Wideband Communications

Wideband Communications Lecture 14-17: CDMA 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

IS-95 • DSSS • 1.2288 Mchips/sec • Downlink • Synchronous CDMA • Quadrature spreading • 2 Extended M-seq. (215-chip long) • Offsets identify BTS • 64 orthogonal Walsh codes • Codes 0 : pilot, 1 : sync, 2: paging • max. 61 data channel (users) • Coherent reception • Uplink • Asynchronous CDMA • No pilot channel (Non-coherent reception) • Long M-seq. (242-1 long) to distinguish users • Walsh coded symbols • OQPSK

Synchronous CDMA • Codes are synchronous • Basis functions are all between 0-T • sk(t) : codes • y(t) = SXksk(t) + n(t) • Xk : kth user data symbol (bk bits) • rk = bk / T • Correlations • Normalized codes : rii= 1 • Cross-correlations matrix : R = {rij} • R is positive definite • Codes are linearly independent

Asynchronous CDMA • Users are not synchronous • Basis functions are all between 0-T • sk(t) : codes • y(t) = S SXk,isk(t-iT-tk) + n(t) • Cross correlations • Correlations with different delays needed

Multi-user receiver • Bank of matched filters (correlators) at RX • No information is lost (optimum solution ) • MF outputs: • Matrix format • y = R x + n = RAb + n • E[nnT] = s2R

Signal space • Projection on orthogonal bases • fn (t) : orthonormal bases • s(t) = Ssnfn (t) ; n=0,…,N-1 • Vector representation : s = [s0 s1 … sN-1]T • For K users • S = [s1 | s2 | … | sK] • R = SHS

Single user detection • Matched filter (Correlator) receiver • y(t) = A1b1 s1(t) + n(t) • y1 = A1b1 + n1 • SNR = (A1/s)2 • BER = Q(A1/s) • Projection on y(t) on s1(t) vector • Orthogonal CDMA • MF is optimal for all users • yk = Akbk + nk • SNR = (Ak/s)2 • BER = Q(Ak/s) • sk(t) are orthogonal • projections are independent

Single user detection (2) • Non-orthogonal CDMA • 2 user case • y(t) = A1b1 s1(t) + A2b2 s2(t) + n(t) • y1 = A1b1 + A2b2r21+ n1 • y2 = A2b2 + A1b1r12+ n2 • BER = ½Q( [A1-A2r]/s) + ½Q( [A1+A2r]/s) • BER < Q( [A1-A2|r|]/s) • A2/A1 < 1/|r| • SNR = ([A1-A2|r|]/s)2 • A2/A1 > 1/|r| • Near-far problem • BER = ½ without noise • Some noise improves BER • A2/A1 = 1/|r| • BER = ¼ + ½Q( 2A1/s)

Single user detection (2) • Power control • Minimum power for a given BER • Users have same SNR • Example • BER = 3x10-5 • SNR = 12 dB

Signal space analysis • y = X1 s1 + X2 s2 + n • s1 and s2 not orthogonal • y1 and y2 are projection on s1 and s2 • n1 and n2 are noise projection on s1 and s2 • Noises are dependent • Near-far problem • y2 are outside the proper region

Signal space • K users • Near-far avoided if • Open-eye condition • Gaussian approximation • Eexample : • 10 equal energy users • r = 0.08

Reading • Verdu 3.1, 3.2, 3.4

Asynchronous receiver • Delay assumption • RX MF outputs: • Matrix format • Y[i] = R[-1] xi+1 + R[0] xi + R[1] xi-1 + ni= R[-1] Abi+1 + R[0] Abi + R[1] Abi-1 + ni • E[ninjH] = s2R[i-j]

Wideband Communications