can receive the signal of a particular user, because they all use the same channel. Moreover, two base stations can simultaneously transmit to the same user terminals. The mobile receiver can resolve the two signals separately and combine them. This feature is called soft handoff. Soft capacity or graceful degradation. In FDMA and TDMA, N channels can be used virtually without interference from other users in the same cell but potential users N+1, N+2, ..., are blocked until a channel is released. The capacity of FDMA and TDMA is therefore fixed at N users and the link quality is determined by the frequency reuse pattern. In theory, it does not matter whether the spectrum is divided into frequencies, time slots, or codes, the capacity provided from these three multiple access schemes is the same. However, in CDMA, all the users in all cells share one radio channel and are separated by codes. Therefore, an additional user may be added by sacrificing somewhat the link quality, with the effect that voice quality is just slightly degraded compared to that of the normal N-channel cell. Thus, degradation of performance with an increasing number of simultaneous users is "graceful" in CDMA systems, versus the hard limits placed on FDMA and TDMA systems. Multipath tolerance. Spread spectrum techniques are effective in combating frequency selective fading. The underlying principle is that when a signal is spread over a wide bandwidth, a frequency selective fade will corrupt only a small portion of the signal's power spectrum, while passing the remaining spectrum unblemished. As a result, upon despreading there is a better probability that the signal can berecovered correctly. For a narrowband signal whose spectral density happens to be misplaced in a deep fade, an unrecoverable signal at the receiver is virtually assured.

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 There are, of course, a number of disadvantages associated with CDMA; two of the most severe are the problem of "self-interference," and the related problem of the "near-far" effect. Self-interference arises from the presence of delayed replicas of signal due to multipath. The delays cause the spreading sequences of the different users to lose their orthogonality, as by design they are orthogonal only at zero phase offset. Hence in despreading a given user's waveform, nonzero contributions to that user's signal arise from the transmissions of the other users in the network. This is distinct from both TDMA and FDMA, wherein for reasonable time or frequency guardbands, respectively, orthogonality of the received signals can be preserved. The near-far problem arises from the fact that signals closer to the receiver of interest are received with smaller attenuation than are signals located further away. Therefore the strong signal from the nearby transmitter will mask the weak signal from the remote transmitter. In TDMA and FDMA, this is not a problem since mutual interference can be filtered. In CDMA, however, the near-far effect combined with imperfect orthogonality between codes (e.g. due to different time sifts), leads to substantial interference. Accurate and fast power control appears essential to ensure reliable operation of multi-user DS-CDMA systems.

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 The downlink is the link from base to mobile It is also called the forward or outbound link. Here all signal originate at the same transmitter. Thus it is fairly simple to reduce mutual interference from users within the same cell, by assigning orthogonal (e.g. Walsh-Hadamard) codes. MS 1 MS 2

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 One of the Walsh codes is the all “one” word (1,1,1,1,...), which would result in a narrowband (not spread) signal. Thus a maximum length PN sequence is superimposed, which is the same for all users and has the same time phase for all users. The long PN code provide a measure of voice privacy and improves time synchronization. The short PN code in the forward link has a limited resolution but makes synchronization easier. Chip rate 1.2288 Mchip/s = 128 times 9600 bit/sec. IS-95 combines 64 Walsh-Hadamard (for orthogonality among users) and a maximum length code sequence (for effective spreading and multipath resistance) Transmit bandwidth 1.25 MHz Convolutional coding with rate 1/2 The Forward IS95 Channel consists of several code channels: the Pilot Channel, The Pilot tone is always transmitted by the base station on each active Forward CDMA Channel. It is an unmodulated spread spectrum signal (i.e., it does not contain spreading by the short Walsh Hadamerd code). The pilot tone is a PN-sequence, which is used for synchronization. a Sync Channel, operating at a fixed rate of 1200 bit/s up to seven Paging Channels, (at a fixed rate of 9600 or 4800 bit/s.) and a number of Forward Traffic Channels (at 9600, 4800, 2400, and 1200 bit/s).

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

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 In a practical multi-user system with intermittent transmissions, inbound messages are sent via a multiple-access channel, whereas in outbound channel, signals destined for different users can be multiplexed. In the latter case, the receiver in a mobile station can maintain carrier and bit synchronisation to the continuous incoming bit stream from the base station, whereas the receiver in the base station has to acquire synchronisation for each user slot. Moreover, in packet-switched data networks, the inbound channel has to accept randomly occurring transmissions by the terminals in the service area. Random-access protocols are required to organise the data traffic flow in the inbound channel, and access conflicts ('contention') may occur. In cellular networks with large traffic loads per base station, spread-spectrum modulation can be exploited in the downlink to combat multipath fading, whereas in the uplink, the signal powers from the various mobile subscribers may differ too much to effectively apply spread-spectrum multiple access unless sophisticated adaptive power control techniques are employed. MS 1 MS 2

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. The Reverse (uplink) Channel (mobile to base station) contains Access Channels and Reverse Traffic Channels. The Reverse Traffic Channel carries (or other user data) and network signaling data from mobile to the base station, while the Access Channel is used by the mobile to request the base station to set up a call and to respond to Paging Channel messages (call set-up by the base stations). A Traffic Channel has a distinct user long code sequence. This allows separation of different user signals at the base station. Moreover, each Access Channel uses a distinct Access Channel long code sequence. On the reverse link, every user uses the same set of short sequences for modulation. The length of these sequences is 215, i.e., it is a modified 15 bit Linear Feedback Shift Register maximum length sequence (215+1-1). Each access channel and each traffic channel gets a different long PN sequence. The long sequences are used to separate the signals from different users on the reverse link (CDMA). Walsh codes are used solely to provide m-ary orthogonal modulation waveform. The reverse link uses rate 1/3 convolutional coding. The reverse is95 channel uses convolutional encoding, block interleaving to combat burst errors, 64-ary orthogonal modulation, and spreading by an m-sequence. Speech segments or data is grouped into frames of 20 milliseconds each. Reverse Traffic Channel frames consists of 192 bits. These 192 bits is composed of 172 information bits followed by 12 frame quality indicator bits and eight Encoder Tail Bits. The Reverse Traffic Channel runs at 9600, 4800, 2400 or 1200 bit/s, which can be selected on a frame-by-frame basis. While the channel burst transmission rate is fixed at 28,800 symbols per second, these different rates are created by varying the transmit duty cycle; for 9600 bit/s frames it is 100 percent, for 4800 bit/s frames it is 50 percent, and so forth.

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

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 The theory for signal transmission over AWGN LTI channels is very well developed and covered in many excellent text books. Many fundamental theorems in signal detection theory have been deveoped during World War II, to improve and automate the radar detection of enemy airplanes and ships. The theory of the matched filter receiver is of particular interest. The concept was introduced by D.O. North with the RCA labs in Princeton, in 1943. The matched filter correlates the incoming signal with a locally stored reference copy of the transmit waveform. The matched filter maximizes the signal-to-noise ratio for a known signal. It can be shown to be the optimal detector if the channel produces Additive White Gaussian Noise (AWGN), the channel is linear and time-invariant (LTI), and an exact time reference is available, the signal amplitude as a function of time is precisely known. Channel Noise

Matched Filter with Dispersive Channel What is an optimum receiver? Integrate S Locally stored reference copy of transmit signal H-1(f) Channel Noise Transmit Signal H(f) Integrate S Locally stored reference copy of transmit signal H(f) In a CDMA system no channel equalization is used (in the traditional sense). When the transmission rate is much higher than 10 kbps in both FDMA and TDMA, an equalizer is needed for reducing the intersymbol interference caused by time delay spread. This is because when the bit period becomes smaller than about ten times the time delay spread, intersymbol interference becomes significant. However, in CDMA a correlator is needed at minimum. To achieve good performance a rake receiver is needed combat delay spread. The rationale behind the rake receiver starts with the observation that the optimum receive filter is one that is ‘matched to the expected receive signal’. In the matched filter receiver, the signal is correlated with a locally generated copy of the signal waveform. If, however, the signal is distorted by the channel, the receiver should correlate the incoming signal by a copy of the expected received signal, rather than by a copy of transmitted waveform. Thus the receiver should estimate the delay profile of channel, and adapt its locally generated copy according to this estimate. If the channel is dispersive, the matched filter concept can still be used, but one must multiply the incoming signal with a locally generated copy of the expected waveform after transmission over the channel. That is, the receiver must estimate the channel impulse response and apply this to the reference signal waveform. The incoming signal is correlated with a reference waveform, which is dispersed in the same manner as the channel disperses the radio signa A complication is that such dispersion causes intersymbol interference. Theorectically, it is no longer optimum to detect the received symbols one by one. The "maximum likelihood" (ML) receiver correlates the incoming sequence with dispersed sequences of potentially transmitted waveforms, containing multiple successive bits.

Rake Receiver 1956: Price & Green S H(f) H(f) Two implementations of the rake receiver: Delayed reference Delayed signal Integrate S H(f) D Channel estimate H(f) D H*(f) Channel estimate Ref code sequence S Ref code sequence The rake receiver consists of multiple correlators, in which the receive signal is multiplied by time-shifted versions of a locally generated code sequence. The intention is to separate signals such that each finger only sees signals coming in over a single (resolvable) path. The spreading code is chosen to have a very small autocorrelation value for any nonzero time offset. This avoids crosstalk between fingers. In practice, the situation is less ideal. It is not the full periodic autocorrelation that determines the crosstalk between signals in different fingers, but rather two partial correlations, with contributions from two consecutive bits or symbols. It has been attempted to find sequences that have satisfactory partial correlation values, but the crosstalk due to partial (non-periodic) correlations remains substantially more difficult to reduce than the effects of periodic correlations. The rake receiver is designed to optimally detected a DS-CDMA signal transmitted over a dispersive multipath channel. It is an extension of the concept of the matched filter. Like a garden rake, the rake receiver gathers the energy received over the various delayed propagation paths. According to the maximum ratio combining principle, the SNR at the output is the sum of the SNRs in the individual branches, provided that we assume that only AWGN is present (no interference) codes with a time offset are truly orthogonal

BER of Rake Ignoring ISI, the local-mean BER is where BER Wireless BER of Rake Ignoring ISI, the local-mean BER is where with gi the local-mean SNR in branch i. LR = 1 LR = 2 LR = 3 BER Eb/N0 According to Rayleigh's model, the channel coefficients hk are independent complex Gaussian random variables. The power received or the signal-to-noise ratio in the k-th bin of the delay spread is gk, which is exponentially distributed. Powers in various paths are independent, but usually not identically distributed. The delay profile describes the expected power in each path. The pdf of S gk is found considering the Laplace images (or characteristic function) of the pdf of individual received powers. For an exponential signal-to-noise ratio, the image is Uk(s) = 1/(1+sGk), with Gk the local-mean signal-to-noise ratio. So for all paths combined, the image of the post-combiner signal-to-noise ratio is the product of individual images. Thus, U(s) = Pk Uk = Pk 1/(1+sGk), Inverse transformation yields f(g) = S Ck /Gk exp(-gk/Gk) where Ck = Pi, i not equal k Gk /(Gk - Gi) We now average the instantaneous BER (for fixed {gk}) over the pdf of the f(g) . The local-mean BER is P = (1/2) Sk Ck [ 1- SQRT(Gk / (1+Gk ) ) ] J. Proakis, “Digital Communications”, McGraw-Hill, Chapter 7.

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

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?