Multiuser detection techniques for Code-Division Multiple ...read.pudn.com/.../comm/wireless/812502/report.pdf · EE359 Final Project Report Wireless Communications Frederic SARRAT

EE359 Final Project Report Wireless Communications Frederic SARRAT – SUID 4898581

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EE359 Project Report

Multiuser detection techniques for Code-Division Multiple Access

by Frederic Sarrat

Stanford University Dec 8th, 2002


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I. CDMA description_____________________________________________________ 3

1. Multiple access techniques....................................................................................................3 1.1 The main multiple access schemes ....................................................................................3 1.2 Code-Division Multiple Access.........................................................................................3 1.3 Code generation ................................................................................................................5

2. Theoretical analysis of CDMA (Code Division Multiple Access).......................................8 2.1 Single user .........................................................................................................................8 2.2 Multiple Users .................................................................................................................10

3. Multi-user reception............................................................................................................12 3.1 Basic principles of multi-user detection...........................................................................12 3.2 Conventional detection...................................................................................................13 3.3 Linear detectors. ..............................................................................................................16 3.4 Non-linear detectors ........................................................................................................19 Conclusion ............................................................................................................................23

II. Simulating the different receiver in real communication channels _____________ 24

1. Simulation framework ........................................................................................................24 1.1 Single user bound ...........................................................................................................24 1.2 Codes matrix ..................................................................................................................25 1.3 Simulation Parameters.....................................................................................................25 1.4 Rayleigh fading channel generation ................................................................................26

2. The conventional receiver...................................................................................................26

3. Performance comparison with perfect power control ......................................................32 3.1 System Capacity..............................................................................................................32 3.2 Receivers performance comparison in AWGN................................................................34

4. Real channel impairments ..................................................................................................35 4.1 Near-far situation.............................................................................................................35 4.2 Flat Rayleigh fading channel...........................................................................................37 4.3 Flat Rayleigh fading channel...........................................................................................38

Conclusion ___________________________________________________________ 40


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I. CDMA description

1. Multiple access techniques We recall here the different techniques used to assign dedicated channels to multiple users through bandwidth division 1.1 The main multiple access schemes The radio channel has a very important specificity. Not considering highly directional antennas, the signal transmitted by a user can be received by any receiver close by. While this can be a very attractive feature for applications such as broadcasting, it is a problem for one-to-one mobile communications. The main methods to divide the spectrum include frequency-division, time-division, and code-division.

Frequency domain: Signals occupying non overlapping frequency bands can be easily separated, and provided that the carrier frequencies are sufficiently spread apart from each other, the different transmitted signals do not interfere with each other. This technique is called FDMA (Frequency Division Multiple Access).

Time domain : Signals can be transmitted on non-overlapping timeslots. All users share the same bandwidth, but they do not emit at the same time. Synchronization is required for this technique called TDMA (Time Division Multiple Access).

Code domain : in CDMA (Code Division Multiple Access), the users send signals which are uncorrelated. Using a bank of matched filter, each individual signal can be recovered. This is the technique that we want to study.

1.2 Code-Division Multiple Access In CDMA systems, several users have access to a shared channel on which they can transmit simultaneously. The capacity of the system depends on the codes that are used. Orthogonality of the codes ensures that interference is limited between users, but yields a hard limit on how many users can have a distinct code at the same time. Otherwise, capacity is interference-limited. CDMA is a spread spectrum technique that has been used for many years, in military applications because of the security inherent to it. It consists in spreading the signal at the transmitter over a larger bandwidth. Ideally, it becomes invisible to other users. At the receiver, the inverse operation is performed to recover the original signal, while interfering signals are considered as noise, and mainly suppressed by the matched filter.


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Power spectral density before and after spreading

Two spread spectrum techniques can be used for CDMA systems :

• FH / CDMA (Frequency Hopping) • �DS / CDMA (Direct Sequencing)

In the frequency-hopping protocol, the carrier frequency of the modulated signal periodically changes, according to a scheme defined by the code. We will study direct sequencing CDMA, in which a pseudo-random spreading sequence is used to modulate the transmitted signal in such a way that the resulting signal has the same bandwidth as the rate of the spreading sequence. Intercorrelations among signals are thus highly determined by the intercorrelations among sequences. In the CDMA protocol, the data signal is directly modulated by a digital code signal, and the resulting signal modulates the broadband carrier. That’s where the name Direct Sequencing comes from. In systems with N users, all the signals are summed either in the channel, or in the base station. The resulting signal is a spread signal with the same bandwidth as each of the signals. To “un-spread” the signal, not only must the receiver know the code sequence, but also, it must synchronize this sequence with the received signal.

Before spreading

Signal bandwidth Same area = same power

After spreading

Chip bandwidth


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1.3 Code generation

a) Tree

The codes used to differenciate the channels are Orthogonal Variable Spreading Factor codes. The correlation between any two codes of this family is zero. They can be defined using a tree. The underlying principle is the following :

A root yields two branches. Codes on each of these branches come from the root code. Indeed, the code of a branch is made of the root code, and its complementary code. Using this principle, we can generate, the OVSF code tree.

Direct Sequencing Modulation

A

AA

AA

Root 2 branches


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The spreading factor (SF) is equal to the length of the code used. This means that SF can only take

values that are powers of 2. This tree also shows the relationship between the number of available codes and the spreading factor. To use orthogonal codes, it is necessary to respect certain rules. In a cell, one cannot use all OVSF codes simultaneously. They are indeed not orthogonal to all others. A code in a branch is correlated to the one on its root. Thus, a simple root to use this tree is the following. When a code is allocated, all codes located either on the root path of this branch or on branches deriving from the one chosen must be discarded.

In this figure, C4,1 is allocated, thus codes derived from this one cannot be used : C8,1, C8,2, etc. The same way, codes located up towards the root of the tree cannot be used either.

b) Generation using the Hadamard matrix

1 1

1 1 1 1

1 1 –1 -1

1 –1 –1 1

1 –1 1 -1

1

1 -1

SF=8 SF=4 SF=2 SF=1

1 1

1 1 1 1

1 1 –1 -1

1 –1 –1 1

1 –1 1 -1

1

1 -1

SF=4 SF=3 SF=2 SF=1


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[ ]

=

=

==

01101100

10100000

10

000 4221 H

HH

HH

HHH

NN

NN

N

Fig.: The Hadamard Matrix

Each line of Hn represents a code. The codes generated this way are orthonormal.


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2. Theoretical analysis of CDMA (Code Division Multiple Access)

User codes have to be used to modify the original signal. We will define here a formal model for this technique, that we will use later in simulations 2.1 Single user Before we move on to the more intersting case of multiple users, let’s define the notations for the case of a single user. Let y(t) be the transmitted signal. It can be written as :

∑+∞

−∞=

−=n

Tsntwnsty ).().()( [1]

where s(n) is the digital signal, and TS is the bit duration w(t) is the code signal :

∑=

−=Lc

k

Tcktpkctw1

).().()( [2]

Where

- c(k) are the elements of the code vector (of length LC) ; c(k) =±1 - TC is the duration of a code bit - p(t) is the pulse signal. For simplification, we will use a rectangular impulse of height 1

and duration TC

Transmitter á+

+

Receiver

AWGN


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The relationship SF = TS/TC (SF : spreading factor), representing the maximum number of users. Each symbol in s(n) is decomposed into LC bits. Each symbol can hence be represented as a vector:

)(.

)(

...

)2(

)1(

),(

....

)2,(

)1,(

)( ns

Lcc

c

c

Lcny

ny

ny

ny

=

= [3]

where y(n,i)=y(nTS+i.TC) Thus we can write the received signal as a vector:

)().().()( tnTsntpnytyn

+−= ∑ [4]

where n(t) is the additive white gaussian noise and p(t) is a pulse of duration TS. This formula does not accounts for attenuation in the channel. We can thus add a coefficient á(t), to consider attenuation and/or flat Rayleigh fading

∑=

−=Lc

k

Tcktptkctw1

).().().()( α [5]

Each user will have a different attenuation coefficient, depending on its position in the cell and the fading it is experiencing.

p(t)

1

0 Tc t


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2.2 Multiple Users We now want to study the case of multiple users in the transmission channel. In the general case, the maximum number of users in the channel is equal to the spreading factor, which is the number of different codes that are used.

Let y be the vector containing all components in the transmission channel at time n. This vector can be expressed the following way:

sAcy ∗∗= [6]

where c is a matrix of dimension SFxSF containing the orthogonal codes for each user:

[ ]cccc SF 110 −= L [7]

−

=

−

=

−

=

−

−

−

−

)1(

)2(

)1(

)1(

)2(

)1(

)1(

)2(

)1(

1

1

1

1

1

1

1

1

0

0

0

0

LcLcLc c

cc

c

c

cc

c

c

cc

c

SF

SF

SF

SF

LLL [8]

Thus, the matrix can be written:

−−−

=

−

−

−

)1()1()1(

)2()2()2(

)1()1()1(

110

110

110

LcLcLc ccc

cccccc

c

SF

SF

SF

L

LLLL

L

L

[9]

A is a diagonal matrix containing the attenuation coefficients ái for each user. This matrix has dimension SFxSF as well.

=

−α

αα

1

1

0

SF

A

LLL

LLLL

LLL

LLL

[10]

Eventually, s is a vector of dimension SFx1 containing the emitted symbol for each userat time n.


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=

−)(

)(

)(

1

1

0

n

n

n

s

ss

s

SF

L [11]

Hence equation [6] can be written:

−−−

=

−

=

−−−

−

−

)(

)(

)(

**

)1()1()1(

)2()2()2(

)1()1()1(

)1,(

......

)1,(

)0,(

1

1

0

1

1

0

110

110

110

n

n

n

LcLcLcSFny

ny

ny

s

ss

ccc

cccccc

y

SFSFSF

SF

SF

LLLL

LLLL

LLL

LLL

L

LLLL

L

L

α

αα

[12]

and y(n,i) is the sum of the ith bit of each code sequence modulated by the signal to be transmitted at time n. It does not correspond to the user i only. Adding the white gaussian noise, we get

)()()()()(1

0, tnsAcy tttt

k

SF

kkkk

+⋅⋅= ∑−

=

[14]


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3. Multi-user reception 3.1 Basic principles of multi-user detection The practical problem that often arises in CDMA is the fact that the code sequences are not completely orthonormal, either because they are chosen not orthonormal, to avoid capacity limitation, or because the signal coming from each user at the receiver have a random delay, and thus the matched filter corresponding to one code will not totally suppress the interference caused by other signals. A conventional DS/CDMA system treats each user separately as a signal, with other users considered as noise or multiple access interference. This yields what is referred to as the near/far effect : users near the base station are received at higher powers than those far away. Thus, those for away suffer a degradation in performance, because the ration signal to interference is low. A tight power control is needed to alleviate this problem, or one can use multi-user detection techniques. Multi-user detection considers all users as signals for each others, and detect them jointly. This leads to reduced interference, and alleviates the near/far problem. Before we study the different techniques of multi-user detection, let’s list its advantages and limitations Limitations

• Multiple Access Interference caused by adjacent cells: Since multiuser used the whole spectrum, adjacent cell will experience interference ; if the codes in adjacent cells are not orthonormal to each other, for example if the same codes are re-used, there is no way to separate this interference from the signal, since the receiver does not know the code sequences.

• Difficult detection in the downlink: reasons for these difficulties are obvious. For mobile

terminals, price, size and weight requirements are stringent, and implementation of these techniques has been mostly concentrated for base stations, which moreover have the knowledge of all chip sequences.

Advantages Though it has limitations, it presents the following advantages :

• Significant increase in capacity :

• More efficient use of the power: reduced interference implies a diminution of the required transmission power, or a better cell coverage, keeping the same power, which we can use to increase the cell radius

• Less precision required for the power control : As the multiple access interference diminishes, the

Near-far problem is less of a burden, and the necessity to compensate for it by strict power control is released. Thus, the added complexity in the base stations by implementing multi-user detection systems will reduce the complexity in the mobiles.

• More efficient usage of the spectrum: Using inferior gains, the required bandwidth will be smaller

as well, and the additional bandwidth can be used either to increase the capacity, or to allow larger bit rates.


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3.2 Conventional detection 3.2.1 Received signal model The first stage of the receiver is a bank of matched filter, which yields a set of scalars yk, which can be proven to form a set of sufficient statistics. To study the multi-user receivers, we’ll use the matrix notation used in the previous section. We consider a synchronous channel with k different users. The signals yk inputs to the detectors can be written as:

kk

N

kii

kiiik bAbAy ⋅+⋅⋅= ∑≠=1

,ρ [15]

where bk(i) is the ith symbol, Ai is the channel attenuation for the path between the ith user and the receiver, ni the noise at the receiver, and ik ,ρ is the correlation between the codes used by users i and j.

dttwtwTb Tb

ikik ⋅⋅= ∫ )()(1

,ρ [16]

where Tb is a bit duration, and wk(t) is as defined previously. Note that ik ,ρ satisfy the following conditions:

≠<≤=

=ikif

ikif

ikik 10

1

,, ρ

ρ [17]

Using the matrix notation :

+

⋅

⋅

=

3

2

1

3

2

1

3

2

1

3,23,1

2,2,1

1,1,2

2

1

00

00

00

1

1

1

n

n

n

b

b

b

A

A

A

y

y

y

k

k

k

MM

L

MOM

L

L

L

MOM

L

L

M

ρρ

ρρ

ρρ

[18]

or

nbARy +⋅⋅= [19]


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For a system with K users, y, b et n are Kx1 vectors. A is a diagonal matrix with received amplitudes on the diagonal, and R is the correlation matrix, of size KxK, whose values are the correlations between each

pair of code sequences. Since ik ,ρ = *,kiρ , R is hermitian.

In order to set up the upcoming analysis, it is useful to split it into the autocorrelation part, and the intercorrelation part. Thus, equation [19] transforms into:

nbAQbAy +⋅⋅+⋅= [20]

Indeed, the correlation matrix R can be written as R=I+Q, where I is the identity matrix and Q is the intercorrelation matrix:

=

0

0

0

3,23,1

2,32,1

1,31,2

L

MOM

L

L

ρρ

ρρ

ρρ

Q [21]

Equation 20 shows that the first term is the desired one at the receiver, the second one is the multiple access interference, and the third one is the noise. 3.2.2 Optimal multi-user detection. In a channel introducing interference either between symbols or between users, it is hard to implement receivers that minimize the probability of error. Thus, when ISI occurs, we use a criterion of Maximum Likelihood Sequence Estimation. The objective of maximum-likelihood sequence estimation is to find the input sequence which maximizes the conditional probability, or likelihood of the given output sequence. For the simplified synchronous CDMA problem considered, the maximum-likelihood decision for the received signal r(t) is the vector b that maximizes

P(séquence b transmise | r(t) reçu) = P(b | r(t)) = Max [22]

This equation dictates a search over the 2K possible combinations of the components of the bit vector b. We assume all sequences to be equiprobable. Estimation and correlation must be computed for each possible transmitted sequence, and the one that yields the largest correlation is chosen to be the most likely. For asynchronous CDMA, the MLSE detector can be implemented using the Viterbi algorithm. Although the optimal detector has excellent performance, it is too complex for practical implementation, and we will not discuss it in further detail, and concentrate on sub-optimal receivers. 3.2.3 Sub-optimal multi-user detection Because of the complexity of the MLSE, many other solutions have been investigated. These solutions approximate the optimal receiver.


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We will divide the sub-optimal receivers into two main categories : the linear and non-linear detectors. In the linear case, we will study the decorrelator, and the MMSE detector. In the non-linear case, we will study the Successive interference cancellation receiver, the Multistage Parallel Interference Cancellation Receiver, and the Decision Feedback receiver. 3.2.4 Asynchronous channel Detection in an asynchronous channel yields problems that do not exist in the synchronous case. In a synchronous channel, by definition, the bits for each user are lined up in time ; hence, detection can be performed by focusing on a bit interval, independently from the others. Detection of N bits for K users is a problem of size N. But more realistic cases show interferences between the bits of a user, and those of others shifted in time. Thus, the codes are not completely orthonormal. The model chosen for the transmitted signal does not change much compared to the synchronous case, except that relative displacements between signals are added. Writing the synchronous case

∑=

+⋅⋅=K

kkkk tntctstAtr

1

)()()()()(

where Ak(t), sk(t) and ck(t) are the amplitude, the transmitted symbol, and the modulation for the kth user respectively, and n(t) represents the additive noise. We can write similarly for the asynchronous case:

∑=

+−⋅−⋅=K

kkkkkk tntctstAtr

1

)()()()()( ττ

where kτ is the time offset for user k. We can also note that the matrix model that we chose for the received signal does not change much ; we can still use the same notation as in equation [19], except the fact that now the matrix R contains the correlation between each pair of bits in a symbol for each user. The dimension of the matrix is now NK x NK. We use partial correlation, because in the asynchronous channel, codes for each bit overlap with each other. Let’s consider an example to clarify. Assume that 2 users transmit 3 bits each.


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Thus, it is equivalent to the problem of 6 users, each transmitting one bit within the time interval

123 ττ ++bT . Now, we get a 6x6 matrix R where the ki,ρ are the partial correlations between the code

associated to the bit i, and the code associated to the bit k.

=

10000

1000

0100

0010

0001

00001

6,5

5,65,4

4,54,3

3,43,2

2,32,1

1,2

ρ

ρρ

ρρ

ρρ

ρρ

ρ

R

Given this equivalence, we will now restrict ourselves to the case of synchronous channels.

3.3 Linear detectors. 3.3.1 Common elements to linear detectors The linear detectors process the input (the sufficient statistics yk) with a linear operation. At the output of the detector, we have:

ylin = Ly [23] Different choices for the matrix L will lead to different types of detectors. The simplest choice for L is to take the identity matrix:

L = I [24] This leads to a conventional detector for each user.

1 3

2

5

4 6

User 1

User 2

t

1τ 2τ 1τ+bT 23 τ+bT

Figure 3. Transmission sequence in an asynchronous channel.


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The Matched Filter Bank is one of the most important elements in the receiver, used to detect the received signal. Similarly to the case of single users, instead of only matching the pulse shape, the matched filters match the chip sequences. By simply multiplying by the corresponding sequence in each matched filter, we can recover the signal before spreading. Here we have considered a rectangular pulse shape for simplicity:

∫ ⋅Tb

k trtpTb

)()(1

[25]

A matched filter is denoted as follows :

At the output of the linear detector, a set of sign detectors are used. These boxes return +1 if their input is positive, and –1 if it is negative. 3.3.2 The decorrelator

∫Tb

Tb

1 MF

y1

y2

yk

)( 1τ−∗ tp

r(t)

MF

MF

MF

Linear

Transformation

L

)( 2τ−∗ tp

)( ktp τ−∗

y1

y2

yk

y1

y2

yk

Matched filter bank

Figure 4. Conventional Detector


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The decorrelator applies the inverse of the correlation matrix. It suppresses the entire correlation between the signals.

L = R-1 [26] Where R is as shown here:

=

1

1

1

3,23,1

2,32,1

1,31,2

L

MOM

L

L

ρρ

ρρ

ρρ

R [27]

According to equation [23], the output of the decorrelator can be written:

ydec=R-1y=R-1(RAb+n)=Ab+R-1n=Ab+ ndec [28]

We can see that we get the transmitted data multiplied by the diagonal matrix of amplitudes, and with an additional noise term ndec.

Some of the advantages of the decorrelator are:

- Significantly increases the capacity - No need to estimate the received amplitudes. - Computation cost much lower than for the maximum likelihood detector. The complexity is linear

with respect to the number of users. We can identify two main drawbacks :

- Similarly to the zero forcing equalizer in the single user case, it enhances the noise [28]. - The computation cost for inverting the matrix are high, and hard to do in real time.

3.3.3 MMSE receiver. The MMSE detector (Minimum Mean Squared Error) attempts to solve the problem of noise enhancement, by taking it into account. The linear transformation minimizes the mean squared error at the output of the detector, i.e. the following expression:

[ ]2LybE − [29]

This yields the linear transform, LMMSE

1

20

2

−

−

⋅

+= AN

RLMMSE [30]


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yMMSE = LMMSE.y [31]

The MMSE transform is a modification of the one used in the decorrelator, and the modification becomes more important when the noise power increases (relatively to the signal power). Since the receiver considers noise in the channel, generally the output of the MMSE is better than the one of the decorrelator. The two outputs converge when the signal to noise ratio goes to infinity. Unlike the previous one, a main drawback of the MMSE receiver is to require estimation of the received amplitudes and the noise level. Moreover, we still have the problem of inverting a matrix.

3.4 Non-linear detectors 3.4.1 Introduction. Another family of detectors groups non-linear transformations, also called interference cancellers. The basic premise of these detectors is to substract the estimated contributions of each user’s MAI to the signal of other users. These detectors can be implemented using multiple stages, allowing to adapt the complexity and delay of the detectors to the particular system, the more stages we have, the better the signal response will be. The problem of estimating the channel and the amplitudes of the different signals is important, to correctly estimate the MAI. We present several categories of non-linear detectors. These categories do not exclude each other ; detectors can be implemented combining different techniques:

• Successive Interference Cancellation (SIC) • Parallel Interference Cancellation (PIC)

• Decision Feedback detector (DFD)

3.4.2. Successive Interference Cancellation (SIC). The successive Interference cancellers make decision, regenerate a user’s signal and cancel it in the received signal at each step. This way, at the next step, less MAI is seen and better estimation is performed for remaining users. Figure 7 shows a simplified diagram for the first step of this detector. This step comes after a re-ordering of the signals in decreasing power order, which is not shown here. This ordering is based on the signals that come out of the conventional detector.


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First step of successive interference cancellation

1. Detect the strongest signal s1 using the conventional detector. 2. Hard decision �1. 3. Estimate the transmitted signal corresponding to �1, using:

- The bit decision. - The pseudo-random chip sequence - Delays and amplitude estimates

4. Substract � 1*A1*c to the received signal r(t), yielding a new version of the received signal r(1)(t), without the interference from user 1.

This procedure is repeated. If at each step the bit estimate � i is correct, the output of each step is:

• A bit decision for the strongest remaining user • A new version of the received signal without interference from the i strongest users

Signals are orders in decreasing power order for two main reasons :

• Cancelling the strongest signal is the most reliable cancellation • Cancelling the strongest signal has the most benefit for other signals

Thus this algorithm will not improve the MAI as seen by the first user. However, for weaker users, there will be a significant reduction in MAI.

SIC detectors have two main drawbacks:

• Each step introduces a delay of one bit, thus there must be a trade-off between the number of

users and the acceptable delay.

MF1 Décision

Tb

Amplitude estimation r(t)

r(t-Tb)

A1(t-Tb) p1(t-τ 1-Tb)

b1 ^

s1(t-Tb) ^

r(1)(t) -

+

Figure 7. First step in a SIC detector


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• Every time the channel varies, the signals must be re-ordered, which happens often in Rayleigh fading.

3.4.3 Parallel Interference Cancellation (PIC). Unlike its successive counterpart, the Parallel Interference Cancellation scheme suppresses MAI from all users simultaneously. The first stage of this detector is shown below in figure 8. This detector is often used in a multiple stage detector, such that at every stage the bit estimates are more reliable.

The inputs, b i (0), are the outputs of the conventional detector at step 0. These bits are multiplied by amplitude estimations, and spreading codes, and we obtain a delayed estimation of each user’s signal, �k(t-Tb). Then, summing all signals except one at each output creates an estimation of the MAI for the corresponding user, and can be subtracted to the received signal r(t). Assuming perfect estimation of amplitudes and delays, the result after subtraction of the MAI is the following, here is the result for the kth user:

r(t-Tb)

A1(t-Tb)

A2(t-Tb)

Ak(t-Tb)

S P R E A D I N G

∑≠1i

∑≠2i

∑≠ki

+

+

+

_

_

_

Matched

Filter

Bank

^ b2(0)

^ bk(0)

^ b1(0) ^ s1(t-Tb)

^ s2(t-Tb)

^ sk(t-Tb)

Figure 8. One step of a PIC detector for K users

^ bk(t)

^ b1(t)

^ b2(t)


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∑

∑

≠

≠

−−−−−−−−−+

−+−−−−−−=−−−

K

kibiibiibiibii

K

kibbkkbkkbkkmib

TtpTtATtbTtb

TtnTtpTtATtbTtsTtr

)().()).(ˆ)((

)()().().()(ˆ)(

ττττ

τττ

[35]

3.4.4 Decision feedback detector The decision feedback detector is characterized by two matrix transformations : a forward filter, and a feedback filter. These detectors are analogous to the decision-feedback equalizers employed in single user ISI channels. However, in addition to equalization, the decision feedback multiuser detectors employ successive cancellation. In each time frame, decisions are made in the order of decreasing user’s strength, i.e., the stronger user make decisions first, allowing the weaker users to utilize their decisions. The DFD is based on the Cholesky factorization of the correlation matrix, which yields a resulting MAI matrix that is lower triangular: R=FT .F, where F is lower triangular. Multiplying by (FT )-1 at the output of the filter bank, as we can see in figure 9, we get the following expression:

yDF = (FT )-1.(RAb + n) = (FT )-1 . (FT FAb + n) = FAb + n ZF-DF [36]

F being a lower triangular matrix, the signal of the kth strongest user is not corrupted by MAI, and can be demodulated first. This decision is then used to substract MAI from the signal of the second user, and so on. Assuming perfect estimations for F and the received amplitudes, the output for the kth user is:

∑−

=

−=1

0,,

ˆ..ˆk

iiiikkDFk bAFyb [37]

where b i= sign[ b i] are the results of detection of stronger users, detected earlier and Fk,i is the (k,i) element of the matrix F.


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The main drawback of the DF detector is the necessity to perform:

• A Cholesky transformation

• A matrix inversion for F

• Received signal amplitudes estimation Conclusion In this part of the project, we have described how useful CDMA is, along with the different techniques to implement it. The receivers presented above have complex mathematical formulation, and it is useful to simulate them to study the practical performances. This will be the purpose of the next part : simulation using MATLAB.

r(t)

Matched

Filter

Bank

(FT)-1

Decision

+ _

+ _

Decision

+ _

+ _

+ _

A1F2,1

A1F3,1

A1Fk,1

A2F3,2

A2Fk,2

b1(0)

b2(0)

bk(0)

y yDF

Figure 9. Decision Feedback Detector.


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II. Simulating the different receiver in real communication channels In the first part of this project, we’ve been describing several systems to receive and decode data transmitted over a digital wireless channel using CDMA modulation. Many parameters are involved in this problem, such as the spreading factor, the power of users, the load of the channel, and the type of receiver used, and the channel parameters. All those elements tend to. This complicated framework makes this problem more suitable to simulations than to theoretical studies, at least for this project. Thus, Monte-Carlo simulations have been run in Matlab. Performance have been measured using the rate of bit errors between the signal sent and the one decoded (BER). We will see how this BER is affected by varying the main parameters of the system. First, we’ll describe the simulation framework, and the assumptions that we made. In the second part, we’ll study the conventional detector for different system loads. In the third part, we’ll compare the capacity with the different receivers. In the fourth part, we’ll compare how the different receivers solve the near-far problem In the last part, we’ll compare how the different receivers perform in flat Rayleigh fading channels.

1. Simulation framework 1.1 Single user bound

Whatever the quality of the receivers and the channel, noise will always affect the received signal. Thus it is interesting to derive the optimal performance level, to have a bound on the performance of receivers. This bound is obtained for a single user in AWGN channel. Using BPSK modulation, we derived in class that the receiver bound on the probability of error for a single user in a AWGN channel is:

dxev

Pe v

mx

²

)²(.

2

1

0

..2

1 −−∞

∫=π .

)²/( σEbQPe =

where Q is defined as:

∫∞

−=x

u duexQ 2/².21

)(π

The optimal receiver cannot perform better than this bound, and we’ll see how close we can get in our simulations by plotting this bound along with BER of multi-user received signals.


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1.2 Codes matrix

In the ideal theory of CDMA, the codes are orthogonal to each other. However, in real transmission channels, it is impossible to ensure pure orthogonality. To simulate this in Matlab, I started out with orthogonal codes, obtained with the Hadamard algorithm, which I perturbed by adding a little bit of white noise to it. The random nature of the correlation matrix is a good assumption because it accounts for random synchronization errors for example. Hence, figure shows the codes correlation matrix, and we see the two cases of orthogonal and modified codes for a spreading factor of 16.

This non-orthogonality will lead to multiple access interference, which we want to study. This will yield a lower bound on the BER as the SNR becomes larger.

1.3 Simulation Parameters

The first parameter to specify is the number of signal bits to transmit. This length will limit the simulations, because bit error rates inferior to 10/(number of samples) will not be considered as meaningful points, since the average number of errors over the whole sequence will be inferior to ten, which is not enough for good Monte Carlo simulations. Thus, we will not be able to consider very high signal to noise ratios. Computation time in Matlab and memory requirements are the limitations on the signal length. Thus, we will limit the standard signal length to 100.000 (discarding BER smaller than 10-4) and the number of users to 16, unless specified otherwise (for capacity simulations, for example) Users are specified an average power at which they transmit, which accounts for their position within the cell. Indeed, considering the uplink transmission, users that are near the base station are received at higher power than those far away. Even though this can be attenuated in practice with tight power control, it is still a problem in a wireless link because Rayleigh fading makes power control strategies quite inefficient.


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1.4 Rayleigh fading channel generation To construct the Rayleigh fading process, we passed two independent white Gaussian noise sources with power spectral density N0/2 through lowpass filters with frequency response H(f) that satisfies

20 )(2

)()( fHN

fSfSQi rr ==

The filter outputs then correspond to the in-phase and quadrature components of the Rayleigh fading process.

2. The conventional receiver The goal of this part is to study the performances of the matched filter bank receiver, and to compare it to the single user bound in several conditions. We’ll vary the system load, and the relative powers of different users. Thus, we want to simulate a system in which different classes of users have different powers, and vary both the number of users and their relative powers. We’ve considered 5 classes and an equal number of users in each class. The three next plots show the influence of the channel load, and the differences in user powers. In a channel lightly loaded (5 users out of 16 maximum), emitting with a power varying from a factor of one to two, we can see that the weakest user suffers from this power difference. The others are relatively close to the single user bound. The differences can be seen much better in high SNR, because otherwise, noise becomes the limiting factor instead of MAI. The 4 strongest users taken separately wouldn’t bother the weakest too much, but together, the power transmitted in the channel is too strong.


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When the system load increases, the matched filter bank performances drop as can be seen on the next plot. The curves tend to reach a horizontal asymptot, when the noise power goes to zero ; there is an irreducible error floor caused by MAI.

. As the channel becomes heavily loaded, only the strongest users get to have correct performances to the detriment of other’s. The order of the curves might not exactly correspond to the power ranking ; this is due to the fact that a specific user is considered for the simulations, with a specific code. Even though this user has the smallest power, other users may have a higher correlation with the strong user’s signal, thus resulting in poorer performance than the user with the lowest power. However, if the chip sequences were chosen in such a way that all correlations would be equal, there is no reason why the order of the curves would not correpsond to the powers ranking order.


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Hence we note that even with little received power spread, the weakest users are hidden by strongest ones. The reason is the power discrepancies as well as the load of the channel. For the channel with 15 users, three of them show a horizontal asymptot, having an irreducible error floor due to MAI. These tests illustrate the drawbacks of the conventional receiver for multi-user reception. Even with a perfect power control scheme, which is hard to implement in rapidly changing wireless channels, there is still a limit due to the number of users in the system. Let’s now study a system in which the different user categories are received with power that are more spread out. We expect the results to be worse than before.


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We can see in this situation that the results are effectively worse than before ;

With the same power spectrum and a more heavily loaded system, all classes reach their error floor.


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By icnreasing the power difference even more, we can see that the strongest user gets a better performance out of it. Indeed, its signal to interference ratio becomes lower, because the relative power of other users is smaller. It gets closer to the single user bound. User powers now have a ratio strongest/weakest of 7. In this case, even with a lightly loaded system, only the two most powerful classes will be correctly detected. For the weakest signals, error rates show that the reception is totally unreliable.

For a more loaded system, all classes reach a saturation. We’re now very far from ideal performances, and results are very different from one class to another.


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To conclude, we can say that the matched filter is a receiver that cannot be used in real systems, without a good power control algorithm. Since this is not easy to do in rapidly varying channels, we rether want to use multiuser detection systems, as the ones presented earlier. We aim at designing a receiver that is less sensitive to system load, and received power differences.


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3. Performance comparison with perfect power control In this part, we’ll study the behaviour of the receivers presented above, in a situation where the system is loaded, but when all users are received with the same power.

3.1 System Capacity The figure below shows capacity curves, with SNR = 8 dB, a spreading factor of 32, and perfect power control. As can be seen in [1], the real curves have the same shape, and the same order between each other. The Matched filter looks like a logarithmic -shaped curve, which is bad, because with a few users, the BER goes to unacceptable values very fast. For the perfect power control case, we find that the decorrelator, MMSE, parallel canceller, and DF detectors all provide roughly similar performance, with the nonlinear detectors (excluding SIC) provide an improvement of four times. The performance of the successive interference canceller is significantly poorer due to the lack of variance in the received powers. Since the successive canceller orders cancellation based on average powers and average powers are the same, the performance of signals detected early in the cancellation process suffers. In fact, the performance of the first user is equivalent to that of the conventional receiver. This can be ameliorated by ordering based on reliability. That is, the matched filter outputs which are furthest from the decision boundary are the most reliable and should be detected and cancelled first. However, this requires ordering to be re-calculated after each cancellation which significantly increases complexity. Gains provided are of the order of 20 dB improvement for the DFD


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Running the same simulations with different SNR is interesting because it shows how the multiuser detector perform. With a greater SNR, the matched filter has a little better performances, but now the main limiting factor is MAI. Since they can cancel this type of interference, the difference between the conventional receiver and others is larger (30 dB for the DFD and PIC)

The same way, for a SNR of 6 dB, noise is a more limiting factor.


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3.2 Receivers performance comparison in AWGN The following plots now show the same difference, with BER versus SNR. For different number of users, we look at the fifth user. What we assumed above about the successive interference canceller is proved here, meaning that with only five users, the fifth is the last one to be decoded, and this yields a performance as good as other non-linear schemes. However, as can be seen on the other plots, the considered in this scheme suffers from interference coming from users that are to be decoded later, and which have the same received power.


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4. Real channel impairments 4.1 Near-far situation Previously we examined the improvement in capacity and BER performance possible with multiuser structures in perfect power control. However, as assarted earlier, one of the drawbacks of the conventional receiver is its subjection to the near-far problem. Thus we wish to examine the performance of each of the receiver structures in situations where a single interferer dominates the received power. The following plots present simulations of the receivers in the presence of interferers, with the relative power of the strongest to the weakest varying from 0 to 40 dB. As expected, the conventional receiver degrades quickly in the presence of strong interference. The successive canceller and the decision feedback receiver which benefit diverse powers are found to be robust to strong interferers, as is the decorrelator which has a performance which is independent of users energies. The MMSE having a theoretical near-far resistance identical to the decorrelator also displays robustness. Surprisingly, we find that the parallel canceller shows good performance in near-far situations. Indeed, the following problem is reported in most of the papers I read : the weak user is inaccurate in the first stage of cancellation due to the dominating interference. This poor cancellation serves to degrade the channel gain estimate of the strong user in the succeeding stage. Consequently, when the strong user is cancelled from the weak user’s signal in the second stage of cancellation it is done inaccurately, causing problems for the weak user. Since the first stage of cancellation is the decorrelator, this may explain why we don’t see this phenomenon. As before, we see that successive interference cancellation is limited in situations of similar powers among interferers.


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For the stronger user, the performance is good. I’d expect it to improve when the signal to interference ratio grows, but it doesn’t seem to be the case.


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4.2 Flat Rayleigh fading channel The performance for each of the receiver structures in flat Rayleigh fading, with perfect channel information, is presented in the following figures. The channel is assumed flat with a single path experiencing Rayleigh fading. Again we find significant improvement over the conventional receiver with each if the receivers providing nearly equivalent performance. Although some references report that successive interference cancellation significantly outperforms parallel cancellation, we obtain similar performance, probably because we used the decorrelator as the first stage of the parallel canceller, which combines advantages of both, but probably wouldn’t be done in practical systems, since both of them have significant complexity.

With a bigger number of users, we see that the performance of all users degrades.


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4.3 Flat Rayleigh fading channel with channel estimation The output of the matched filter is now used to estimate the channel. This is obviously not a very refined one, but it shows the influence of estimation. Basically, not all schemes need channel estimation, and those which use it will suffer from bad estimates, namely the non-linear ones.


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As a result of channel estimation, we can see that the performance of the interference cancellers degrades compared to the linear and decision feedback approaches. In fact, an irreducible error floor is seen due to estimation errors. While the non-linear approaches were superior in AWGN and equivalent in Rayleigh fading with perfect channel estimation, when channel estimation is a factor, the linear approaches provide superior performance. The interference cancellers generate their channel amplitude estimate from a moving average over ten consecutive bits. Thus the fading is sufficiently slow so that amplitude variations can be tracked with sufficient accuracy.


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Conclusion In this project, we have provided a description of Code-Division Multiple Access, and the problems of receiver designs in this spread spectrum technique. Specifically, five multiuser detectors and the conventional receiver have been described, implemented and simulated thoroughly using Matlab. We have shown that the conventional receiver presents two main weaknesses, namely its capacity limitation for correct performance, and its sensitivity to the near-far problem. We have shown that in an AWGN channel with perfect or imperfect power control multiuser detectors provide a significant gain over the conventional matched filter, with a better increase for non-linear receivers. Finally, we also have simulated a Rayleigh fading channel, and we have seen that in this situation, receiver still provide an increase in performance, with not much difference among types of receivers, and that channel estimation yields a drawback for the non-linear structures, resulting in a smaller improvement.

Documents

Multiuser detection techniques for Code-Division Multiple ...read.pudn.com/.../comm/wireless/812502/report.pdf · EE359 Final Project Report Wireless Communications Frederic SARRAT