Lecture 12-13: Multi-access Aliazam Abbasfar

Outline

Multi-access channel Messages share a common channel A user = A message source/destination Multi-point to point communications (Uplink/Reverse channel) Point to Multi-point communications (Downlink/Forward channel) Channel partitioning Time (TDMA) Guard time Frequency (FDMA) Guard band Orthogonal partitioning Orthogonal basis functions Non-orthogonal basis Potential users are greater than active users Fixed allocation wastes resources Dynamic allocation needs back channels Random access One user occupies the channel at a time Collision control ( sense / retransmit )

CDMA Code division multiple access Users are assigned “codes” signature waveforms (basis functions) Basis functions can overlap in time and frequency Orthogonal/non-orthogonal codes Synchronous/Asynchronous TDMA/FDMA are CDMA with orthogonal codes Non-overlapping in time/freq Number of users : K = 2 T B Number of dimensions

Synchronous CDMA Codes are synchronous Basis functions are all between 0-T s k (t) : codes y(t) =  X k s k (t) + n(t) X k : k th user data symbol (b k bits) r k = b k / T Correlations Normalized codes :  ii = 1 Cross-correlations matrix : R = { ij } R is positive definite Codes are linearly independent

Asynchronous CDMA Users are not synchronous Basis functions are all between 0-T s k (t) : codes y(t) =  X k,i s k (t-iT- k ) + n(t) Cross correlations Correlations with different delays needed Ts might be different as well

Spread spectrum Signature waveforms with big duration- bandwidth product Basis function’s B T >> 1 One of many dimensions in signal space

Spread spectrum Principles Transmitted signal bandwidth is much greater than the rate of information A spreading signal (independent of data) is used to spread the information Some signals other than information are sent too De-spreading at the receiver is done by correlating the received signal with the spreading code Properties Transmitted signal power spectral density is minimized The receiver de-spread the information, but not the interference

Applications Military Resistant to jamming Needs a lot more power to jam Spread the jammer energy Resistant to narrowband or pulse noises Hard to detect Signal power is below noise power Hard to decode Spreading signal is also needed Commercial CDMA ( code division multiple access) Proposed and standardized by Qualcomm Digital cellular networks IS95, CDMA2000, WCDMA

Spread spectrum signals

Spread spectrum types Direct sequence spread spectrum (DSSS) Multiply the digital signal by a much higher rate PN-sequence Frequency hopping spread spectrum (FHSS) Slow hopping Every M data symbols are modulated by a different carrier Hopping pattern is determined by a PN-sequence Fast hopping A single symbol are transmitted on M carriers Time hopping spread spectrum (THSS) Available time is divided into time slots Time slots are selected based on PN-sequence

Spreading sequence Desired properties A sequence of independent random variables Implementable and easily reproduced TX and RX use the same sequence DSSS : good one-dimensional correlation property of bipolar binary sequences Pseudo noise (PN) sequence or M-sequence Gold sequence Kasami sequence FHSS : good two-dimensional correlation property of integer sequences THSS : good one-dimensional correlation property of integer sequences

M-sequence codes Maximal length A 2 N -1 long sequence Generated by a N-stage linear feedback shift register (LFSR) Generator polynomial g(x) = g N x N + … + g 1 x + 1 Should be primitive Used in IS-95 standard Properties All zero state is forbidden All other states are generated just once 2 N-1 ones and 2 N-1 -1 zeros

M-sequence example g(x) = x 4 + x + 1 o[i+4] = o[i]+o[i+1] Initial state =[ ] o 1 = { } Bipolar sequence Mapping : 0  (-1) 0 = 1 and 1  (-1) 1 = -1 o 1 = { }

correlation Periodic cross-correlation Discrete Autocorrelation Bipolar M-sequence R x (0) = 1 R x (m) = -1/N, m  0 Continuous signal correlations Periodic M-sequence with rectangular pulse (p(t)) Similar to white noise (Pseudo noise)

DSSS Bits are translated into PN-sequences Bits (T b ) and chips (T c ) Data rate(R b ) and chip rate (R c ) Bandwidth expansion (T b /T c ) Example x(t) = b(t) s(t) r(t) = x(t) + n(t) y(t) = r(t) s(t) = b(t) + n(t) s(t) Processing gain E b /N o = G SNR G = E b /E c = T b /T c Narrowband interference rejection

Rake receiver ISI mitigation h(t) =  0 (t) +  1 (t-) y(0) =  0 b 0 +  1 R x () b 0 L diversity branches Resolvable paths increased due to spreading (frequency diversity) MRC combiner A matched filter

Ch. 13 Goldsmith Tse ch. 3.4 Reading

Cioffi Ch. 4.10