1 multi-user detection gwo-ruey lee. wireless access tech. lab. ccu wireless access tech. lab. 2...
TRANSCRIPT
![Page 1: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/1.jpg)
1
Multi-user Detection
Gwo-Ruey Lee
![Page 2: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/2.jpg)
2
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Outlines
Multiple Access Communication Synchronous CDMA Model/ Asynchronous CDMA Model Single-user Matched Filter Optimum Multi-user Detection Decorrelating Detector Non-Decorrelating Linear Multi-user Detection Decision-Driven Multi-user Detection
![Page 3: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/3.jpg)
3
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Multiple Access Communication
Several transmitters share a common channel, e.g., mobile telephones transmitting to a base station ground stations communicating with a satellite, ...
![Page 4: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/4.jpg)
4
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Multiple Access Communication
The receiver obtains the superposition of the signals sent by the active transmitters
Receiver
User 1
User 2
User 3
User 4
User K Noise
![Page 5: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/5.jpg)
5
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Multiple Access Communication
Frequency Division Multiple Access (FDMA) FDMA assigns a different carrier frequency to each user so that
the resulting spectra so not overlap
![Page 6: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/6.jpg)
6
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Multiple Access Communication
Time Division Multiple Access (TDMA) In TDMA, time is partitioned into slots assigned to each
incoming digital stream in round-robin fashion. Synchronization is required.
![Page 7: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/7.jpg)
7
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Multiple Access Communication
Code Division Multiple Access (CDMA) Users are assigned different signature waveforms.
Each transmitter send its data stream by modulating its own signature waveform as in a single-user digital communication system.
![Page 8: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/8.jpg)
8
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Multiple Access Communication
Code Division Multiple Access (CDMA) Direct Sequence Spread Spectrum (DS-SS)
![Page 9: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/9.jpg)
9
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Multiple Access Communication
Code Division Multiple Access (CDMA) Frequency Hopping Spread Spectrum (FH-SS)
![Page 10: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/10.jpg)
10
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Multiple Access Communication
Near-far problem: Any interferer that is sufficiently powerful receiver
causes arbitrarily high performance degradation.
The objective of multi-user detection is: the design and analysis of digital demodulation in the
presence of multi-access interference (MAI).
![Page 11: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/11.jpg)
11
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Synchronous CDMA Model
Basic Synchronous CDMA Model
where is the inverse of the data rate. is the deterministic signature waveform assigned to the
k-th user. It is normalized such that
is the received amplitude of the k-th user's signal. is the bit transimitted by the k-th user. is the white Gaussian noise, which is uncorrelated with
the transmitted signals, and has unit power spectral density.
1
, 0,K
k k kk
y t A b s t n t t T
T ks t
2 2
01
T
k ks t s t dt
kA
n t 1, 1kb
![Page 12: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/12.jpg)
12
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Synchronous CDMA Model
b1
A1s1(t)
b2
A2s2(t)
bK
AKsK(t)
...
y(t)
n(t)
1
( ) ( ) ( ), [0, ].K
k k kk
y t A b s t n t t T
![Page 13: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/13.jpg)
13
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Synchronous CDMA Model
The crosscorrelation of two signature waveforms, and , is
By Cauchy-Schwarz inequality, the crosscorrelation satisfies
The cross correlation matrix, defined by
has diagonal elements equal to 1 [see (29) and (30)], and is symmetric nonnegative definite, i.e.,
is t js t
0
,T
ij i j i js t s t s t s t dt
, 1ij i j i js t s t s t s t
ij
, , 1, 2,..., ijR i j K
2
1
0K
Tk k
k
a Ra a s t
![Page 14: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/14.jpg)
14
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Asynchronous CDMA Model
Basic Asynchronous CDMA Model
where are the time offsets that correspond to users
One special case happens when then asynchronous model reduces to synchronous model
Another special case happens when and (a single user undergoes multipaths), it becomes
1 1
, - 2K M
k k k kk i
y t A b i s t iT n t MT t MT T
1 20 K T 1,2, , K
1 20 ,K
1 2 ,KA A A A 1 2 ,Ks k s k s k s t
1k
K T
K
1 1
1
1, - 2
,
K M
kk i
MK K
j MK
K Ty t Ab i s t iT n t MT t MT T
K
TAb j s t j n t
K
1 kb iK k b i
![Page 15: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/15.jpg)
15
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
CDMA Model
Direct-sequence spread spectrum Direct-sequence waveforms
where is the chip waveform that satisfies
and
N is the number of chips per bit N,
1 1
1 11 1i
c i c
N Nc
T c k T c ci i
s t P t i T d P t iT TN N
cTP t
1, 0
0, 1,2,...p c
nR nT
n
c cP T TR P t P t dt
1 2, , , , 0,1 , , is the binary sequence (code)N ic c c c i 1, 1 , 1,2, , and 1,2, ,
ikd k K i N
![Page 16: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/16.jpg)
16
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Single-user Matched Filter
Consider the synchronous CDMA model, where only a single user exist:
The signal listed above is passed through a linear filter, the output of which is then sampled at T
, 0y t Abs t n t t T
, , , 0y t Ab s t h t n t h t t T
![Page 17: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/17.jpg)
17
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Single-user Matched Filter
One problem is: Find the linear filter h(t) that maximize the signal-to-noise ratio at the filter output Y , i.e.,
By Cauchy-Schwarz inequality, we have
22
2
222
, ,max
,h t
E Ab s t h t s t h tAJ
h tE n t h t
2 2 2 2,s t h t s t h t h t
![Page 18: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/18.jpg)
18
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Single-user Matched Filter
The objective function satisfies , where the equality holds when
Notice that in this derivation, we did not invoke the fact that noise is Gaussian.
Note that is a Gaussian r.v. with zero-mean and unit variance.
2
2
AJ
, 0h t s t t T
,n t s t
, ,
,
Y Ab s t s t n t s t
Ab n t s t
![Page 19: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/19.jpg)
19
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Single-user Matched Filter
The probability of error, in determining from , is
b Y
2 2
2 2
0
| 1 | 10
2 2
1 1 1 1
1 1
2 2
1 1 1 1
2 22 2
Y b Y b
v vA
A
AQ
P error P b P error b P b P error b
f v dv f v dv
Ae dv e dv Q
A
A
![Page 20: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/20.jpg)
20
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Single-user Matched Filter
Single-user Matched Filter in Rayleigh Fading single user model
Assuming that A and s(t) are given, we want to find the estimate of b, , that minimizes
The first and second terms on the RHS of above equation are irrelevant to b, and we can write the minimization problem as a maximization problem:
, 0y t Abs t n t t T
ˆ 1, 1b
2 2 2 *
0 0 0 0
T T T Ty t Abs t dt y t dt As t dt y t Abs t dt
*
* *
01, 1 1, 1max max
T
b b
y
Ab y t s t dt b Ay
![Page 21: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/21.jpg)
21
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Single-user Matched Filter
The solution to
*ˆ sgnb Ay
![Page 22: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/22.jpg)
22
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Single-user Matched Filter
Discrete-time Synchronous Models Multi-user detection commonly have a front-end,
whose objective is to obtain a discrete-time process from the received continuous-time waveform y(t).
Matched filter outputs
. . .Sync K
. . .Sync 3
. . .Sync 2
. . .Sync 1
Matched FilterUser 1
Matched FilterUser 1
Matched Filter User 2
Matched Filter User 2
Matched Filter User 3
Matched Filter User 3
Matched Filter User K
Matched Filter User K
y(t)
y1
y2
y3
yK
......
![Page 23: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/23.jpg)
23
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Single-user Matched Filter
In the synchronous case, the outputs of the bank of matched filters are
0
01
0 01
, 1, 2,...,
, 1, 2, ,
jk k
T
k k
KT
j j j kj
K T T
j j j k kj
n
k k j j jk kj k
y y t s t dt k K
A b s t n t s t dt
A b s t s t dt n t s t dt
A b A b n k K
![Page 24: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/24.jpg)
24
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Single-user Matched Filter
The vector form of above equation is
where
and n is a zero-mean Gaussian random vector with covariance matrix equal to , i.e.,
y RAb n
1 2
1 2
1 2
, , ,
, , ,
, ,
T
K
jk
K
T
K
y y y y
R
A diag A A A
b b b b
2TE nn R
0 0
2 2
0 0
j k
T T
j k j k
n n
T T
j k jk
E n n E n s d n s d
E n n s s d d
![Page 25: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/25.jpg)
25
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Maximum A Posteriori (MAP) and Maximum Likelihood (ML) Detectors
The MAP-detector chooses the hypothesis that maximizes the a posteriori probability, and achieves the minimum probability of error.
The ML-detector chooses the hypothesis that maximizes the likelihood function, it achieves the minimum probability of error, when the hypotheses are equally probable (P0 = P1).
1
1 0
0
| 1 | 0| |
H
H r H r
H
P H r P H r
1
1 0
0
| 1 | 0| |
H
r H r H
H
P r H P r H
![Page 26: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/26.jpg)
26
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Maximum Likelihood (ML) Detectors
![Page 27: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/27.jpg)
27
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Maximum Likelihood (ML) Detectors
![Page 28: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/28.jpg)
28
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Maximum Likelihood (ML) Detectors
![Page 29: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/29.jpg)
29
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Maximum Likelihood (ML) Detectors
![Page 30: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/30.jpg)
30
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Maximum Likelihood (ML) Detectors
Are they the same?
![Page 31: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/31.jpg)
31
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Individual Optimum ML-Detector
![Page 32: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/32.jpg)
32
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Individual Optimum ML-Detector
![Page 33: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/33.jpg)
33
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Individual Optimum ML-Detector
![Page 34: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/34.jpg)
34
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Joint and Individual Optimum ML-Detector for the K-User Scenario
Recall the discrete-time synchronous CDMA model that
The joint optimum ML-detector is the solution to
, 0y t Abs t n t t T
11/ 2 2/ 2 2
1
1 1max | exp
22
max
max 2
T
Kb
T
b
T T
b
P y b y RAb R y RAbR
y RAb R y RAb
b Ay b ARAb
![Page 35: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/35.jpg)
35
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Joint and Individual Optimum ML-Detector for the K-User Scenario
The maximization problem is a combinatorial optimization one, which means that the set of possible arguments comprises a finite set.
Combinatorial optimization problems can always be solved by exhaustive search, i.e., we evaluate the objective function at all possible arguments, and select our detected value to be the argument that produces the maximum.
Joint optimum decisions would be preferable to minimum bit-error-rate decisions due to their complexity.
![Page 36: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/36.jpg)
36
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Decorrelation Detector
Recall that the output vector of the bank of K matched filters is
Assume that R is invertible.
Premultiplying by give
In the absence of noise n, the k-th component of
is The decorrelating detector detects through
y RAb n
1R
1 1R y Ab R n
1R yk kA b
kb
1sgnk
R y
![Page 37: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/37.jpg)
37
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Decorrelation Detector
. . .Sync 3
. . .Sync 2
. . .Sync 1
Matched FilterUser 1
Matched FilterUser 1
Matched Filter User 2
Matched Filter User 2
Matched Filter User 3
Matched Filter User 3
Matched Filter User K
Matched Filter User K
y(t) R-1R-1
......
][1 ib
][2 ib
][3 ib
][ˆ ibK . . .Sync K
![Page 38: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/38.jpg)
38
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Decorrelation Detector
Note that the decorrelating detector is influenced by additive noise, and not by other interferers ( ).
Two features of the decorrelating detectors are 1. It does not need to know the received amplitudes (
). 2. Detection of each user can be implemented
independently.
Note that
, jb j k
, iA i
1 1 1
1 1
1
1
,
, ,
K K
j jk kj kjj j
K
j kkjj
R y R y R y t s t
y t R s t y t s t
![Page 39: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/39.jpg)
39
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Decorrelation Detector
From the fact that
We know that is orthogonal to any linear combination of .
If is linearly independent, we can find from for all k, and can have the modified decorrelating detector.
1
1
1 1
1 1
1
1
, ,
,
, ,
K
k l j ljkj
K K
j l ljjk jkj j
K
lklkj
s t s t R s t s t
R s t s t R R
RR l k
ks t j j k
s t ks t
js t
, ky t s t
![Page 40: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/40.jpg)
40
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Decorrelation Detector
Modified decorrelating detector
. . .Sync 3
. . .Sync 2
. . .Sync 1
Matched FilterMatched Filter
Matched FilterMatched Filter
Matched FilterMatched Filter
Matched FilterMatched Filter
y(t)
......
][1 ib
][2 ib
][3 ib
][ˆ ibK . . .Sync K
1s
2s
3s
Ks
![Page 41: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/41.jpg)
41
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Decorrelation Detector
In the two user scenario,
![Page 42: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/42.jpg)
42
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Decorrelating Detector and ML-Criterion
![Page 43: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/43.jpg)
43
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Non-Decorrelating Detector - LMMSE
![Page 44: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/44.jpg)
44
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Non-Decorrelating Detector - LMMSE
. . .Sync 3
. . .Sync 2
. . .Sync 1
Matched FilterUser 1
Matched FilterUser 1
Matched Filter User 2
Matched Filter User 2
Matched Filter User 3
Matched Filter User 3
Matched Filter User K
Matched Filter User K
y(t) [R+2A-2]-1[R+2A-2]-1
......
][1 ib
][2 ib
][3 ib
][ˆ ibK . . .Sync K
![Page 45: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/45.jpg)
45
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Properties of the LMMSE Detector
![Page 46: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/46.jpg)
46
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
LMMSE Detector for the Bank of Orthonormalized Filters
![Page 47: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/47.jpg)
47
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
LMMSE Detector Maximizes Signal to Interference Ratio
![Page 48: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/48.jpg)
48
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Minimum Output Energy Detector
![Page 49: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/49.jpg)
49
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Successive Cancellation
![Page 50: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/50.jpg)
50
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Successive Cancellation
1 1
2 2 2 1
1 2 2
1 2 2
1 1 2 2 2 1
ˆ ˆsgn( , )
ˆ sgn ( ) ( ),
ˆ sgn( )
sgn( sgn( ))
ˆ sgn( ( )) , )
b y s
y t A b s t s
y A b
y A y
Ab A b b n s
2 2
ˆ sgnb y
2 2 2
1 1 1 2 2 2 2
ˆˆ( ) ( ) ( )
ˆ
y t y t A b s t
Ab s t A b b s t n t
1 1 2ˆ sgn( )b y y
2
1( ) ( ) ( )k k kk
y t A b s t n t
k k k ky A b n
![Page 51: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/51.jpg)
51
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Successive Cancellation
Equivalent implementation of successive cancellation for two synchronization users
![Page 52: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/52.jpg)
52
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Successive Interference Cancellation (SIC)
It requires knowledge of the received amplitude. User weaker than the user (or users) of interest are
neglected. In contrast to the (nonadaptive) multi-user linear
detectors, successive cancellation require no arithmetic computations with the crosscorrelation beyond their product with the received amplitudes.
The time complexity per bit is linear in the number of user
It applies not only to the basic CDMA model (where signals
are linearly modulated) but to any multiple-access channel where the receiver observes the additive superposition of the transmitted signal.
The demodulation delay in successive cancellation grows linearly with the number of user.
![Page 53: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/53.jpg)
53
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Partial Parallel Interference Cancellation (PPIC)
Multistage PPIC detection scheme with the discrete-time equivalent complex
baseband representation for synchronous CDMA systems.
![Page 54: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/54.jpg)
54
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Partial Parallel Interference Cancellation (PPIC)
Discrete-time signal r(m) at the chip rate
Decision statistic of the ith bit of the conventional receiver for the kth user
),()(
),()(
)()()(
1
1
1
memabA
mmbA
mmAm
kjK
kkkk
K
kkkk
K
kkk
n
na
nsr
iN
Nimkik mm
NZ
1)1(
*, )()(
1ar
![Page 55: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/55.jpg)
55
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Adaptive NLMS-PPIC
.
.
.
)1(,1 ib )(ˆ )1(
1 ms
y(m-N)Delay
N
a1(m)exp(-j1)
aK(m)exp(-jK)
1A a1(m)exp(j1)
KA aK(m)exp(jK)
)1(,
ˆiKb
.
.
.
.
.
.
.
.
.
wK(1)
w1(1)
)(ˆ )1( mKs
Stage 1 Stage 2
)2(,1 ib
)2(,
ˆiKb
y(m)
Delay
N
.
.
.
…y1
(1)(m-2N)
yK(1)(m-2N)
aK(m)exp(-jK)
a1(m)exp(-j1)
Normalizeed LMS
algorithm
K
k 2
)(
Delay
N
Delay
N
…
iN
NiT 1)1(
)(1
1
1
)(K
k
iN
NiT 1)1(
)(1
iN
NiT 1)1(
)(1
iN
NiT 1)1(
)(1
.
.
.
![Page 56: 1 Multi-user Detection Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech. Lab. 2 Outlines Multiple Access Communication Synchronous CDMA](https://reader036.vdocument.in/reader036/viewer/2022062515/56649c9d5503460f9495cada/html5/thumbnails/56.jpg)
56
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
Multi-user Detection
Readings SERGIO VERDU, Multi-user Detection, CAMBRIDGE,
1998. Chapter 2 – 2..1, 2.2, 2.9 Chapter 4 – 4.1 Chapter 5 – 5.1 Chapter 6 – 6.1, 6.2 Chapter 7 – 7.1