On Multirate DS-CDMA Schemes with Interference Cancellation

On Multirate DS-CDMA Schemes with Interference Cancellation Ann-Louise Johansson & Arne Svensson Department of Signals and Systems Chalmers University of Technology S-412 96 Gothenburg Sweden E-Mail: [email protected] E-Mail: [email protected] Personal Wireless Communications, Vol 9, No. 1, January 1999

Abstract

This paper investigates interference cancellation (IC) in direct-sequence code-division multiple access (DS-CDMA) systems that support multiple data rates. Two methods for implementing multiple data rates are considered. One is the use of mixed modulation and the other is the use of multicodes. We introduce and analyze a new approach that combines these multiple data rate systems with IC. The cancellation in the receiver is performed successively on each user, starting with the user received with the highest power. This procedure can in turn be iterated, forming a multistage scheme, with the number of iterations set as a design parameter. Our analysis employs a Gaussian approximation for the distribution of the interference, and it includes both the AWGN and the at Rayleigh fading channel. The systems are also evaluated via computer simulations. Our analysis and simulations indicate that the IC schemes used in mixed modulation or multicode systems yield a performance close to the single BPSK user bound and, consequently, give a prospect of a considerable improvement in performance compared to systems employing matched lter detectors.

Keywords: Direct-sequence code-division multiple access (DS-CDMA), multiple data rates,

interference cancellation, mixed modulation, multicodes, multiuser detection.

1 Introduction An important feature of future mobile communication systems is the ability to handle other services besides speech, e.g., fax, Hi-Fi audio and transmission of images, services that are not readily available today. To achieve this, it is essential to have a exible multiple access method that maintains both high system capacity and the ability to handle variable data rates. Directsequence code-division multiple access (DS-CDMA) is believed to be a multiple access method able to ful ll these requirements [1]. There are two main factors that limit the capacity of a multiuser DS-CDMA system and make the signal detection more dicult. They are signal interference between users, referred to 1

A.-L. Johansson, A. Svensson: On Multirate DS-CDMA Schemes : : :

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as multiple access interference (MAI), and possibly large variations in the power of the received signals from dierent users, which is known as the near-far eect. The power variations that causes the near-far eect is due to the dierence in distance between the mobile terminals and the base station as well as fading and shadowing. One way to counteract the near-far eect is to use stringent power control [2]. Another approach would be to use more sophisticated receivers which are near-far resistant [3]. Because of the MAI's contribution to the near-far problem and its limiting of the total system capacity, much attention has been given to the subject of multiuser detectors that have the prospect of both mitigating the near-far problem and cancelling the MAI. Research in this area was initiated by Verdu [4, 5], who related the multiple access channel to a periodically time varying, single-user, intersymbol interference (ISI) channel and who derived the optimal multiuser detector. Unfortunately, the complexity of this detector increases exponentially with the number of users. This has motivated further research in the area of suboptimal detectors with lower complexity [6{21]. The objective of our work is to propose and evaluate an ecient detector for a multiuser and multirate DS-CDMA system. The proposed multiuser detectors in [6{18] are all designed for single rate systems. In [22], however, a dual rate scheme based on multi-processing gains is considered for the decorrelating detector. In this paper we consider two other multirate schemes together with a single- and multistage non-decision directed interference canceller (NDDIC) [19{21]. The IC1 schemes are generalizations and extensions of the single-stage SIC scheme for BPSK derived by Patel and Holtzman in [14,15]. The operation of the IC scheme is as follows. The receiver is composed of a bank of lters matched to the I and Q spreading sequences of each user. Initially the users are ranked in decreasing order of their received signal power. Then the output of the matched lter of the strongest user is used to estimate that user's baseband signal, which is subsequently cancelled from the composite signal. In other words, the projection of the received signal in the direction of the spreading sequence of the strongest user is subtracted from the composite signal. This is how we attempt to cancel the interference that aects the remaining users. Since we consider the uplink, that is, communication from the mobile terminal to the base station, we are interested in detection of all received signals and, thus, we continue by cancelling the second strongest user successively followed by all the other users. This scheme may be extended to an iterative multistage IC scheme by repetition of the IC one or more times. In the multistage IC scheme the estimated signal from the previous stage is added to the resulting composite signal and the output of the matched lter is used to obtain a new estimate of the signal, which in turn is cancelled. Hence, in this manner the interference can be further reduced and the signal estimates improved. The IC scheme is generalized to apply to the two multiple data rate schemes, mixed modulation and multicodes. Mixed modulation refers to the use of dierent modulation formats to change the information rate. That is, given a speci c symbol rate, each user chooses a modulation format, for example, BPSK, QPSK or any M-ary QAM format, depending on the required data rate [23]. Multicodes is the second approach for implementing multiple data rates. It allows the user to transmit over one or several parallel channels according to the requirements [23]. Hence, the user transmits the information synchronously employing several signature sequences. 1

To simplify notation IC is used both for interference cancellation and interference canceller.


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This approach can, of course, also be used in combination with dierent modulation formats. For our analysis and simulations we consider coherent demodulation, known time delays and two types of channels: a stationary AWGN channel and a channel with frequency-nonselective Rayleigh fading. Perfect power ranking is assumed in the performance analysis and in most of the simulations, which implies knowledge of the channel gain for each signal. This knowledge is, however, not used in the IC scheme itself. The paper is organized as follows. In Section 2 we present the system model and the decoder structure for rectangular M-ary QAM. A single- and multistage IC are then presented for this model in Section 3. The performance of a single-rate system with IC in AWGN and in at Rayleigh fading is analysed in Section 4 and Section 5. Thereafter, the performance of mixed modulation systems with IC is analysed in Section 6 and the corresponding analysis for multicodes is given in Section 7. Numerical results are presented in Section 8 and in Section 9 we discuss performance improvements for high-rate users in mixed modulation systems. Finally, the conclusions and future considerations are discussed in Section 10.

2 System Model and Decoder Structure We consider a model for a system with square lattice QAM, where the received signal for K users is modelled as

r(t) =

K X k=1

r

k 2TE0 dIk (t ? k )cIk (t ? k ) cos(!ct + k ) + r 2 E 0 Q Q k T dk (t ? k )ck (t ? k ) sin(!ct + k ) + n(t);

(1)

which is the sum of all transmitted signals embedded in AWGN. dI=Q k (t) is a sequence of rectanI=Q gular pulses of duration T with amplitude Ak;l , where I=Q denotes in-phase (I) or quadrature (Q) branch. T is the inverse of the symbol rate, which is assumed to be equal for all users. The amplitudes of the quadrature carriers for the kth user's lth symbol element, AIk;l and AQk;l , generate together M equiprobable and independent symbols. They take the discrete values

p

n

p

p

o

AI=Q k;l 2 ? M + 1; ? M + 3; : : :; M ? 1 ;

p

(2)

since M amplitude levels are required for the I and Q components to form a signal constellation for M-ary QAM. The energy of the signal with lowest amplitude is then 2E0 . The kth user's signature sequence that is used for spreading the signal in the I or Q branch is denoted cI=Q k (t). It consists of a sequence of antipodal, unit-amplitude, rectangular pulses of duration Tc . The period of all the users' signature sequences is N = T=Tc , hence there is one period per data symbol2. k is the time delay and k is the phase of the kth user. These are, in the asynchronous case, i.i.d. uniform random variables in [0; T ) and [0; 2). Both parameters are assumed to be known in the analysis and in the simulations with known channel parameters. However, if complex spreading 2

In this paper

N

is also referred to as processing gain.


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and despreading is used, k is only needed for the coherent detection and not for the NDDIC scheme [18]. Furthermore, !c represents the common centre frequency, k represents the channel gain, which could be constant or Rayleigh distributed, and n(t) is the AWGN with two sided power spectral density of N0 =2. Figure 1 shows the structure of the kth user's receiver when detecting the lth symbol. The receiver is the standard coherent matched lter detector for M-ary QAM, from which we obtain I and S Q , which are the sucient statistics for the I and Q components. two decision variables, Sk;l k;l The low pass lter removes the double frequency components and for the I branch we get K r X I (t) = k 2TE0 dIk (t ? k )cIk (t ? k ) cos2k + k=1 r 2 E sin 0 k Q Q k T dk (t ? k )ck (t ? k ) 2 + nI2(t)

=

K X X k=1 l

(3)

sIk;l(t ? k ) + nI2(t) ;

I (t) is the baseband signal for the lth symbol of the kth user. A similar expression can PSfrag sreplacements where k;l be derived for Q (t) [19], where nI (t) + jnQ (t) is the baseband equivalent of n(t).

cos !c t

cIk (t ? k ) cos k II kR T Zk;l dt 1

LPF

I (t)

+

T k

+

cQk (t ? k ) sin k IQ +T Zk;l 1 kR dt

+

?

I Sk;l

T k

r(t)

cIk (t ? k ) sin k LPF

Q (t)

+T 1 kR T k dt

Z QI cQk(t ? k ) cos k;l k QQ kR T Zk;l

sin !c t

+

T k dt 1

+

+ +

Q Sk;l

Figure 1: M-ary QAM receiver for DS-CDMA systems. The I branch as well as the Q branch is correlated with both the I and Q signature sequences of the kth user to form four dierent correlator outputs, which are the outputs at integer multiples of T . These outputs contain all information about the amplitudes and they are used to form I and S Q . Let us consider detection of the rst user's zeroth symbol. the decision variables, Sk;l k;l


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Then, Z1II;0 , from the rst correlator, is determined as r

Z1II;0 =

K 2E0 AI cos2 + X Ik;II1 (AIk ; AQk; k;1 ; k ) cos 1 + 1 T 1 1;0

k=2

1 Z +T AQ cI (t ? )cQ (t ? ) sin cos dt + 1 nII ; 1 1 1 1 1 T 1 1;0 1 2 1 1

(4)

1

i

h

h

i

where AIk = AIk;0; AIk;1 , AQk = AQk;0 ; AQk;1 and the noise component is given by

nII 1

Z +T 1 =T nI (t)cI1 (t ? 1 ) cos 1 dt: 1

1

(5)

The sum of Ik;II1 terms in (4) represents the interference due to the remaining K ? 1 users and each term can be expressed as

Ik;II1 (AIk ; AQk; k;1 ; k ) = Z T 1 X k I I I =T Ak;l pT (t ? k;1 ? lT )ck (t ? k;1)c1 (t) dt cos k + 0 l=0 1 k Z TX Q Q I T 0 l=0 Ak;l pT (t ? k;1 ? lT )ck (t ? k;1)c1 (t) dt sin k ;

(6)

where pT (t) is a unit-amplitude, rectangular pulse of length T and k;1 = k ? 1 . The delay k is assumed, without loss of generality, to be shorter than 1 . This is discussed more in the next section. All the other Z1;0 terms are derived in the same manner as above and we get the decision variables r

E0 AI + N I 2T 1 1;0 1 r E0 Q IQ Q S1Q;0 = (Z1QQ ;0 + Z1;0 ) = 2T 1 A1;0 + N1 ; S1I;0 = (Z1II;0 ? Z1QI;0 ) =

(7)

where N1I=Q is the noise term of the decision variable including both Gaussian noise and noise caused by multiuser interference. The noise term depends actually on the symbol but for convenience and reasons explained later we write N1I=Q instead of N1I=Q ;0 . It can be shown with the help of trigonometric functions that the noise terms are given by r

K X E 0 QI = 2T Ik;II1(AIk ; AQk ; k;1 ; k;1 ) + 12 [nII 1 ? n1 ] k=2 r K X IQ N1Q = 2ET0 Ik;QQ1 (AIk ; AQk; k;1 ; k;1 ) + 12 [nQQ 1 + n1 ]; k=2

N1I

(8)

where k;1 = k ? 1 . Ik;II1 is the function given in (6), where k has been replaced by k;1. Ik;QQ1 is given by a similar expression with the appropriate changes in indices. The four noise components are assumed to be uncorrelated Gaussian random variables. The two pairs of noise components,


Page 6

IQ QI QQ Q I nII 1 and n1 , and, n1 and n1 , are uncorrelated only if the signature sequences, c1 (t) and c1 (t),

are orthogonal, which is a mild restriction. We assume, however, that the correlation is zero also for non-orthogonal signature sequences with large processing gain to enable analytical evaluation of the system performance.

3 Non-Decision Directed Interference Cancellation 3.1 Single-Stage Interference Cancellation The receiver for M-ary QAM is composed of a bank of lters matched to the I and Q signature sequences of each user according to Figure 1. From the lter outputs we obtain the decision variables, which are used both for determining which of the users is the strongest and in the cancellation of that user's signal. The users are then decoded and cancelled in decreasing order of their power. The detector is a coherent demodulator and we assume decision boundaries according to minimum Euclidean distance. A block diagram of a receiver for M-ary QAM with IC is shown in Figure 2. Without loss of generality, we assume that 1 > 2 > > K > 0. Hence, if the users have the same average transmitted power, the rst user is the strongest. The strongest user is cancelled rst, since this user is likely to cause most interference and also the one less aected by the interference from the other users. The decision variables of the strongest user is used to estimate its baseband signal, which is subsequently cancelled from the composite signal. In other words, the projection of the received signal in the direction of the spreading sequence, is subtracted from the composite signal. The scheme continues with cancellation of PSfrag replacements the second strongest user and thereafter all the users in order of their received power.

cos !c t

S2I;l S2Q;l

LPF

I (t) ? +

+

MF 1

r(t)

S1I;l S1Q;l

MF 2

LPF

sin !c t

cQk (t ? k ) sin k cIk (t ? k ) cos k

+

Q (t) +

I SK;l +

+

?

MF K

Q SK;l

I SQ Sk;l k;l Select Max & Decode

I SQ Sk;l k;l

cIk (t ? k )(? sin k ) cQk(t ? k ) cos k

Figure 2: M-ary QAM receiver with interference cancellation. For the sake of notational simplicity we assume that 1 > 2 > > K > 0. This ensures that all the interfering symbols of the stronger users have been cancelled before the considered symbol is decoded. That is, all the symbols prior to the zeroth have already been decoded and cancelled and we can consider the detection of the zeroth symbol for all users. This is not a


Page 7

restriction, since it does not aect the results of the analysis and it is not used in the simulations. It only simpli es the expressions, thus we avoid considering dierent symbols for dierent users. We use the decision variables in (7) to estimate the baseband signal of the rst user's zeroth symbol and subsequently cancel it from the composite signal. The cancellations are however not perfect: besides the desired signal, the lter output also contains Gaussian noise and noise caused by MAI, and, for each cancellation, noise is projected in the directions of the other users in the system. Nevertheless, the scheme has the advantage of being simple. We proceed by cancelling the users successively and after h ? 1 cancellations the decision variable for the hth user is given by

Sh;I=Q 0 =

r

E0 AI=Q + N I=Q : h 2T h h;0

(9)

After cancellation of the hth user, the resulting baseband signal of the I branch is expressed as

h;I 0 (t) =hI ?1;0 (t) ? Sh;I 0pT (t ? h)cIh (t ? h ) cos h ? Sh;Q0pT (t ? h)cQh(t ? h ) sin h;

(10)

where there are h cancelled and K ? h remaining zeroth symbols. When h is equal to 1 the term 0I;0 (t) corresponds to the remaining baseband signal after cancellation of all symbols prior to the zeroth, and consequently, we get 1I;0 (t) after cancelling the rst user's zeroth symbol. We rewrite the expression in the following way

h;I 0 (t) =

K X X

sIk;l (t ? k ) ?

K X X

Ik;l + nI2(t) ?

k=1 l0 r h X j 2ET0 AIj;0 pT (t ? j )cIj (t ? j ) cos j + j =1

j h X j =1

r

(11)

E0 AQ p (t ? )cQ (t ? ) sin ? j j j j 2T j;0 T

pT (t ? j ) NjI cIj (t ? j ) cos j + NjQcQj (t ? j ) sin j ;

where the rst sum is the remaining baseband signal after cancellation of all symbols prior to the zeroth. The second sum is the additional noise caused by imperfect cancellation of these symbols and it is de ned as

I cI (t ? ) cos + N Q cQ (t ? ) sin ; Ik;l = pT (t ? k ) Nk;l k k k k k k;l k

(12)

I=Q an additional subscript, l, specifying the symbol. This where we have given the noise term Nk;l index indicates that the noise term do vary over time. The third term in (11) is the in-phase Gaussian noise and the subsequent sum is the cancelled baseband signals corresponding to the zeroth symbol of the h strongest users in the system. Finally, we have the additional noise components caused by imperfect cancellation of these h users' zeroth symbols. The omission of


Page 8

a second subscript in the noise term in the last line of (11) is explained below. The total noise component in (9) for the hth user in the I branch is

NhI

r

K X II (AI ; AQ ; ; ) + 1 [nII ? nQI ] ? Ik;h = 2ET0 k k k;h k;h h 2 h k=h+1 h?1 X j =1

(13)

II ( ; ) ? N QJ QI ( ; ); NjI Jj;h j;h j;h j j;h j;h j;h

where the rst sum consists of noise caused by the remaining interfering users, the second term is Gaussian noise and the last sum is the resulting noise caused by imperfect cancellations. NhQ II and J QI , are given by is given by a similar expression. The correlation terms, Jj;h j;h II ( ; ) = 1 Jj;h j;h j;h T

Z

T

cIj (t ? j;h)cIh(t) cos(j;h) dt

0

(14)

Z T 1 QI Jj;h (j;h; j;h) = T cQj(t ? j;h)cIh (t) cos(j;h) dt;

0

where the correlation is over the noise caused by imperfect cancellation of the symbols -1 and 0 of the j th user, since we assume j > h for j < h. This is illustrated in Figure 3, where shaded lines indicate cancelled symbols. However, since we consider a slowly fading channel, which implicates that the channel changes slowly and the interference-power can be regarded as equal for two subsequent symbols, we do not distinguish between, e.g., the noise terms Nj;I ?1 and Nj;I 0 . This is the reason for simply using NjI and NjQ in (11) and (13). -1

PSfrag replacements

-T

User 1 User 2

0 T

1 ? T 2 ? T

1

0

1 2

2T

1 + T 2 + T

Figure 3: Cross-correlation between users in an asynchronous system.

3.2 Multistage Interference Cancellation The derived single-stage scheme may be iterated to form a multistage scheme. The motivation for this is that the users received with high power have the advantage of being strong but they are still exposed to interference from the weaker users. Hence, if better estimates of the strong users' signals can be achieved the estimates and the cancellations of the weak users' signals would be improved. Therefore, iterating the IC scheme can improve the performance of the whole system. We still have to keep in mind that in our simple IC scheme we make non-decision directed or 'soft' cancellations using the matched lter outputs. The eect is that the Gaussian noise is not removed through hard decisions and for each cancellation a small amount of noise is projected


Page 9

in the directions of the other users in the system. Hence, the performance of a system can be improved through cancellation of the MAI by employing a limited number of IC stages, but after the optimum number of stages the performance will degrade. However, simulated results in [18] and analytical results in [24] show that the multistage NDDIC in a synchronous system performs better than the decorrelator [6] after a limited number of stages and that they are asymptotically equivalent. To simplify the notations when describing the multistage IC, we drop the subscript for the symbol and replace it with a subscript that represent the stage. That is, the rst subscript of a variable de nes the user and the second subscript de nes the stage and the assumption of detection of symbol zero is implicit. To describe the multistage IC scheme we use an interference cancellation unit (ICU), which is illustrated in Figure 4 using a simpli ed block diagram. First we add the estimated baseband signal from the previous stage (denoted sk;i?1 in Figure 4) to the resulting composite signal. Then we use the output of the matched lter to obtain a new estimate of the signal, which in turn is cancelled. The variable rk;i de nes the composite baseband signal after cancellation of user k ? 1 and ck denotes the I and Q signature sequences, which are used to regenerate the estimated baseband signal sk;i of the kth user. The scheme is repeated for all the users in the system for the desired number of stages. This is shown in Figure 5, where each block, IC k(i) , is the kth user's ICU at the ith stage. ri;k si?1;k PSfrag replacements

ck

+ +

+

MF k

yi;k

si;k

+ -

+

ri;k+1

Figure 4: Linear non-decision directed interference cancellation unit. The corresponding expression to (10) for the resulting baseband signal in multistage IC is determined as I (t) =I (t) ? S I aI ? S Q aQ + h;i h;i h h?1;i h;i h Q ShI +1;i?1aIh+1 + Sh+1;i?1 aQh+1 ;

(15)

where aIh = pT (t ? h )cIh (t ? h ) cos h . aQh is given by a similar expression using the sine-function. The decision variable for the hth user at the ith stage is given by I=Q = Sh;i

r

E0 AI=Q + N I=Q ; h;i 2T h h

(16)

s1;K +1


r1;1 ICU 1(1)

r1;2 ICU 2(1)

s1;1 s1;2

Page 10 r2;1 ICU 1(2)

r2;2 ICU 2(2)

r2;K r1;K s s 1 ;K ICU K (2) 2;K ICU K (1) r1;K +1

ICU 1(i)

si;1

ri;2

s2;2

.. .

.. .

ri;1

s2;1

ICU 2(i)

si;2

.. .

ri;K ICU K (i)

si;K

r2;K +1

Figure 5: Multistage successive interference cancellation. I=Q contains only Gaussian noise and noise caused by imperfect cancellations. For the where Nh;i I branch the noise term is given by hX ?1

I = 1 [nII ? nQI ] ? Nh;i h 2 h

II ( ; ) ? N Q J QI ( ; ) ? Nj;iI Jj;h j;h j;h j;i j;h j;h j;h

j =1 K X I J II ( ; ) ? N Q J QI ( ; ); Nk;i ?1 k;h k;h k;h k;i?1 k;h k;h k;h k=h+1

(17)

where the rst term is Gaussian noise, the rst sum is the noise caused by imperfect cancellation at the ith stage and the second sum is the noise caused by imperfect cancellation at the (i ? 1)th II and J QI are de ned in (14) and N Q is given by an expression similar to (17). stage. Jj;h j;h h;i

3.3 Ranking of the Users In this paper we do not consider algorithms for ranking the users. We assume perfect ranking in the analysis and in most of the simulations. In simulations where we estimate the channel, power ranking is performed before the IC using pilot symbols for initial channel estimates. In mixed modulation systems, the QAM users are scaled with their average power giving a ranking according to the channel gain. Discussions about ranking is found in [15,19].

4 Performance Analysis of Systems in AWGN In this section we analyse the performance of a single-rate system in an AWGN environment. To analyse the scheme, we let the noise components caused by MAI be modelled as independent Gaussian noise [25, 26]. We have chosen to use a Gaussian approximation partly since it is commonly used and partly because it yields a practical way to evaluate the performance of an asynchronous system. When a Gaussian approximation is used, an increase in noise and interference variance immediately leads to an increase in error probability, which is likely to occur


Page 11

also for the true distribution. Absolute performance, however, is likely to be too optimistic [26]. In this section we consider an AWGN channel where all the users are received with equal power, which corresponds to perfect power control. This will make the ranking of the users completely random and the order of cancellation will change continuously. Thus, the average probability of symbol error for each user is obtained taking the average of the symbol error rates (SER) for all the users.

4.1 Single-Stage Interference Cancellation First we calculate the variance of the decision variable of the I branch conditioned on , i.e.,

hI = Var NhI j ;

(18)

where NhI is de ned in (13) and includes all k . k is constant for stationary AWGN channels but we write the variance conditioned on to enable the use of (18) in the analysis for Rayleigh fading channels. With the assumption that all the Gaussian noise terms are uncorrelated (which is true if cIk and cQk are orthogonal), it can be shown that all the random variables in NhI=Q are independent and with zero mean. Consequently, we model NhI=Q as an independent Gaussian random variable with zero mean and variance hI=Q . Rewriting (18) we get

hI =Var

h1?

2

h?1 X j =1

i

QI nII h ? nh

K X E 0 Q I II + 2T Var Ik;h(Ak ; Ak ; k;h; k;h )j + k=h+1

h

i

i

h

II ( ; ) + Q Var J QI ( ; ) ; jI Var Jj;h j;h j;h j j;h j;h j;h

(19)

where the rst term is the variance of the Gaussian noise, the rst sum results from the MAI and the last sum is due to imperfect cancellations. For deterministic signature sequences and rectangular chip pulses, the variance in (19) is

hI =

K M ? 1 E0 X 2 ?rII + rQI + 3 3 12N T k=h+1 k k;h k;h

?1 ? 1 hX I rII + Q rQI + N0 ; j j;h j j;h 3 6N 4T

(20)

j =1

II where (M ? 1)=3 is the normalized average transmitted power in each branch, T = NTc and rk;h is the average interference [25] between the signature sequences in the I branches of user k and h. We have also assumed that j;h and j;h are uniformly distributed over [0; T ) and [0; 2). For random sequences the variance is

hI =

M ? 1 E0 3 3NT

X K

k=h+1

2k + 32N

hX ?1 j =1

0; jI + N 4T

where we have used jI = jQ and that the average interference is 2N 2 [25].

(21)


Page 12

It is straightforward to obtain the probability of error from the theory of single transmission of QAM signals over an AWGN channel [27] when the distribution of the MAI is approximated to be Gaussian. We use the variance given in (20) or (21) and de ne a signal-to-noise ratio, Ih , for the hth user in the ideal coherent case as r

E0 h Ih = q2T : hI

(22)

The probability of error for transmission over the I branch is then [27]

PeIh

=2

p

M ? 1 p Q(Ih ); M

(23)

where the Q-function de nes the complementary Gaussian error function3. PeQh is obtained in a similar manner and together they give the SER

Peh = 1 ? (1 ? PeIh )(1 ? PeQh ):

(24)

Finally, the average probability of symbol error is obtained taking the average of all the users' SERs.

4.2 Multistage Interference Cancellation The multistage scheme is analysed in the same manner as the single-stage scheme. The expression I in (17) is used in (18) to obtain the variance of the decision variable. The variance for for Nh;i deterministic sequences is given by K X 1 I I rII + Q rQI + h;i = 6N 3 k;i ?1 k;h k;i?1 k;h k=h+1 ?1 1 hX I rII + Q rQI + N0 ; j;i j;h j;i j;h 6N 3 j =1 4T

(25)

while for random sequences we get I = 2 h;i 3N

K X k=h+1

2 I k;i ?1 + 3N

hX ?1 j =1

I + N0 ; j;i 4T

(26)

I = Q is used. The variance in (25) or (26) is used in (22) to obtain the signal-to-noise where j;i j;i ratio, Ih;i , which in turn is used together with (23) and (24) to calculate the average probability of symbol error for the multistage scheme. 3

2 R ( ) = p12 u1 (? x2 ) d

Q u

e

x


Page 13

5 Performance Analysis of Systems in Flat Rayleigh Fading In this section we analyse single-rate systems in at Rayleigh fading. That is, systems where the users' signals are received through independent, frequency-nonselective, slowly fading channels. This model is suitable in areas with small delay spread and for mobiles with slow speed (small Doppler frequency). These conditions also make estimation of k and k feasible, which is needed for coherent detection and to obtain decision boundaries for M-ary QAM [27]. The expressions for noise variances and error probabilities, that were derived in the previous sections, are all conditioned on the channel gain. We will use them as in [14, 15] to derive the error probabilities for at Rayleigh fading channels.

5.1 Single-Stage Interference Cancellation The users' amplitudes are assumed to be Rayleigh distributed with unit mean square value. That is, the average power of the received signals at the base station is equal, assuming perfect power control for shadowing and distance attenuation. To obtain the unconditional probability of error, P^eIh , we average the conditional probability of error over the fading as follows

P^eIh =

Z

1

0

PeIh fh(x) dx;

(27)

where fh (x) is the pdf of the hth ordered amplitude, which is obtained using order statistics [28] and stated here for convenience, i.e., fh(x) = (K ? hK)!(!h ? 1)! F K ?h(x) 1 ? F (x) h?1 f (x):

(28)

We de ne a conditional signal-to-noise ratio, Ih, for the hth user in the I branch according to (22). The only dierence is that hI is replaced by E [hI ], which is the expected value of the conditional variance with respect to . The expected value is taken with respect to all k ; k 6= h. When using a Gaussian approximation we calculate the second moment of the MAI and add it to the variance of the Gaussian noise. The expected value is therefore determined as

E hI =

M ? 1 E0 3 3NT

hX ?1 0; E 2k + 32N E jI + N 4 T j =1 k=h+1 K X

(29)

where E 2k is the mean square value of the ordered amplitude, k , given by Z 1 E 2k = x2 fk(x) dx:

0

(30)

It should be noted that this integral, as well as the integral in (27), is calculated numerically in the analysis. Taking the average of the dierent users' SERs, yields the average probability of symbol error. This is the proper measure of performance, since the order of cancellation will change with the fading and the average of all users will be the same as the time average for each user.


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5.2 Multistage Interference Cancellation The multistage scheme is analysed in the manner described above using order statistics. The expected value, with respect to , of the variance of the hth user's decision variable at the ith stage is given by

I = E h;i

K h?1 X I 2 2 X I + N0 E E + j;i ? 1 j;i 3N k=h+1 3N j =1 4T

(31)

when using random spreading sequences. The variance in (31) is used in (22) to form Ih;i, which in turn is used in Eqns. (23), (24) and (27) to calculate the unconditional SER.

6 Mixed Modulation Systems with IC Mixed modulation is one possible scheme that can be used when handling multirate systems [23]. In this scheme, the information rate is determined by the modulation format, which can be BPSK, QPSK or any M-ary QAM format. Accordingly, if a user transmits with a speci c data rate using BPSK modulation, the user would change to QPSK modulation when a twice as high information rate was required. In the following paragraphs we evaluate the performance of a system where the users employ dierent modulation formats, in this case, a combination of BPSK, QPSK and 16-QAM.

6.1 Mixed Modulation Systems with Single-Stage NDDIC We consider a system where we have K1 BPSK, K2 QPSK and K3 16-QAM users. To compare dierent forms of modulation, we let the transmitted bit energy, Eb , be equal for all users independent of modulation format. Rewriting the energy E0 as a function of Eb yields log2 M ; E0 = Eb 2(3 M ? 1)

(32)

which is valid for M-ary QAM. For BPSK modulation, E0 = Eb . The expression for the variance of the decision variable for a BPSK user is given in [15], and it is reproduced here for convenience together with the expression for a M-ary QAM user, i.e., K nX ?1 Eb X 0 BPSK : n = 6NT 2k + 31N j + N 4 T j =1 k=n+1 K m?1 2 M X 2 + 2 X I + N0 : QAM : mI = Eb6log NT k=m+1 k 3N j=1 j 4T

(33)


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If we de ne M1 = 4 (QPSK) and M2 = 16 (16-QAM), we can express the signal-to-noise value conditioned on , for the hth QPSK user as s

Ih =

3Eb 2h log2 M1 4(M1 ? 1)T q

hI n;m (

;

(34)

)

where hI n;m is the variance of the decision variable of the hth QPSK user in the mixed modulation system. n, h ? 1 and m is the number of cancelled BPSK, QPSK and 16-QAM users, respectively. Rewriting (34), using (33) to derive hI n;m , we get (

)

(

)

K h?1 2 X 2 + 2 X(I )?2 + + 3 Eb log2 M1 3N k=h+1 k 3N j=1 j K m 2(M1 ? 1) log2 M2 X 2 + 2(M1 ? 1) log2 M2 X(I )?2 + 9N log2 M1 k=m+1 k 3N (M2 ? 1) log2 M1 j =1 j

Ih =h

M1 ? 1

N0

2

3

(35)

?1=2 K n X 2(M1 ? 1) X 2( M ? 1) 1 ? 2 2 9N log2 M1 k=n+1k + 9N log2 M1 j =1 j ; 1

where the noise variance caused by interference from QPSK users is found on the rst line, from 16-QAM users on the second line and from BPSK users on the last line. For BPSK and 16-QAM users we get similar expressions.

6.2 Mixed Modulation Systems with Multistage NDDIC The variance of the noise in mixed modulation systems with multistage IC is derived in a similar manner as for the single-stage case. The signal-to-noise ratio, Ih;i, for the hth QPSK user is formed using (34) together with the for multistage modi ed expressions in (33). We then obtain

Ih;i =h

K hX ?1 (M1 ? 1)N0 + 2 X I )?2 I ? 2 ( ( ) + j;i 3Eb log2 M1 3N k=h+1 k;i?1 j =1 2

K m X 2(M1 ? 1) log2 M2 X I )?2 ? 2 I ( ) + ( j;i 3N (M2 ? 1) log2 M1 k=m+1 k;i?1 j =1 3

(36)

K n ?1=2 X 2(M1 ? 1) X ? 2 ? 2 9N log2 M1 k=n+1 k;i?1 + j =1 j;i ; 1

where the rst line results from imperfect cancellation of QPSK users, the second line from 16QAM users and the last line from BPSK users. The signal-to-noise ratios for BPSK and 16-QAM users are given by similar expressions.


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6.3 Performance Analysis for Stationary Channels To evaluate the performance of a mixed modulation system, we rst calculate the bit error rate (BER) for each user before the BER for the whole system can be derived. For BPSK users the BER is determined by

= Pr S^n < 0jbn = 1 = Q(In ): PbBPSK n

(37)

To compare the results obtained for QAM users with BPSK users we assume a Gray encoded version of M-ary QAM. The log2 M -bit Gray codes dier only in one bit position for neighbouring symbols, and when the probability of symbol error is suciently small, the probability of mistaking a symbol for the adjacent one vertically or horizontally is much greater than any other possible symbol error. The SER is easily derived using (23) in (24) and then the BER is obtained through

PbQAM logPehM : h 2

(38)

To get the BER for the whole system, each user's BER is weighted together as

Pb = tot

P P QPSK QAM BPSK n Pbn R1 + h Pbh R2 + m Pbm R3 ; K1 R1 + K2 R2 + K3 R3

P

(39)

where R1 , R2 and R3 are the data rates for the BPSK, QPSK and 16-QAM users, respectively, and the Pb terms are the individual BERs.

6.4 Performance Analysis for Rayleigh Fading Channels In mixed modulation systems, the average transmitted energy per bit is equal for all users independent of modulation format. The average power of the QAM users is therefore log2 M times higher than for the BPSK users. For the mixed modulation scheme, we have ordered the users according to the channel gain and not the received power. This will improve the performance of the high-rate users, which are more sensitive to noise, and, consequently, it improves the performance of the whole system. However, the improvement is mainly noticed for single-stage IC, since the eect of ranking is less important when the interference in the system is due only to imperfect cancellations. The expected values, with respect to , of the variances in (33) are used in (34) to obtain the corresponding expressions of the conditional signal-to-noise ratio. The signal-to-noise ratio is then used to derive the error probability for each user according to (23) or (37), depending on the user's modulation format, and the unconditional error probability is obtained using (27). Finally, the weighted BER is obtained using Eqns. (37) - (39). The corresponding signal-to-noise ratio, Ih;i, in (36), after taking the expected value of the variances with respect to , is used to calculate the performance of the multistage IC. The procedure for obtaining the BER of the whole system is then the same as described above.


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7 Multicode Systems with IC Multicodes is the second of the two considered multirate schemes [23]. In this scheme we let each user transmit information simultaneously over as many parallel channels as required for a speci c data rate. Thus, a user employs several spreading codes and the information is transmitted synchronously at a given base rate. If there are users with very high rates in the system, there can be a large number of interfering signals. However, this aects the high-rate user itself very little, since sequences with low cross-correlation or orthogonal sequences can be used, in which case the synchronous signals interfere little or nothing with each other.

7.1 Synchronous Systems with Single-Stage NDDIC We consider rst a system with only synchronous transmission. We have parallel channels with identical channel parameters, since we assume that the signals are transmitted simultaneously from the same location. In other words, the relative time delay and phase between the channels are equal to zero. The variance of the noise component in (13) when both k;h and k;h is zero is given by

? 1) hI = E06(M 2 NT

hX ?1 ? ? II II (0)2 + N0 ; 2k k;h (0) 2 + N12 jI j;h 4T j =1 k=h+1

X

(40)

II (0) is the periodic cross-correlation function [25]. The expression for random sequences where k;h II (0))2 ] = N [26]. follows using E[(k;h

7.2 Multicode Systems with Single-Stage NDDIC We consider a system with K users, where each user, k, transmits over k channels. The total number of information bearing channels is then equal to the sum of all k and there are both synchronous and asynchronous interferers. When deterministic sequences are used, all, or the major part, of the interference comes from the asynchronous users, depending on if the sequences are orthogonal or not. Therefore, cancellation of parallel signals is excluded and instead we consider a receiver where each user's parallel signals are decoded and cancelled simultaneously. Combining (20) and (40) we can write the variance of the decision variable of the hth user's gth signal in a QAM system with both asynchronous and synchronous transmission as h ? 1) X 2 II (0) 2 + hI g = E06(M h hj ;hg N 2T j =1 j 6=g k K X X

E0 (M ? 1) 2 rII + rQI + 36N 3 T k=h+1 j =1 k kj ;hg kj ;hg

(41)

k h h?1 X i 1 X I rII + Q rQI + N0 ; k ;h k k k ;h g j j j j g 6N 3 4T k=1 j =1

where rkIIj ;hg denotes the average interference between the in-phase signals, and kj denotes the


Page 18

j th channel of the kth user and hg the gth channel of the hth user. The variance in (41) is used together with Eqns. (22) - (24) to obtain the probability of error in stationary AWGN channels.

7.3 Multicode Systems with Multistage NDDIC The use of orthogonal spreading sequences does not improve the performance considerably for single-stage IC, since the interference caused by the remaining asynchronous users in each step of the cancellation scheme determines the performance. However, when employing a multistage scheme it is preferable to use orthogonal spreading sequences, because after the rst complete stage of IC the MAI is partly rendered for noise caused by imperfect cancellation. Hence, there are not any remaining users that dominates the interference. The corresponding variance of the decision variable for multistage IC and orthogonal spreading sequences is given by a similar expression to (25), i.e.,

hI g ;i = 6N1 3

k h K X X k=h+1 j =1 k h hX ?1 X

i

kIj ;i?1 rkIIj ;hg + kQj ;i?1rkQIj ;hg +

N0 1 Q QI I II 6N 3 k=1 j =1 kj ;i rkj ;hg + kj ;i rkj ;hg + 4T ; i

(42)

where g is one of the signals belonging to user h. The average error probability for stationary AWGN channels is then obtained using (42) in Eqns. (22) - (24) as above.

7.4 Performance Analysis of Multicode Systems in Fading The performance of a multicode system in fading is analysed using order statistics as described in Section 5. The K users are ordered, each one with k parallel channels, according to their total received power. The same pdf, fk(x), and mean square value, E [2k ], are assigned to all the k channels of user k and, for the single-stage IC, (41) is used to obtain the expected value of the variance with respect to . The error probability is then derived using Eqns. (22) - (24) and (27). The performance of the multistage scheme is evaluated for orthogonal spreading sequences. Thus, the remaining noise consists only of the noise caused by imperfect cancellation of the asynchronous users and Gaussian noise. The expected value with respect to of the variance in (42) is used to obtain the error probability using order statistics as described above.

8 Numerical Results 8.1 Simulations All presented simulations are for asynchronous systems. We consider both stationary AWGN channels and slow, frequency-nonselective Rayleigh fading channels. The stationary AWGN channel corresponds to a system with perfect power control and, for the Rayleigh fading channel, we assume average power control for distance and shadow fading. The average received power is assumed to be equal for all users in single-rate systems and it is equal for all channels in multicode


Page 19

Table 1: Parameter settings for the simulations. Simulation Parameters Single/Mixed Mod. Channel Stationary AWGN/ Rayleigh Fading Detection Coherent Modulation BPSK, QPSK, 16-QAM Channel Estimation Known Channel/ Pilot Symbols Ranking Perfect Ranking/ MF Outputs Signature Sequences Random Codes Time Delays Perfect Estimates Processing Gain 127 Block Length 18

Multicodes Stationary AWGN/ Rayleigh Fading Coherent QPSK Known Channel/ Pilot Symbols Perfect Ranking/ MF Outputs Orth. Gold Codes Perfect Estimates 128 18

systems. In mixed modulation systems, the Eb =N0 value is the same for all users, which makes the M-ary QAM users log2 M times stronger in average power than the BPSK users. The IC scheme is performed block-wise on the data and it is assumed that the channel does not change during the transmission of a block, which corresponds to slow vehicle speed. We also assume that pilot symbols are added between the data blocks in those cases where we consider estimation of channel parameters. The estimate is then obtained from an average of the pilot symbols in the beginning as well as at the end of each block of data. For QPSK modulation, the kth user's channel estimate is obtained from X (43) YI +YQ ; ^ ej ^k = 1 k

P p2Ip

k;p

k;p

I and Y Q are the matched lter outputs when the received baseband signal is despread where Yk;p k;p with cIk and cQk respectively. Moreover, Ip denotes the indices for the P complex pilot symbols, which are de ned as 1 + j . For QAM we get a similar expression. Furthermore, in simulations using known channel parameters we assumed perfect ranking of the users. On the other hand, in simulations with estimated parameters, ranking is performed using the pilot symbols to obtain initial channel estimates. Note that k is only used to determine the decision boundaries of the QAM users and not in the IC scheme. All the resulting parameter settings for the simulations are given in Table 1. All the simulated systems are chip-rate sampled, which limits the possible time lags between users to multiples of chip times. It should also be pointed out that, as a consequence of reduced simulation time, the con dence level is not suciently high to give completely accurate results for BER values below 10?3 . However, we have considered a higher con dence level in the simulations


Page 20

of single-rate and mixed modulation systems in Figures 8, 9 and 10.

8.2 Stationary AWGN Channels 8.2.1 Multicode Systems

The performance of a multicode system in AWGN is shown in Figure 6. There are 15 asyn0

Average Bit Error Probability

10

MF Rec. Simulation Analysis IC 1 Stage IC 2 Stages IC 5 Stages Single BPSK

−1

10

−2

10

−3

10

Processing Gain = 128 Orth. Gold Sequences QPSK (15, P=2)

−4

10

0

5

10 E /N (dB) b

15

20

0

Figure 6: Performance of a multicode system with 15 QPSK users and two parallel channels per user. The graph shows analytical and simulation results for one, two and ve stages of IC and simulation results for an MF receiver. chronous QPSK users in the system. Each user transmits over two parallel channels and orthogonal Gold codes of length 128 are used. The graph shows analytical and simulation results for one, two and ve stages of IC and we can see that a Gaussian approximation is too optimistic for the single-stage IC, but the analytical and simulation results for two and ve stages of IC agree well. A Gaussian approximation is probably good for evaluating the performance of the users cancelled rst in the single-stage IC scheme, however, as the scheme proceeds, the Gaussian approximation of the MAI becomes less accurate, especially for high Eb =N0 values. This is due to the relatively strong interference, compared to the Gaussian noise, from a small group of users. That is, the central limit theorem does not apply. For multistage IC a Gaussian approximation is good, since then the interference is due only to imperfect cancellation of the users. As can be seen in the graph, after the second stage of IC, most of the performance gain is acquired and the performance is close to the single-user bound.

8.2.2 Mixed Modulation Systems Simulations as well as analytical results of a mixed modulation system is shown in Figure 7. There are 20 BPSK, 10 QPSK and 5 16-QAM users in the system and random sequences of length 127 are used. The analytical results are obtained from an average of 100 rankings, where


Page 21

0


10

Processing Gain = 127 Random Sequences Mix (20/10/5)

−1

10

−2

10

−3

10

−4

10

0

MF Rec. Simulation Analysis IC 1 Stage IC 2 Stages IC 5 Stages Single BPSK 5

10 E /N (dB) b

15

20

0

Figure 7: Performance of a mixed modulation system with 20 BPSK, 10 QPSK and 5 16-QAM users. The graph shows analytical and simulation results for one, two and ve stages of IC and simulation results for an MF receiver. each ranking gives a dierent ordering of the users according to the modulation format. That is, when the users in the mixed modulation system are ranked according to the channel gain, the order according to modulation format is completely random. As noted from the results, a Gaussian approximation is not reliable for single-stage IC, and using higher modulation formats increases the average BER compared to multicodes. The eect is noticed especially for high values of Eb =N0 . However, after ve stages of IC the analytical and simulation results agree well. Studying the average BER of the BPSK, QPSK and 16-QAM users respectively we see that the BER of the 16-QAM users clearly dominates the performance and causes the relatively high average BER in Figure 7. Nonetheless, for the two- and ve-stage IC we get a considerable reduction in average BER compared to the single-stage IC and the MF receiver.

8.3 Flat Rayleigh Fading Channels 8.3.1 Single-Rate Systems

The average BER of a single-rate system with 20 QPSK users in Rayleigh fading is shown in Figure 8. The length of the random sequences is 127. The results from one, two and ve stages of IC are compared with the single-user bound for BPSK users and the results from the corresponding system employing a conventional detector. The graph shows that a Gaussian approximation is too optimistic for a single-stage IC, but it works well for Eb =N0 values up to 20 dB. For multistage IC, the performance is close to the single-user bound and a Gaussian approximation works better, even though the results do not agree perfectly. Nevertheless, in [15] Patel and Holtzman show simulation results for BPSK users and single-stage IC that support the analytical results, which are obtained employing a Gaussian approximation, surprisingly well. We have, however, not been able to reproduce their results. The results for BPSK and 16-QAM


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0


10

Processing Gain = 127 Random Sequences QPSK, 20 users

−1

10

−2

10

−3

10

Simulation Analysis MF Rec. IC 1 Stage IC 2 Stages IC 5 Stages Single BPSK

−4

10

0

5

10

15 Eb/N0 (dB)

20

25

30

Figure 8: Performance of a QPSK system with 20 users in Rayleigh fading. Analytical and simulation results for an MF receiver and an IC with one, two and ve stages are shown. users are similar to the results presented in Figure 8 for QPSK users. The performance of a multistage IC is in both cases close to the respective single-user bound.

8.3.2 Mixed Modulation Systems Average analytical performance and simulation results of a mixed modulation system with 20 BPSK, 10 QPSK and 5 16-QAM users and random sequences of length 127 are shown in Figure 9. The results show that the analysis is too optimistic for the single-stage IC but the accuracy improves with an increasing number of stages. After ve stages of IC the analytical performance is 1 dB from the single-user bound. The simulation results for the same mixed modulation system are shown in Figure 10, where average system performance is presented together with average BER for each modulation format. The gure shows great improvement in performance for each additional stage of IC and after ve stages the average BER of the dierent users is close to their respective single-user bound.

8.3.3 Multicode Systems Figure 11 depicts analytical and simulation results for a multicode system with 15 QPSK users, two parallel channels per user and orthogonal Gold codes of length 128. The correspondence between the curves is relatively good for single-stage IC, but for multistage IC, the results agree well for Eb =N0 values up to 20 dB. In this region, the multicode system with multistage IC has a performance within 1 dB of the single-user bound. In Figure 12 we compare the performance of a multicode system (15 QPSK users and two parallel channels per user), with the performance of two single-rate systems (30 QPSK users and 15 16-QAM users, respectively). Eb is equal for all users in the systems. The simulation results


Page 23

0

10



−1

10

−2

10


−3

10

0

5

10 15 E /N (dB) b

20

25

0

Figure 9: Performance of a mixed modulation system with 20 BPSK, 10 QPSK and 5 16-QAM users in Rayleigh fading. Both analytical and simulation results are shown. for one, two and ve stages of IC show that QPSK modulation together with two parallel channels are preferable to 16-QAM. However, it should be noted that the 16-QAM system outperforms the other two systems for a two-stage IC in the high Eb =N0 region, where the interference is limiting instead of the Gaussian noise. The performance of the 16-QAM system is then close to its single-user bound. The other two systems, the asynchronous QPSK system and the multicode system, have almost the same performance. They perform well and both systems are within 1 dB of the single-user bound for a ve-stage IC. The dierence in performance for high Eb =N0 values is presumably mainly due to inaccuracy in the simulation results.

8.3.4 Systems with Parameter Estimation In simulations with channel estimation, the channel parameters were estimated using pilot symbols according to (43). In this case we did not assume perfect ranking. The order of the users was instead determined from initial channel estimates as described in Section 3.3. In Figure 13, we compare the simulated performance of a multicode system using estimated channel parameters to a system where the channel parameters are assumed to be known. The degradation due to estimated channel parameters is several dB for a single-stage IC but for two- and ve-stage ICs the degradation is only about 1 dB. It can also be noted that the degradation in systems employing a conventional detector is very large. Note that Eb is the energy per bit on the channel. That is, there is no compensation for the energy used for the pilot symbols.


Page 24

0


10


−1

10

−2

10

−3

10

Ave.BPSK Ave. QPSK Ave. 16−QAM MF Rec. IC 1 Stage IC 2 Stages IC 5 Stages Single BPSK

−4

10

0

5

10

15 Eb/N0 (dB)

20

25

30

Figure 10: Performance of a mixed modulation system with 20 BPSK, 10 QPSK and 5 16-QAM users in Rayleigh fading. Simulation results show average system performance and average BER for each modulation format.

9 Performance Improvements for M-ary QAM Users in Mixed Modulation Systems A disadvantage of using mixed modulation when handling multiple data rates is that high-rate users (16-QAM users) have a higher average BER than low-rate users (BPSK and QPSK users) for the same Eb , as indicated in Figure 10. A possible way to reduce the BER for the 16-QAM users is to increase their transmitted power such that they are received with higher Eb than the BPSK and QPSK users. The average BER for a mixed modulation system where the users have unequal energy per bit is shown in Figure 14. The system has 20 BPSK, 10 QPSK and 5 16-QAM users and the length of the signature sequences is 127. The Eb =N0 value for the 16-QAM users is increased in steps of 2 dB relative to the Eb =N0 for the other users, which is kept constant to 18 dB. This value for the Eb =N0 was chosen since it seemed to give a relevant bit error probability for the system. We have not evaluated the performance for other xed Eb =N0 values because of the time consuming simulations. The graph depicts that the average BER of the 16-QAM users may be decreased, by increasing the Eb of these users, with almost no degradation of the performance of the BPSK and QPSK users. For the single-stage IC a minor degradation can be noticed for the BPSK and QPSK users but for the ve-stage IC the performance of the BPSK and QPSK users is unchanged. That is, after ve stages of IC, most of the interference is removed and the signals are separated in the signal space independently of their power. Accordingly, increasing the power of the 16-QAM users with an amount corresponding to an increase of Eb =N0 by approximately 2 dB, the average BER for the 16-QAM users is the same as the average BER for the BPSK and QPSK users for both one and ve stages of IC.


Page 25

0


10

Processing Gain = 128 Orth. Gold Sequences QPSK, 15 users, P=2

−1

10

−2

10

−3

10


−4

10

0

5

10

15 Eb/N0 (dB)

20

25

30

Figure 11: Performance of a multicode system with 15 QPSK users and two parallel channels per user. Simulation and analytical results for an IC with one, two and ve stages and simulation results for an MF receiver are shown in the graph.

10 Discussion and Conclusions The development in mobile communications makes it essential to evolve an ecient system capable of supporting both multiuser detection and variable data rates for the users. The optimum detector is too complex to be implemented in a practical system and the conventional matched lter detector does not perform well without stringent power control. Suboptimal multiuser detectors that has less computational complexity than the optimal detector, but performs better than the conventional detector, are therefore required. In this paper we have demonstrated the use of M-ary rectangular QAM with multistage non-decision directed interference cancellation (NDDIC), which has computational complexity that is linear in the number of users and stages. The two multiple data rate schemes, mixed modulation and multicodes, were analysed for both stationary AWGN channels and at Rayleigh fading channels, and analytical performance estimates using a Gaussian approximation of the MAI were presented. The analytical results for at Rayleigh fading channels agreed well with the results from computer simulations for Eb =N0 values up to 20 dB and the correspondence between the results improved with increasing number of IC stages. The performance of the multistage IC, even for systems with many users, was then close to the single-user bound. Consequently, the multistage IC scheme yields a considerable increase in performance compared to the conventional matched lter detector. Considering a mixed modulation system, we found that the users have dierent average BER depending on their modulation format. That is, the BPSK and QPSK users have lower BER than the 16-QAM users, like in ordinary single-user transmission. However, a small increase in received energy per bit for the 16-QAM users (relative to the BPSK and QPSK users) decreases


Page 26

0


10

QPSK, 15 users, P=2 QPSK, 30 users 16−QAM, 15 users −1

10

−2

10

−3

10

QPSK (15, P=2) QPSK(30) 16−QAM (15) MF Rec. IC 1 Stage IC 2 Stages IC 5 Stages Single BPSK

−4

10

0

5

10

15 E /N (dB) b

20

25

30

0

Figure 12: Performance of three dierent systems in Rayleigh fading. Simulation results for a multicode system (15 QPSK users, P = 2) is compared with two single-rate systems (30 QPSK users and 15 16-QAM users). their BER without great eect on the other users in the system. On the other hand, if we consider a multicode system, the users' average performance is equal when all users have the same number of parallel channels. To take advantage of the synchronous signalling between a user's parallel channels, orthogonal signature sequences can be used, which improves the overall performance and makes the high-rate users perform better than the low-rate users. To conclude, comparing the performance of the two multirate schemes for the same number of IC stages, multicodes is the preferable scheme. Although, the greatest system exibility is obtained if the two schemes are combined in such a way that for each new user that is added to the system a decision is made in favour of a number of parallel channels and/or a certain modulation format. Future work within this project will be to study multistage IC schemes together with multipath Rayleigh fading channels. The inclusion of channel coding and channel estimation will also be investigated. Some of this work has been carried out since this paper was rst submitted. It can be found in [24,29,30].

Acknowledgment The authors would like to acknowledge Karim Jamal at Ericsson Radio Systems for his initial assistance in obtaining the simulation results. This work was supported by the Swedish National Board of Industrial and Technical Development (NUTEK), project 9303363-5.


Page 27

0

10


Processing Gain = 128 Orth. Gold Sequences QPSK, 15 users, P=2 −1

10

−2

10

Known Channel Est. Channel MF Rec. IC 1 Stage IC 2 Stages IC 5 Stages Single BPSK

−3

10

0

5

10 15 E /N (dB) b

20

25

0

Figure 13: Performance of a multicode system with 15 QPSK users and two parallel channels per user. Simulation results for known and estimated channel parameters for an IC with one, two and ve stages and an MF receiver are shown in the graph.

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Eb/No=18 dB BPSK & QPSK −1

10

−2

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Ave. BPSK Ave. QPSK Ave. 16−QAM MF Rec. IC 1 Stage IC 5 Stages

−4

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21 E /N (dB) b

22

23

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Figure 14: Performance of a mixed modulation system in Rayleigh fading, where the 16-QAM users have higher Eb than the BPSK and QPSK users. [9] A. Duel-Hallen, J. Holtzman, and Z. Zvonar, \Multiuser detection for CDMA systems," IEEE Personal Commun., vol. 2, pp. 46{58, Apr. 1995. [10] Y. C. Yoon, R. Kohno, and H. Imai, \A spread-spectrum multiaccess system with cochannel interference cancellation for multipath fading channels," IEEE J. Select. Areas Commun., vol. 11, pp. 1067{1075, Sept. 1993. [11] U. Madhow and M. Honig, \MMSE interference suppression for direct-sequence spread spectrum CDMA," IEEE Trans. Commun., vol. 42, pp. 3178{3188, Dec. 1994. [12] A. Duel-Hallen, \Decorrelating decision-feedback multi-user detector for synchronous codedivision multiple access channel," IEEE Trans. Commun., vol. 41, pp. 285{290, Feb. 1993. [13] A. Kaul and B. D. Woerner, \Analytic limits on performance of adaptive multistage interference cancellation for CDMA," IEE Electron. Lett., vol. 30, pp. 2093{2095, Dec. 1994. [14] P. Patel and J. Holtzman, \Analysis of successive interference cancellation in M-ary orthogonal DS-CDMA system with single path rayleigh fading," in Proc. International Zurich Seminar, Zurich, Switzerland, Mar. 1994, pp. 150{161. [15] P. Patel and J. Holtzman, \Analysis of a simple successive interference cancellation scheme in a DS/CDMA system," IEEE J. Select. Areas Commun., vol. 12, pp. 796{807, June 1994. [16] M. Ewerbring, B. Gudmundson, G. Larsson, and P. Teder, \CDMA with interference cancellation: A technique for high capacity wireless systems," in Proc. IEEE ICC '93, Geneva, Switzerland, May 1993, pp. 1901{1906.


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