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Transcript of Principles of Spread Spectrum and CDMAbhaskar/wireless_course/cdma_wirelesscourse.pdf · Principles...
Dr Bhaskar Ramamurthi CDMA_Wireless_Course 1
Principles of Spread Spectrum and CDMA
Principles of Spread Spectrum and CDMA
Dr Bhaskar RamamurthiProfessor
Department of Electrical Engineering
Indian Institute of Technology Madras.
Dr Bhaskar Ramamurthi CDMA_Wireless_Course 2
Principles of Spread Spectrum and CDMA
Separation of Overlapping Signals
• Frequency Division Multiplexing
• signals non-overlapping in frequency
• signals overlap in time
• separation achieved by filtering
- “window” in f-domain
- convolution with filter impulse response in t-domain
• if ↔ filters out signal in [f1 , f2]
desired_signal =
⇒ sliding correlation with h1(-t)
f1
f2
f r
e q
t i m e
)f(H1 )t(h1
∫ −∞
∞−τττ d)t(h)(signal_sum
1
Dr Bhaskar Ramamurthi CDMA_Wireless_Course 3
Principles of Spread Spectrum and CDMA
Separation (contd…)
• Time Division Multiplexing
• signals non-overlapping in time
• signals overlap in frequency
• separation achieved by windowing
− multiplication in t-domain
− convolution in f-domain
• if u(t; t1 , t2) is non-zero in [t1 , t2]desired_signal = sum_signal . u(t; t1 , t2)
t1time
t2 tN
freq
Dr Bhaskar Ramamurthi CDMA_Wireless_Course 4
Principles of Spread Spectrum and CDMA
Orthogonality and Separation of Signals
• in FDM, signals are orthogonal in frequency
⇒ Signal_1(f) . Signal_2(f) = 0
• in TDM, signal are orthogonal in time
⇒ signal_1(t) . signal_2(t) = 0
• signals can be continuous-time or discrete-time
however in TDM, signal is usual a d-t digital signalor digitally-modulated c-t signal
• Is any other form of orthogonality possible?
Dr Bhaskar Ramamurthi CDMA_Wireless_Course 5
Principles of Spread Spectrum and CDMA
Orthogonality: Any Other Way?
• Yes, if we consider only discrete-time signals
• Let c1(t) and c2(t) both of duration T be such thattheir cross-correlation = 0 when time-aligned
• Let signal_1 be x1 and signal_2 be x2 in [0,T]
• Consider sum_signal(t)= x1c1(t)+ x2c
2(t)
⇒ xi can be extracted by correlating with ci(t)
∫ =T
dt)t(c)t(c0
21 0
]dt)t(c[xT
i
i ∫0
2
=∫T
i dt)t(c).t(signal_sum0
Dr Bhaskar Ramamurthi CDMA_Wireless_Course 6
Principles of Spread Spectrum and CDMA
• How many orthogonal functions ci(t) can we get?
• Landau-Pollak Theorem: N∼ 2WT whereW is the bandwidth available
⇒ given symbol duration T,
N ∼ W / (1/T)
↑bandwidth expansion factor
• ci(t) have to be time-aligned, i.e. synchronous
• signals overlap in time and frequency
Orthogonality (contd..)
time
code
freq
Dr Bhaskar Ramamurthi CDMA_Wireless_Course 7
Principles of Spread Spectrum and CDMA
Orthogonal Direct-Sequence Code Division Multiplexing
• c i(t) are binary-valued sequences such that
− i.e., ci(t) = where = {0,1},
and Tc is the chip period = T/Lc
• equivalently
• are called codes, hence the terms CDMA andsynchronous CDM
∫ =T
ji dt)t(c)t(c0
0
∑−
=−−
1
0
12cL
kc
ik )Tt(h)c(
}c{ ik
∑−
==
1
0
cL
kc
jk
ik LcXORc
kic
Dr Bhaskar Ramamurthi CDMA_Wireless_Course 8
Principles of Spread Spectrum and CDMA
Orthogon al CDM (contd…)
• Example : Walsh codes
• used in IS-95
10
00
0110
1100
1010
0000 H 2n-1 H2
n-1
H2n-1 H2n-1
H2
H22
H2n
H26
Dr Bhaskar Ramamurthi CDMA_Wireless_Course 9
Principles of Spread Spectrum and CDMA
Asynchronous CDMA• in orthogonal CDM, codes are synchronised
⇒ difficult to ensure between independent transmittersat variable distances from receiver (i.e, multipleaccess)
• synchronous orthogonal codes can have largecorrelation when not synchronised
⇒ not used in CDMA
• employ pseudo-random or pseudo-noise (PN)sequences
⇒ typically, low but non-zero correlation between any twosequences
⇒ quasi-orthogonal codes
x11 x2
1
x12 x2
2
Dr Bhaskar Ramamurthi CDMA_Wireless_Course 10
Principles of Spread Spectrum and CDMA
Asynchronous CDMA (contd..)
• even chip alignment will not be there
• if {bk} and {ck} are two truly-random binary sequences
of length Lc, and cross-correlation β =
• E[β] = 0 and E[β 2] = Lc
⇒ interference power from (N-1) signals ∝ (N-1)
• For the signal we desire to extract,
desired_signal power =
⇒ undesired per-user interference suppressed byfactor 1/Lc on the average
− for large N, variation around average will be less
∑ −−−
=
1
01212
cL
kkk )c()b(
cL
21
0
21212 c
L
kkk L)]c)(c([
c
=∑ −−−
=
Dr Bhaskar Ramamurthi CDMA_Wireless_Course 11
Principles of Spread Spectrum and CDMA
• A fading channel has deep nulls in its frequency response≡ multiple paths taken by signals from Tx to Rx
Signalling over Fading Channels
τ t
Imp. Resp
1/2τ f
Freq. Resp
τ t
Imp. Resp
1/2τ f
Freq. Resp
destructive interference
• Only a small part of a wideband signal’s spectrum is severelydistorted by the nulls
− in FDM or OFDM, a (narrowband) signal located aroundf= 1/2 τ will be lost
• multipath leads to Inter Symbol Interference if τ ~T (symbolduration)
− in TDM, T is small ⇒ tolerable delay spread is less
Dr Bhaskar Ramamurthi CDMA_Wireless_Course 12
Principles of Spread Spectrum and CDMA
• c(t) spreads a narrowband signal uniformlyover a band T/Tc larger
⇒ C(f) must be flat and wide
⇒ Rcc(τ) must be impulse like
• multipath signal α1x1 c(t) + α2x1c(t- τ )correlated with c(t)
⇒ α1x1 Rcc(0) + α2x1 Rcc(τ) ≈ α1x1Rcc(0) if τ > Tc
⇒ delayed signal is suppressed for delay > Tc
• for slow frequency hopping, some bursts ofsymbols falling in spectral nulls are affected
⇒ employ coding across bursts to overcome this
Spread Spectrum Signalling and Fading
C(f)
convolution is uniform wideband
f
Dr Bhaskar Ramamurthi CDMA_Wireless_Course 13
Principles of Spread Spectrum and CDMA
• estimate path delays greater than Tc in a multipath channel• implement one correlator for every significant path :
RAKE receiver
Spread Spectrum Diversity
c1(t)
c1(t-τ1)
c1(t- τ2)
combine
path gains
∫T
0
∫+ 1
1
τ
τ
T
∫+ 2
2
τ
τ
T
RAKE RECEIVER
Dr Bhaskar Ramamurthi CDMA_Wireless_Course 14
Principles of Spread Spectrum and CDMA
• each finger will give α i Rcc(0) x1
⇒ combine to get better decision on x1
• ISI has been resolved and converted todiversity gain
• if path gains [α i ] are also estimated, can weighteach finger proportionately
⇒ “maximal ratio” combining
else “equal gain” combining
SS Diversity (contd…)
Dr Bhaskar Ramamurthi CDMA_Wireless_Course 15
Principles of Spread Spectrum and CDMA
• multiple transmissions on same carrier with differentcodes can be combined
⇒ signals from two base stations can be combined during handoff
Multi-Transceiver (Macro) SS Diversity
c(t)
b(t)∫T
0
∫+τ
τ
T
combinerα1x1 c (t)+ α2x1b(t - τ)
Dr Bhaskar Ramamurthi CDMA_Wireless_Course 16
Principles of Spread Spectrum and CDMA
• The fingers of a RAKE receiver need not be fed by same RFfront-end
⇒ different transceivers at same base station(e.g., adjacent sectors)
⇒ different base stations!
Macro Diversity (contd…)
combiner∫+τ
τ
T
∫T
0
RF
c(t)
c(t-τ)
RF
Dr Bhaskar Ramamurthi CDMA_Wireless_Course 17
Principles of Spread Spectrum and CDMA
• codes employed have low autocorrelation sidelobes, andtypically low cross correlation also
• assume all signals arrive with equal power
⇒ perfect power control at Tx to counteract path loss and fading
• desired_signal energy at each RAKE finger ∝ Lc2
• sum of undesired-signal (interference) energies at eachRAKE finger ∝ NLc
• if MAI is approximated as Gaussian for large N,
⇒ variance of MAI = NLc
⇒ Carrier-to-Interference Ratio (CIR) = Lc / N
Multi-Access Interference in CDMA
Dr Bhaskar Ramamurthi CDMA_Wireless_Course 18
Principles of Spread Spectrum and CDMA
• effect of bandpass transmission
- since each interferer will have a random phaseoffset (actually, small frequency offset),MAI will be less
E[cos2ϕ] = 0.5 for uniformly distributed ϕ
• effect of chip mis-alignment − if interference is y1 for left alignment and
y2 for right alignment,actual interference α y1 + (1- α) y2 where αis uniformly distributed in [0,1]
E{[α y1 + (1- α)y2]}2 = (1/3) [Ey12 + Ey2
2] = 2Lc/3
• Net effect : CIR increases by a factor of 3
• For large cells, thermal noise adds to MAI near cell boundaries : CINR drops
Refinement of MAI Computation
y1
y2
Dr Bhaskar Ramamurthi CDMA_Wireless_Course 19
Principles of Spread Spectrum and CDMA
• BS employ sectoral antenna⇒ downlink adjacent cell interference reduced⇒ uplink uncontrolled interference from
adjacent cells reduced
• capacity improvement factor vis-à-vis circular cell = η × 360o/ sectoral angle (η = 2.8 (4.5) for 3 (6) sectors)
• sectoral gain improves link budget in noise-limited situation⇒ no impact in interference-limited case
• uncontrolled adjacent sector interference reduces capacity by 0.6
⇒ ~ 0.6 x 60 x η (~35 η) users per cell with variable rate coding
Sectoring Reduces MAI
Dr Bhaskar Ramamurthi CDMA_Wireless_Course 20
Principles of Spread Spectrum and CDMA
• if an interferer’s power is higher by, say, 10 times
⇒ equivalent to 10 interferers of equal power
⇒ CIR drops dramatically
• need to control power of each user to ±0.5dB,
- use combination of open-loop and closed-loopcontrol
• path loss due to shadowing similar on up anddown links even if frequencies are different
⇒ open-loop control of Tx power based on local Rx signal strength
Power Control in CDMA
Dr Bhaskar Ramamurthi CDMA_Wireless_Course 21
Principles of Spread Spectrum and CDMA
• fading will be different in up and down link (differentfrequencies)
⇒ closed-loop control of Tx power based on feedback from far-end Rx
- usually a low bitrate binary signal :1/0 → up/down by 0.5 dB
Power Control in CDMA (contd…)
Rx
Tx
duplexer
Open loop
Rx
Tx
Dplx
Closed loop
control
Tx
Rx
Dplx
feed
back
Dr Bhaskar Ramamurthi CDMA_Wireless_Course 22
Principles of Spread Spectrum and CDMA
• individual signal is bursty with activity factor γ
− bursts occur randomly
• for large N, total “traffic” at any time t isequivalent to γ N non-bursty signals
• in CDMA, MAI from M bursty signals is notNPTX/Lc, but γ NPTX/Lc for large N
• if variable rate voice coder employed
⇒ γ ∼ 0.4, N ∼20-30 sufficiently large
• for IP packets, γ ∼ 0.1 or less, but N has to be muchlarger due to long-tailed distributions of ON/OFF periods
Statistical Multiplexing in CDMA
t
Dr Bhaskar Ramamurthi CDMA_Wireless_Course 23
Principles of Spread Spectrum and CDMA
• spread spectrum diversity- multipath, macro
• statistical multiplexing easily exploited- large number of quasi-orthogonal codes
⇒ large number of bursty users• easy to support a variety of bit-rates
e.g; if chip rate is 2.048 Mbps service at n kbps, has a spreading factor of 2048/n
⇒ n can be any power of 2
• strict power control required- combination of open and closed loop control
• difficult to hand over from one carrier to another- seamless handoff not possible between carriers, similar to FDM
Pros and Cons of CDMA