CHAPTER 6 SPREAD SPECTRUM Xijun Wang
WEEKLY READING 1. Goldsmith, Wireless Communications, Chapters 13 2. Tse, Fundamentals of Wireless Communication, Chapter 4 2
WHY SPREAD SPECTRUM n Increase signal bandwidth beyond the minimum necessary for data communication. hide a signal below the noise floor, making it difficult to detect. mitigate the performance degradation due to ISI and narrowband interference. provide coherent combining of different multipath components by using a RAKE receiver. allow multiple users to share the same signal bandwidth. useful for location and timing acquisition. the basis for both 2nd and 3rd generation cellular systems as well as 2nd generation wireless LANs. 3
WHAT IS SPREAD SPECTRUM n Spread spectrum a modulation method applied to digitally modulated signals increases the transmit signal bandwidth to a value much larger than is needed to transmit the underlying information bits. 4
THREE PROPERTIES n The signal occupies a bandwidth much larger than is needed for the information signal. n The spread spectrum modulation is done using a spreading code, which is independent of the data in the signal. n Despreading at the receiver is done by correlating the received signal with a synchronized copy of the spreading code. 5
DSSS n Direct sequence spread spectrum (DSSS) modulated data signal s(t) is multiplied by a wideband spreading signal or code s c (t) 6
DSSS n The spreading code bits are usually referred to as chips n s c (t) is constant over a time duration Tc and has amplitude equal to 1 or -1. n 1/Tc is called the chip rate. n The number of chips per bit, Ts/Tc, is an integer approximately equal to the processing gain G Processing gain G in SIR = 7
SYSTEM MODEL single-user matched-filter detector 8
DSSS IN AWGN CHANNEL n For an AWGN channel the received spread signal is s(t)s c (t) + n(t). n In the absence of multipath and interference, i.e. for h(t) = δ(t) and I(t) = 0 n Since s c (t) = ±1, n If s c (t) is sufficiently wideband then n(t)s c (t) has approximately the same statistics as n(t) 9
DSSS IN AWGN CHANNEL n The matched filter output over a symbol time n The spreading/despreading process has no impact on the baseband signal x(t). 10
NARROW-BAND INTERFERENCE REJECTION n Assume h(t) = δ(t) and consider I(t) = Iʹ(t)cos(2πf c t) n The matched filter output over a symbol time n The spread interference iʹ(t)s c (t) is a wideband signal with bandwidth of roughly 1/tc, n The integration acts as a lowpass filter with bandwidth of roughly 1/Ts << 1/Tc, thereby removing most of the interference power. 11
NARROW-BAND INTERFERENCE REJECTION n the transmitted signal s(t)s c (t) has frequency response S(f) Sc(f). n Receiver despreading has the effect of distributing the interference power over the bandwidth of the spreading code. n The demodulation of the modulated signal s(t) effectively acts as a lowpass filter, removing most of the energy of the spread interference. 12
ISI REJECTION n A two-path channel with impulse response n Suppose that the first multipath component is stronger than the second: α 0 > α 1, and that the receiver synchronizes to the first component n Without narrowband interference 13
ISI REJECTION n Demodulation n Autocorrelation of the spreading code at delay τ 1 over a symbol time n Designing spreading codes with autocorrelation that approximates a delta function. 14
ISI REJECTION n A two-path channel with impulse response n Received signal n Despreading 15
SPREADING CODES n Spreading codes are generated deterministically n Chip sequence is used to amplitude modulate a square pulse train with pulses of duration Tc chip sequence spreading code 16
SPREADING CODES n The shift register, consisting of n stages, has a cyclical output with a maximum period of 2 n 1. n To avoid a spectral spike at DC or biasing the noise in despreading, the spreading code s c (t) should have no DC component, which requires that the bit sequence b have approximately the same number of 1s and 0s. n The number of consecutive 1s or 0s, called a run, to be small. Ideally the chip values change roughly every chip time, which leads to maximal spreading. 17
SPREADING CODES n The resulting spreading code s c (t) is a sinc function in the frequency domain, corresponding to the Fourier transform of a square pulse. n we require spreading codes with ρ c (τ) δ(τ) to minimize ISI effects. 18
MAXIMAL-LENGTH SEQUENCES n m-sequences a type of cyclic code maximum period N = 2 n 1, the sequence repeats every NTc seconds. shift-and-add property roughly the same number of 1s and 0s over a period: 2 n 1 1 zeros and 2 n 1 ones. the number of runs of length r in an n-length sequence is 1/2 r for r < n and 1/2 r 1 for r = n. belong to the class of pseudorandom (PN) sequences 19
MAXIMAL-LENGTH SEQUENCES n The autocorrelation ρ c (τ) of a maximal linear spreading code taken over a full period T = NT c is n By making n (N = 2 n 1) sufficiently large, the impact of multipath at delays that are not within a chip time of kntc can be mostly removed. 20
MAXIMAL-LENGTH SEQUENCES short spreading code long spreading code N = Ts/Tc, the autocorrelation repeats every symbol time. The demodulator computes the autocorrelation over the full period Ts. However, short codes exhibit significant ISI from multipath components delayed by approximately an integer multiple of a symbol time, in particular the first few symbols after the desired symbol N>>Ts/Tc only multipath at very large delays are not fully attenuated, and these multipath components typically have a low power anyway due to path loss. the autocorrelation is taken over a partial period, so multipath delayed by more than a chip time is no longer attenuated by 1/N. 21
RECEIVER REVISITED 22
SYNCHRONIZATION n Align the timing of the spreading code generator in the receiver with the spreading code associated with one of the multipath components arriving over the channel. Adjust the delay τ of the spreading code generator until the function w(τ) reaches its peak value 23
RAKE RECEIVER each branch synchronized to a different multipath component path diversity assumes there is a multipath component at 24 each integer multiple of a chip time.
FHSS n Hop the modulated data signal over a wide bandwidth by changing its carrier frequency according to a spreading code s c (t). n The bandwidth of the FH system is approximately equal to NB, where N is the number of carrier frequencies available for hopping and B is the bandwidth of the data signal. 25
HEDY LAMARR 26
FHSS n The chip time Tc dictates the time between hops, i.e. the time duration over which the modulated data signal is centered at a given carrier frequency fi before hopping to a new carrier frequency. n Slow frequency hopping tc = kts n Fast frequency hopping Tc = Ts/k frequency diversity on every symbol against narrowband interference and spectral nulls due to frequency-selective fading 27
FHSS SYSTEM MODEL hopping carrier signal 28
NARROW-BAND INTERFERENCE REJECTION n Consider a narrowband interferer of bandwidth B at a carrier frequency fi corresponding to one of the carriers used by the FH system. n The interferer and FH signal occupy the same bandwidth only when carrier fi is generated by the hop sequence. n If the hop sequence spends an equal amount of time at each of the carrier frequencies, then interference occurs a fraction 1/N of the time, and thus the interference power is reduced by roughly 1/N. 29
NARROW-BAND INTERFERENCE REJECTION n DSSS results in a reduced-power interference all the time n FHSS has a full power interferer a fraction of the time. In FFH systems the interference affects only a fraction of a symbol time, so coding may not be required to compensate for this interference. In SFH systems the interference affects many symbols, so typically coding with interleaving is needed to avoid many simultaneous errors in a single codeword. 30
ISI REJECTION n Consider a two-path channel that introduces a multipath component with delay τ. n Suppose the receiver synchronizes to the hop sequence associated with the LOS signal path. n Then the LOS path is demodulated at the desired carrier frequency. However, the multipath component arrives at the receiver with a delay τ. 31
ISI REJECTION n If τ > Tc then the receiver will have hopped to a new carrier frequency fj fi for downconversion when the multipath component, centered at carrier frequency fi, arrives at the receiver. n Since the multipath occupies a different frequency band than the LOS signal component being demodulated, it causes negligible interference to the demodulated signal. n Thus, the demodulated signal does not exhibit either flat or frequency-selective fading for τ > Tc. 32
ISI REJECTION n If τ < Tc then the impact of multipath depends on the bandwidth B of the modulated data signal as well as the hop rate. n FFH system where Tc << Ts. we assume τ < Tc, we have τ < Tc << Ts. flat fading. n SFH system where Tc >> Ts. We assume τ < Tc, all the multipath will arrive while the signal is at the same carrier frequency For B < 1/τ, flat fading, For B > 1/τ, frequency-selective fading. 33
MULTIUSER SYSTEMS n Each user is assigned a unique spreading code or hopping pattern, which is used to modulate their data signal. n The transmitted signal for all users are superimposed in time and in frequency. The spreading codes or hopping patterns can be orthogonal, in which case users do not interfere with each other under ideal propagation conditions, They can be non-orthogonal, in which case there is interference between users, but this interference is reduced by the spreading code properties. 34
MULTIUSER SYSTEMS n While spread spectrum for single-user systems is spectrally inefficient, spread spectrum multiuser systems can support an equal or larger number of users in a given bandwidth than other forms of spectral sharing such as time-division or frequencydivision. n However, if the spreading mechanisms are nonorthogonal either by design or through channel distortion, users interferer with each other. n If there is too much interference between users, the performance of all users degrades. 35
SPREADING CODES FOR MULTIUSER DSSS n Multiuser DSSS is accomplished by assigning each user a unique spreading code sequence s ci (t). n The cross-correlation properties of different spreading codes determines the amount of interference between users modulated with these codes. asynchronous users synchronous users 36
SPREADING CODES FOR MULTIUSER DSSS n We would like the orthogonal code asynchronous users synchronous users n However, It is not possible to obtain orthogonal codes for asynchronous users. for synchronous users there is only a finite number of spreading codes that are orthogonal within any given bandwidth. 37
GOLD CODES n Binary addition of two m-sequences each of length 2 n 1. n A very large number of unique Gold codes can be generated, which allows for a large number of users in a multiuser system. n The cross-correlation of the resulting code may be quite poor, if a Gold code are chosen at random. n Gold codes have worse autocorrelation properties than maximal-length codes, but better crosscorrelation properties if properly designed. 38
GOLD CODES n The preferred sequences are chosen so that Gold codes have a three-valued cross-correlation with values 39
WALSH-HADAMARD CODES n Walsh-Hadamard sequences of length N = Ts/Tc are obtained from the rows of an N N Hadamard matrix H N. n The cross-correlation of any two sequences is zero when synchoronized n The number of spreading codes in a Walsh- Hadamard code is N, thereby supporting at most N users. 40
WALSH-HADAMARD CODES n The same number of users could be supported by dividing up the total system bandwidth into N nonoverlapping channels (frequency-division). n The same number of users can be supported by dividing time up into N orthogonal timeslots (timedivision) where each user operates over the entire system bandwidth during his timeslot. n Hence, any multiuser technique that assigns orthogonal channels to the users such that they do not interfere with each other accommodates approximately the same number of users. 41
MULTIUSER DSSS SYSTEM n In the downlink All transmitted signals are typically synchronous, since they originate from the same transmitter. Moreover, both the desired signal and interference signals pass through the same channel before reaching the desired receiver. n In the uplink Users in the uplink channel are typically asynchronous, since they originate from transmitters at different locations. The transmitted signals of the users travel through different channels before reaching the receiver. 42
MULTIUSER DSSS SYSTEM 43
DOWNLINK CHANNELS Baseband modulated signal Baseband multiuser signal Passband signal Could use orthogonal spreading codes such as the Walsh-Hadamard codes, but not always. 44
DOWNLINK CHANNELS Identical to the matchedfilter detector in a single-user DSSS system perfectly synchronized 45
DOWNLINK CHANNELS baseband equivalent lowpass filter for h k (t) interference from other users in the system 46
MULTIUSER INTERFERENCE n Assume that the kth user s has gain α k but no delayed multipath components Cross-correlation for a timing offset of zero n For orthogonal codes, e.g. Walsh Hadamard codes, ρ jk (0) = 0 so there is no interference between users. n For non-orthgonal codes ρ jk (0) depends on the specific codes assigned to users j and k. 47
MULTIUSER INTERFERENCE n Consider a more general channel n Multiuser interference there are more interference terms: each interfering user contributes M interference terms, one for each multipath component the multipath destroys the synchronicity of the channel. 48
UPLINK CHANNELS The transmitters are typically not synchronized the carrier signals for each user have different phase offsets 49
UPLINK CHANNELS a bank of K singleuser matched-filter detectors the impact of this delay on the local carrier phase is incorporated in the phase offset 50
UPLINK CHANNELS 51
MULTIUSER INTERFERENCE n Assume that each user s channel just introduces a gain α j and delay τ j 52
MULTIUSER INTERFERENCE n Near-far effect the kth user s symbol and multiuser interference are attenuated by different channel gains. users far from the uplink receiver will generally have much smaller channel gains to the receiver than the interferers. users that are close to the uplink receiver can cause a great deal of interference to user s farther away n Solution? 53
MAIN POINTS ON MULTIUSER INTERFERENCE n Code waveform design obtaining spread codes with good cross-correlation performance orthogonality n Power control All users arrive to BTs at about the same power fairness MS transmits power inversely to the received power from BTs (open loop) PC command from BTs to MS, based on received power from MS (Closed loop) 54
MAIN POINTS ON MULTIUSER INTERFERENCE n FEC codes Powerful FEC allows the correction the error signal with lower SNR level n Sectored/Adaptive antennas Some MAIs can be rejected out of main beam of directed antennas Adaptive signal processing can be used to direct the antenna beam to a desired user 55
MULTIUSER DETECTION n Multiple access interference The interfering signals have about as much structure and information content as the desired signal. What if the spreading code of the interference signal is known? The pros of near-far effect? What do we need? 56
MUD n Multiuser detector (MUD) The detection of multiple users whose received signals are not orthogonal to one anther. n Focus on DSSS uplink systems Why not downlink? Synchronous Complexity The uplink receiver must detect the signals from all users anyway 57
POTENTIAL BENEFITS n Significant improvement in Capacity The improvement is still important even it is bounded n More efficient UL spectrum utilization UL improvement allows MS to operate at a lower processing gain A smaller bandwidth is required for UL Extra band can be used for UL high data rate or for use by DL n Reduced precision requirements for Power Control 58
MUD Multiuser Receivers Optimal MLSE Suboptimal Linear Non-linear Decorrelator MMSE Multistage Decision -feedback Successive interference cancellation 59
MUD n Sergio Verdú 60
OPTIMAL MUD IN SYNCHRONOUS UPLINK n A two-user synchronous uplink n Consider only one symbol interval, the optimum (maximum-likelihood) detector outputs n This is equivalent to maximize the cost function 61
OPTIMAL MUD IN SYNCHRONOUS UPLINK n K synchronous users b is the bit vector associated with the K users over the given bit time, A is a diagonal K K matrix of the channel gains α k, and R is a K K matrix of the crosscorrelations between the spreading codes. n The optimal choice of bit sequence is obtained by choosing the sequence to maximize the cost function complexity grows as 2 K requiring knowledge of the channel amplitudes 62
RECAP ON OPTIMAL MUD 63
LINEAR MUD n Linear MUDs apply a linear operator or filter to the soft decision of the conventional detector to attenuate the multiple access interference according to a specific criterion. Decorrelating detector MMSE detector 64
DECORRELATING DETECTOR n The decorrelating detector simply inverts the matrix R of cross-correlations The inverse exists for most cases of interest. completely removes MAI. does not require knowledge of the channel gains. Computaional complexity is much lower than that of MLS detector can lead to noise enhancement Difficult to compute the inverse matrix of R in real time 65
MMSE DETECTOR n Find the matrix D to minimize the expected MSE between D and the transmitted bit sequence b n The optimizing D is given by in the absence of noise, the MMSE detector is the same as the decorrelating detector. it has better performance at low SNRs, since it balances removal of the MAI with noise enhancement. Decorrelating detector MMSE Match filter Performance depends on the powers of the interfering users 66
NON-LINEAR MUD n Feedback is used to reduce MAI for future attempts at detection. n Multistage detection each stage consists of the conventional matched-filter bank. The nth stage of the detector uses decisions of the (n 1)st stage to cancel the MAI at its input. can be applied to either synchronous or asynchronous systems. y Match filter y 1 y 2 Stage 1 x! (1) Stage 2 (2) x! x! (n) Stage n 67
NON-LINEAR MUD n Decision-feedback detection It consists of a feedforward and feedback filter require knowledge of the channel gains can also suffer from error propagation when decision errors are fed back through the feedback filter a form of SIC detection partially decorralted the users without noise enhancing 68
n Decision-feedback detection The data bits are partially decorraleted due to the fact that F is lower triangular. The output of the first user cantains no MAI the output of the second user contains MAI only from bit one of first user, and is completely decorrelated from all other users SIC to exloit the partial decorrelation of the bits 69
NON-LINEAR MUD n Interference cancellation each user s contribution is separate estimated at the receiver, in order to subtract out some or all of the MAI seen by each user Successive interference cancellation Parallel interference cancellation 70
SIC n successive interference cancellation takes a serial approach to canceling interference. users are detected one at a time and then subtracted out from users yet to be detected Enjoy the near-far effect suffers from error propagation More users cancellation will need more delay. When the power profile is changed, the signal need to be reordered. 71
SIC n Precedes by an operation which ranks the signals in descending order of received powers. 72
PIC n parallel interference cancellation all users are detected simultaneously and then cancelled out Has a lower latency and is robust to decision errors suffers due to the near-far effect depends heavily on the quality of MAI estimation 73
PIC n One stage of a PIC detector 74
USER CAPACITY n User capacity the maximum number of users per cell that the system can support without violating a required SIR target value. n Interference-limited regime Good cellular system designs are interference-limited the interference power is much larger than the noise power neglect the impact of noise on performance P I is the received power associated with both intracell and intercell interference. 75
ORTHOGONAL SYSTEMS (TDMA/FDMA) n there is no intracell interference n the SIR is determined from the received signal power and the interference resulting from cochannel cells. n the received signal power for a mobile located at distance d from its base station on both the uplink and the downlink is n The average intercell interference power is a function of the number of out-of-cell interferers. n We neglect interference from outside the first ring of M interfering cells. 76
ORTHOGONAL SYSTEMS (TDMA/FDMA) n The resulting SIR is n Assume that the mobile is on its cell boundary, d = R, and all interferers are at the reuse distance D from the intended receiver. n if, we have where D/R is a function of the reuse factor N 77
FREQUENCY RESUE 78
ORTHOGONAL SYSTEMS (TDMA/FDMA) n SIR is expressed as a function of N a1 =.125, a2 = 4 for diamond cells a1 =.167, a2 = 3 for hexagonally-shaped cells n Given a target SIR value SIR 0 required for a target BER, 79
ORTHOGONAL SYSTEMS (TDMA/FDMA) n The user capacity is where Nc is the number of channels assigned to any given cell. n The bandwidth of the total system is B, the bandwidth of an orthogonal channel is Bs. n The total number of orthogonal channels is n The reuse factor N satisfies 80
NON-ORTHOGONAL SYSTEMS (CDMA) n In non-orthogonal systems codes (i.e. channels) are typically reused in every cell, so the reuse factor is N = 1. n these systems exhibit both intercell and intracell interference n assume all signals follow the simplified path loss model with the same path loss exponent n neglect intercell interference from outside the first tier of interfering cells n Considering the uplink 81
NON-ORTHOGONAL SYSTEMS (CDMA) n Let N c = N T = C u denote the number of channels per cell. n There are N c 1 asynchronous intracell interfering signals and MN c asynchronous intercell interfering signals transmitted from mobiles in the M adjacent cells. all interference is reduced by the spreading code cross correlation ξ/(3g) G is the processing gain of the system ξ is a parameter of the spreading codes with 1 ξ 3 82
NON-ORTHOGONAL SYSTEMS (CDMA) n The uplink SIR is n assume perfect power control within a cell the received power of the desired signal and interfering signals within a cell are the same The uplink SIR with power control is for a given SIR target SIR 0, 83