A low complexity partially adaptive CDMA receiver for
downlink mobile satellite communications
Gau-Joe Lin and Ta-Sung Lee
n,yDepartment of Communication Engineering, National Chiao Tung University, Hsinchu, Taiwan, R.O.C.
SUMMARY
A novel CDMA receiver with enhanced interference suppression is proposed for pilot symbols assisted mobile satellite systems in the presence of frequency offset. The design of the receiver involves the following procedure. First, adaptive correlators are constructed at different fingers, based on the scheme of generalized sidelobe canceller (GSC), to collect the multipath signals and suppress multi-access interference (MAI). In particular, a partially adaptive (PA) realization of the GSC correlators is proposed based on the Krylov subspace technique, leading to an efficient algorithm without the need of complicated matrix computations. Second, pilot symbols assisted frequency offset estimation, channel estimation and RAKE combining give the estimate of signal symbols. Finally, further performance enhancement is achieved by an iterative scheme in which the signal is reconstructed and subtracted from the GSC correlators input, leading to faster convergence of the receiver. The proposed low complexity PA receiver is suitable or the downlink of mobile satellite CDMA systems, and shown to outperform the conventional fully adaptive MMSE receiver by using a small number of pilot symbols. Copyright # 2003 John Wiley & Sons, Ltd.
KEY WORDS: CDMA; mobile satellite; interference suppression; generalized sidelobe canceller; partial adaptivity; Krylov subspace technique
1. INTRODUCTION
In order to improve mobility and guarantee worldwide access, satellite based systems have been proposed for the third generation mobile communications [1]. In areas with a small population or low infrastructure, satellite communications are especially superior to terrestrial mobile communications. Satellite based systems can also be used as a complement to existing communication networks in order to increase the availability of services to mobile users. Worldwide access provisioning can be achieved by developing the mobile satellite systems in the form of multi-satellite constellation in non-geostationary earth orbits. For example, the low earth orbit (LEO) satellite systems are a promising solution. The realization of handover
yE-mail: tslee@mail.nctu.edu.tw
Contract/grant sponsor: Ministry of Education and National Science Council, R.O.C.; contract/grant number: 89-E-FA06-2-4
n
Correspondence to: Ta-Sung Lee, Department of Communication Engineering, National Chiao Tung University, Hsinchu, Taiwan, R.O.C.
between different satellites and choosing of a multiple access scheme are two important issues for a LEO satellite communication system. Both problems can be managed by using the code division multiple access (CDMA) technology with multi-satellite diversity. In the present and next generation mobile satellite communication systems, CDMA has been proposed as a major multiple access scheme [1, 2]. However, two factors that limit the overall capacity of a CDMA system are the multiple access interference (MAI) and multipath fading. In the worst case, strong MAI causes the near-far problem and severe multipath propagation induces deep fading and/or inter-symbol interference (ISI). In mobile satellite communications the propagation channel is typically a mild Ricean channel with a short delay spread. Path diversity is usually exploited by introducing artificial delayed paths from multiple satellites. On the other hand, some form of interference mitigation can be employed to boost the system capacity significantly [1].
In mobile satellite systems, diversity can be accomplished by simultaneous transmission to multiple satellites. The waveforms are then retransmitted to an earth station, where they are combined to yield diversity gain [3]. In wideband CDMA systems, the multipath environment can be exploited through the RAKE receiver, allowing signals arriving at the receiver with different propagation delays to be independently received and coherently combined by exploiting the temporal signature of the channel. On the other hand, in order to successfully detect data from the desired user, the MAI need to be suppressed effectively. Adaptive multi-user detectors (MUD) and interference cancellers have been suggested which provide full or partial immunity to the near-far effect [4]. The performance of an optimal MUD [4] in a multi-user system can approach that in a single-multi-user environment. Unfortunately, the optimal MUD is impractically complex. As an alternative, the sub-optimal linear multi-user detector is an improved version of the conventional RAKE receiver, with the improvement due to better MAI suppression via either post- or pre-despread processing [5]. The post-despread MUD works with the outputs of a bank of filters, each matched to a user of interest. The pre-despread MUD can be regarded as an adaptive matched filter that performs despreading and MAI suppression simultaneously. Popular pre-despread MUDs include the minimum mean squared error (MMSE) [6] and minimum output energy (MOE) [7] receivers. In particular, the MOE receiver derives its filter weights by minimizing the output energy subject to a unit response constraint for the desired signal. It is similar in structure to the linearly constrained minimum variance (LCMV) beamformer in array processing [8, 9], and is shown to offer the performance of the MMSE receiver without the need of channel information [7]. Unfortunately, the MOE receiver exhibits high sensitivity to channel mismatch and does not perform reliably in the presence of multipath propagation. Although the pre-despread CDMA receivers provide excellent MAI suppression, they requires an ðM 1Þ-dimensional adaptive processing, where M is the processing gain. To reduce the complexity due to a large M; partially adaptive (PA) realization is suggested as an alternative with which the number of adaptive weights is reduced [8–10]. The advantages of PA implementation include not only reduced complexity but also faster convergence.
In this paper, a novel CDMA receiver with enhanced interference suppression is proposed for pilot symbols assisted mobile satellite systems in the presence of frequency offset. The design of the receiver involves the following procedure. First, a set of adaptive correlators is constructed to collect multipath signals with different delays. The tap weights of each correlator are determined in accordance with the LCMV criterion so that strong MAI can be effectively suppressed blindly. To avoid signal cancellation incurred with channel mismatch, these LCMV correlators are realized in the form of generalized sidelobe canceller (GSC) [8, 9]. For reduced
complexity processing, partial adaptivity is incorporated which is done by selecting a reduced dimension subspace of the column space of the blocking matrix by using the Krylov subspace technique [11]. Second, a simple coherent RAKE combiner with pilot aided channel estimation gives the desired user’s symbol decisions. Since strong interference has been removed, channel estimation can be done accurately with a small number of pilot symbols. Finally, further performance enhancement is achieved by an iterative scheme in which the signal is reconstructed and subtracted from the GSC correlators input, leading to faster convergence of the receiver. The proposed low complexity PA receiver is suitable for the downlink of mobile satellite CDMA systems, and is shown to outperform the conventional fully adaptive MMSE receiver by using a relatively small number of pilot symbols.
2. DATA MODEL AND LINEAR CDMA RECEIVERS
Consider a mobile satellite communications system in which each satellite is equipped with S spot beams. The ground gateways are equipped with directional antennas, one for each satellite as shown in Figure 1. The transmitted field from the satellite is received by a mobile terminal in three basic ways: (1) the direct component, which is the line-of-sight (LOS) wave; (2) the specular component, which represents the field collected from a single reflection and arrives as a delayed version of the direct component; (3) the diffuse component. For simplicity, the downlink transmission channel is modelled as with L resolved Rayleigh or Rician fading paths due to either satellite diversity or multipath. The Rician probability density function is commonly used to model a clear LOS path, while the Rayleigh probability density function models a blocked LOS path with which the received signal comes from multipath. Furthermore, in order to account for users’ mobility when evaluating the performance of a mobile satellite system, a time-shared combination of a ‘good’ state fading for the LOS path and a ‘bad’ fading
for the non-LOS path is introduced. This is described by the mixture envelop probability density function [12,13]: faðaÞ ¼ B a s2e a 2s2þ ð1 BÞ a s2e a 2þA2 s 2s2 I 0 aAs s2 ð1Þ where B is defined as the fraction of time that a path is in a bad fading state, while ð1 BÞ is the
fraction of time that the path is in a good fading state. As is the amplitude of the specular
component of the Rician part of the density, 2s2is the average power of the diffuse component,
and I0ðÞ is the modified Bessel function of the first kind and zeroth order [13].
Consider a scenario in which K active CDMA users are present in the downlink of the system. The kth user’s contribution to the received signal can be written as
rkðtÞ ¼ sk
X
i
dkðiÞckðt iT Þ ð2Þ
where dkðiÞ denotes the ith transmitted information symbol assumed to be i.i.d. with zero-mean
and unit variance, T is the symbol duration, s2
k is the transmit power, and ckðtÞ is the signature
waveform given by ckðtÞ ¼ X M 1 m¼0 ck½mpðt mTcÞ ð3Þ
where ck½m is the spreading sequence of the kth user, M is the spreading factor, pðtÞ is the chip
waveform, and Tcis the chip duration. Putting the K user signals together, the received baseband
data can be expressed in the following form:
xðtÞ ¼X K k¼1 XL l¼1 ak;lej2pDfktrkðt tk;lÞ þ nðtÞ ð4Þ
where Dfk is the frequency offset associated with the kth user (due to oscillator drifting or
Doppler shift), tk;land ak;lare the delay and complex gain, respectively, of the lth path of the
kth user, and nðtÞ is the additive white noise process with power s2n: It is assumed that the L paths
arrive within a delay spread of L chips, with each path having a different delay of integer number of chips. It is also assumed that initial acquisition is performed properly such that a
rough estimate of timing/frequency offset is available for each user. In this case, Dfk is
considered the residual frequency offset. To fully exploit the temporal signature, xðtÞ is chip
matched filtered and then chip rate sampled at t ¼ iTsþ mTc over one symbol duration plus
delay spread, i.e. m ¼ 0; 1;. . . ; M þ L 2: The resulting discrete-time data over the ith symbol is
given by xmðiÞ ¼ XK k¼1 sk XL l¼1
ak;lej2pDfkðiTsþmTcÞrk;mðiÞ þ nmðiÞ ð5Þ
where rk;mðiÞ ¼ rkðt tk;lÞjt¼iTsþmTc and nmðiÞ ¼ nðtÞjt¼iTsþmTc: Assuming that the user 1 is the
vector, we have
xðiÞ ¼ ½x0ðiÞ; x1ðiÞ; . . . ; xM þL2ðiÞT
¼X K k¼1 sk XL l¼1 ak;lðck;l DfkÞdkðiÞej2pDfkiTsþ nðiÞ ¼ h1d1;dðiÞ þ XK k¼2 hkdk;dðiÞ þ nðiÞ
¼ s1ðiÞ þ iðiÞ þ nðiÞ ð6Þ
where T denotes the transpose,
ck;l¼ ½0Tl1; c½0; c½1; . . . ; c½M 1; 0TLlT ð7Þ
Dfk¼ ½1; ej2pDfkTc; . . . ; ej2pDfkðMþL2ÞTcT ð8Þ
denotes the Hadamard (elementwise) product and 0n is the n 1 zero vector. The hk is the
effective composite signature vector (CSV) of user k given by hk¼ sk
XL
l¼1
ak;lðck;l DfkÞ ð9Þ
dk;dðiÞ ¼ dkðiÞej2pDfkiTs ð10Þ
is the ‘frequency shifted’ symbol varying with time index i: Finally, s1ðiÞ ¼ h1d1ðiÞej2pDf1iTs is the
signal vector, iðiÞ ¼PKk¼2 hkdkej2pDfkiTsðiÞ is the MAI vector, and nðiÞ is the noise vector.
A receiver for user 1 is designed to identify and remove h1to retrieve d1ðiÞ from iðiÞ and nðiÞ: In
particular, a linear receiver combines xðiÞ using a weight vector wk to obtain
#dd1;dðiÞ ¼ wH1xðiÞ ð11Þ
where H denotes the complex conjugate transpose. A popular criteria for choosing w1 leads to
the MMSE receiver:
wMMSE¼ R1x #hh1 ð12Þ
where #hh1 is an estimate of h1 and Rx is the data correlation matrix given by
Rx¼ EfxðiÞxðiÞHg ¼ Rsþ Rin ð13Þ
where
Rs¼ Efs1ðiÞs1ðiÞHg ¼ h1hH1 ð14Þ
Rin ¼ EfðiðiÞ þ nðiÞÞðiðiÞ þ nðiÞÞHg ¼
XK
k¼2
hkhHk þ s2nI ð15Þ
Another type of optimal receiver is the maximum SINR (MSINR) receiver given by
However, Rin is not available in practice, and is usually estimated by decision aided schemes.
Finally, from (6), (11), with the frequency offset Df1 estimated as D #ff1; the symbol decision
#dd1ðiÞ can be obtained by
#dd1ðiÞ ¼ decf #dd1;dðiÞej2pD #ff1iTsg ð17Þ
Most existing frequency offset estimators are developed based on the assumption of no or little interference (i.e. AWGN). With the presence of strong MAI, these estimators often degrade seriously. It is thus necessary to perform interference suppression before frequency offset estimation.
3. DEVELOPMENT OF PARTIALLY ADAPTIVE CDMA RECEIVER
In this section, an efficient pre-despread adaptive CDMA receiver is developed which offers the performance of the MMSE or MSINR receiver. The receiver consists of a set of adaptive correlators and a RAKE combiner for exploiting path diversity. A decision aided scheme is included for performance enhancement. The schematic diagram of the receiver is depicted in Figure 2.
3.1. Construction of blind adaptive GSC correlators
A set of adaptive correlators is used to perform despreading and MAI suppression. They are realized in the form of GSC, and require no pilot symbols for channel estimation. In other words, these correlators are ‘blind’ and can utilize the entire received symbols, including data and pilot, to compute the adaptive weights. This is in contrast to non-blind pilot aided methods
+ -Data Symbols x (j+1) y ( ) 1 ˆs j ( ) 1 ˆhj ( ) 1 j d (j 1) L + w ( 1) 1 j+ w Copy Copy + -1, L c + -Finger 1 Finger L 1,1 c Krylov Subspace Krylov Subspace Frequency Offset Estimation Coherent RAKE Combining Tentative Data Decision Pilot Symbol Channel Estimation 1 ˆ ˆ f ∆
Figure 2. Schematic diagram of proposed decision aided CDMA receiver with partially adaptive interference cancellation.
(e.g. MMSE) which cannot achieve reliable channel estimation in the presence of strong MAI by using the limited number of pilot symbols.
In order to restore the processing gain and retain the path diversity, xðiÞ is despread at each of the L fingers using a set of discrete-time correlators:
z1;lðiÞ ¼ wHlxðiÞ ¼ wHlh1d1ðiÞ þ wHliðiÞ þ wHlnðiÞ ð18Þ
for l ¼ 1;. . . ; L; where wl is the correlator weight vector at the lth finger. For an effective
suppression of MAI, these weight vectors can be determined in accordance with the LCMV criterion:
min
wl
wHl Rxwl subject to cH1;lwl¼ 1 ð19Þ
However, the adverse phenomenon of signal cancellation usually occurs with the solution in (19)
due to the mismatch of signature vectors (i.e. mismatch between c1;l and h1). With such a
mismatch present, the signal can be treated as interference and receive a very small gain. To avoid such signal cancellation, the LCMV correlators can be implemented with multiple constraints [14]. Here an alternative solution is suggested based on the GSC technique. The GSC is essentially an indirect but simpler implementation of the LCMV receiver. It is a widely used structure that allows a constrained adaptive algorithm to be implemented in an unconstrained fashion [8, 9].
The concept of GSC, as depicted in Figure 3(a), is to decompose the weight vector into two
orthogonal components as wl¼ c1;l Bul: The matrix B is a pre-designed signal ‘blocking
matrix’ which removes user 1’s signal before filtering. The goal is then to choose the adaptive
weight vector ul to cancel the interference in xðiÞ: According to the GSC scheme, ul is
determined via the MMSE criterion: min
ul
EfjcH1;lxðiÞ uHlBHxðiÞj2g ð20Þ
Since the signal has been removed in the lower branch by B; the only way to minimize the MSE
is such that ul performs a mutual cancellation of the MAI between the upper and lower
(a) (b)
+
–
( )i x B ul 1,l c+
–
1,l( )
( )i x 1,l c B Tl ul 1,l( )
z i
z i
(M + L –1)×1 (M + L –1)× (M–1) (M + L –1)× (M–1) (M –1)× (K–1) (M + L –1)×1) (M–1)×1 (K–1)×1branches. Solving for uland substituting in wl¼ c1;l Bul; we get
wl¼ ½I BðBHRxBÞ1BHRxc1;l ð21Þ
This is called the direct-matrix-inversion (DMI) implementation of the fully adaptive (FA) GSC correlators. Note that B must block signals from the entire delay spread in order to avoid signal cancellation. It can be chosen to be a full rank ðM þ L 1Þ ðM 1Þ matrix whose
columns are orthogonal to fc1;1; . . . ; c1;Lg; i.e. BHc1;l¼ 0; l ¼ 1; . . . ; L: The distortion of
signature vectors c1;l’s due to frequency offset is typically tolerable in signal blocking, i.e. the
signal component can be reliably removed by the above designed B under a moderately small frequency offset.
In the DMI implementation, the computation of adaptive weight vectors in (21) involves the
inversion of BHRxB; which is ðM 1Þ ðM 1Þ: With a large M ; this requires a high
computational load and is likely to incur numerical instability and poor convergence behaviours [8, 9]. To alleviate this problem, the partially adaptive (PA) GSC is proposed which uses only a portion of the available degrees of freedom offered by the adaptive weights. Specifically, the PA
techniques can be employed to reduce the size of B or dimension of ul’s [8–10]. For example, the
Cross-Spectral PA (CS-PA) technique is developed by working with a smaller blocking matrix constructed from a reduced-dimensional subspace of RangeðBÞ to provide the lowest MMSE [10], and requires complicated eigen-computation. In the following, a simple and effective PA technique is proposed which is suitable for the downlink of mobile satellite scenarios.
3.2. Partially adaptive implementation
The PA GSC, as shown in Figure 3(b), works with P ðP 5M 1Þ adaptive weights through the
use of an ðM 1Þ P linear transformation Tlfor the lth finger [8]. This leads to a reduced size
blocking matrix *BBl¼ BTl: The criteria for the selection of Tlinclude: (i) *BBlshould be as small as
possible (ii) MAI should be retained as much as possible in the lower branch. Criterion (i) is for complexity reduction and (ii) is for optimal mutual cancellation of MAI in the upper and lower branches [15]. Criterion (ii) is equivalent to saying that a reduced size blocking matrix should be chosen such that the upper and lower branch outputs of the GSC have a large crosscorrelation [15]. Since the lower branch contains no signal, the only way to maximize the crosscorrelation is to retain as much MAI as possible in the lower branch. By doing so, a maximum mutual cancellation of interference can be achieved between the upper and lower branches. In the
following, an efficient method for finding *BBl’s is developed based on the Krylov subspace
technique.
According to Reference [16], a reliable reduced rank MMSE solution can be found by projecting the data vector xðiÞ onto a P -dimensional subspace represented by the Krylov subspace spanf#hh1; Rx#hh1; . . . ; RðP 1Þx #hh1g:
*xxðiÞ ¼ SH
PxðiÞ ð22Þ
where SP ¼ ½#hh1; Rx#hh1; . . . ; RðP 1Þx #hh1 is the ðM þ L 1Þ P dimension reduction transformation.
The reduced rank solution is then given byw*wMMSE¼ ðSHPRxSPÞ1SHP #hh1[16]. The same technique
can be applied to the GSC problem by considering BHxðiÞ as the data vector and Tl as the
straightforward to see that a reduced size blocking matrix can be chosen as *BBl¼ B½BHRxc1;l; ðBHRxBÞBHRxc1;l; . . . ; ðBHRxBÞðP 1ÞBHRxc1;l
¼ ½BBHRxc1;l; ðBBHRxÞ2c1;l; . . . ; ðBBHRxÞPc1;l ð23Þ
The computation of adaptive weight vectors in (21) requires a matrix inversion, which may be a
demanding task even the reduced size *BBl is used in place of B: In order to avoid such
computation, a scheme is proposed based on a decorrelating (Gram-Schmidt) process that is applied to reconstruct *BBl¼ ½*bb1;l; . . . ; *bbP;l: 1. Initialization: P?0 ¼ BBHand 2. For p ¼ 1;. . . ; P : *bbp;l ¼ P?p1ðBBHRxÞpc1;l P?p ¼ P?p1*bbp;l*bb H p;l *bbH p;l*bbp;l
An interesting observation gleaned from the above procedure is that *bbHi;lRx*bbj;l¼ 0 for ji jj > 1;
i.e. *BBHl RxBl has a symmetric tri-diagonal structure. The following procedure then ‘diagonizes’
*BBH
l RxBl by decorrelating *bbi;land *bbj;l for ji jj ¼ 1:
*uup;l¼ *bbH p;lRx*bbp1;l *bbH p;lRx*bbp;l *bbp1;l¼ *bbp1;l*uup;l*bbp;l ð24Þ
for p ¼ P ;. . . ; 1: With the modification in (24), the columns of *BBl satisfies the Rx-conjugacy
property [11], i.e.:
*bbH
r;lRx*bbs;l¼ Ef*bbHr;lxðiÞð *bbHs;lxðiÞÞ n
g ¼ 0 ð25Þ
for r=s: It follows that the outputs from different columns of *BBl are uncorrelated with each
other. This leads to a significant simplification in the computation of GSC weight vector in (21).
Replacing B in (21) by *BBl; we have wl¼ I XK p¼1 dp*bbp;l*bbHp;l ! Rx " # c1;l ð26Þ
where dp¼ ð*bbHp;lRx*bbp;lÞ1: The new GSC weight vector based on *BBlinvolves no matrix inversion
as desired.
3.3. RAKE combining and decision aided symbol detection
With the adaptive correlator bank constructed, the next step is to perform a maximum ratio combining of the correlator outputs to collect the multipath energy. Since the MAI has been
removed, channel estimation (i.e. #aa1;l’s) and frequency offset estimation (i.e. D #ff1’s) for the
desired user can be done accurately, leading to improved performance as compared to the conventional RAKE receiver. However, the GSC is blind in nature and usually exhibits slow convergence due to the residual signal effect [17]. To remedy this, an iterative decision aided
scheme is introduced in which the signal is estimated and then subtracted from the input data before the computation of GSC adaptive weights.
First, assume that at the jth iteration, the received data xðiÞ is despread at the L fingers into: #zzðjÞ
1;lðiÞ ¼ w ðjÞH
l xðiÞ ð27Þ
for l ¼ 1;. . . ; L; where wðjÞl is obtained by (21) or (26) using the ‘signal-subtracted’ data vector
yðjÞðiÞ as the GSC input:
yðjÞðiÞ ¼ xðiÞ #ssðj1Þ1 ðiÞ ð28Þ
with#ssðj1Þ1 ðiÞ being the desired signal estimated at the ðj 1Þth iteration ð#ssð0Þ1 ðiÞ ¼ 0Þ: That is, the
correlation matrix Rx in (21) or (26) is replaced by RðjÞy ¼ EfyðjÞðiÞyðjÞðiÞ
Hg: After filtering, the
MAI is suppressed to a certain extent, and the frequency offset estimate D #ff1 can be obtained
reliably by either the discrete Fourier transform or maximum likelihood method [18], and the
channel gain estimates at the L fingers can be obtained using a sequence of Nppilot symbols:
#aaðjÞ 1;l¼ 1 MNp XNp i¼1 #zzðjÞ 1;lðiÞd n 1ðiÞe j2pD #ff1iTs ð29Þ
for l ¼ 1;. . . ; L; where M is the normalizing factor accounting for the processing gain. Note that
#aaðjÞ
1;lincludes the effect of transmit power s21: Using these channel estimates, a coherent RAKE
combining of #zzðjÞ1;lðiÞ’s is achieved by #zzðjÞ 1 ðiÞ ¼ XL l¼1 #aaðjÞ * 1;l #zz ðjÞ 1;lðiÞ ð30Þ
which is then sent to the data decision device: #ddðjÞ
1 ðiÞ ¼ decf#zz ðjÞ 1 ðiÞe
j2pD #ff1iTsg ð31Þ
Second, signal reconstruction is done by exploiting the channel estimates#aaðjÞ1;l’s, D #ff1’s, the desired
user’s signature c1;land symbol decisions #ddðjÞ1 ðiÞ as follows:
#ssðjÞ 1 ðiÞ ¼ XL l¼1 #aaðjÞ 1;lc1;l ! #ddðjÞ 1 ðiÞej2pD #ff1 iTs ð32Þ
Note that #aaðjÞ1;l’s are used for both signal reconstruction and symbol detection. Finally, the
reconstructed signal is subtracted from the data sent to the ðj þ 1Þth iteration, which yields
yðjþ1ÞðiÞ ¼ xðiÞ #ssðjÞ1 ðiÞ ð33Þ
By using yðjþ1ÞðiÞ as the GSC input, the adverse slow convergence can be effectively improved,
and the PA CDMA multi-user receiver can achieve its optimal performance with a moderate size of data samples. Due to signal subtraction, the receiver will act like the optimal MSINR
receiver operating on Rin; which offers the best comprise between MAI plus noise suppression
4. COMPUTER SIMULATIONS
Simulation results are demonstrated to confirm the performance of the proposed PA receiver in a time-multiplexed pilot symbols assisted system. The receiver output SINR is used as the
evaluation index. Also, the input SNR is defined as SNRi¼ s21=s2n; and the near-far-ratio is
defined as NFR ¼ s2
k=s21; k ¼ 2; . . . ; K; where we assume equal power MAI for convenience. It is
assumed that the Ricean factor A2s=2s2¼ 6 dB and the fraction of time of fading state B ¼ 0:3 in
(1). The path gains ak;l’s are assumed independent, identically distributed unit variance complex
Gaussian random variables, the path delays tk;l’s are uniform over ½0; 3Tc; and the number of
paths is L ¼ 4: All CDMA signals are generated with BPSK data modulation and random codes of length M ¼ 32 are used as the spreading codes. The chip rate is assumed to be 3.84 Mcps,
corresponding to a chip period of Tc¼ 0:26 ms: For each trial, Ns symbols (including data and
pilot) are used to obtain the sample estimate of Rx and Ry; and Np pilot symbols are used to
obtain #aa1;land D #ff1: In particular, the ML method is used for frequency offset estimation. Each
simulation result is obtained by 200 independent trials, with each trial using a different set of
ak;l’s and data/noise sequence. Unless otherwise mentioned, the following parameters are
assumed: K ¼ 10; SNRi¼ 0 dB; NFR ¼ 10 dB; Ns¼ 100; Np¼ 20; D #ff1¼ 20 KHz (or
D #ff1Ts¼ 1=6), PA dimension P ¼ dðK 1Þ=2e and the number of iterations is J ¼ 3 in Section
3.3. For comparison, we also include the results obtained with the optimal, MMSE and MOE
receivers. The optimal receiver is defined to be the MSINR receiver with Rin obtained by
artificially removing s1ðiÞ from xðiÞ and true CSV h1used. The MMSE receiver is given by (12),
with #hh1 and D #ff1 obtained using Np pilot symbols. The MOE receiver is based on the method
presented in Reference [14]. The proposed receiver uses Np¼ Ns=5 pilot symbols, and the
MMSE receiver uses either Np¼ Ns=2 (1/2) or Np¼ Ns(full) pilot symbols. The MOE receiver is
blind without using any pilot symbols ðNp¼ 0Þ:
In the first simulation, the output SINR performance of the proposed receiver is evaluated as a function of iteration number J with P ¼ 5: Included are the FA receiver (FA dimension 32)
and the proposed PA receiver. For channel estimation, Np¼ Ns=5 pilot symbols are used. The
results in Figure 4 show that the proposed two receivers successively approach the optimal receiver in three iterations. After convergence, the PA receivers have almost the same
performance of the FA receive, confirming that the reduced dimension *BBl retains the full
interference suppression capability of the FA receiver. The second simulation, the output SINR performance versus dimension of blocking matrix of PA receiver is demonstrated. The results given in Figure 5 show that the proposed PA receiver successively approach the proposed FA receiver at PA dimension P ¼ 5 and reaches the performance of MMSE receiver using full pilot symbols at P ¼ 2: The simulation results confirm that the proposed PA receiver is able to offer the performance of the FA receiver with a P ¼ dðK 1Þ=2e dimensions.
In the third simulation, the tolerance of the proposed PA receiver against different frequency
offsets is evaluated. The resulting SINR curves as a function of Df1Ts are plotted in Figure 6.
They show that the proposed receiver performs reliably within a wide offset range, indicating that with successful signal reception and MAI suppression by the adaptive GSC correlators, an accurate frequency offset estimate can be obtained to guarantee a satisfactory performance. In the fourth simulation, the output SINR performance is evaluated as a function of input SNR. The results shown in Figure 7 indicate that the proposed PA receiver successively approaches the optimal receiver within a wide range of input SNR. In the fifth simulation, the near-far resistance is evaluated with different NFR values. Figure 8 shows the output SINR curves. It is
observed that the proposed PA receiver achieves its excellent near-far resistance by success-fully canceling the MAI using the temporal degree of freedom offered by the pre-despread data. The system capacity is then evaluated with different values of K: As shown in Figure 9, the proposed PA receiver is able to offer the performance of the optimal receiver in a heavily loaded system with effective MAI suppression using the smallest dimension for adaptive filtering. 1 2 3 4 5 6 7 8 9 10 0 5 10 15 20 25 30 Output SINR (dB) Number of Iterations (J) Optimal (Ideal) Proposed FA (1/5) Proposed PA (1/5) MMSE (Full) MMSE (1/2) MOE (Blind)
Figure 4. Receiver output SINR versus number of iterations J ; with K ¼ 10; SNRi¼ 0 dB;
NFR ¼ 10 dB; Ns¼ 100; Df1Ts¼ 1=6 and P ¼ 5: 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 0 5 10 15 20 25 30 Output SINR (dB)
Dim. of Blocking Matrix (P)
Optimal (Ideal) Proposed FA (1/5) Proposed PA (1/5) MMSE (Full) MMSE (1/2) MOE (Blind)
Figure 5. Receiver output SINR versus PA dimension P ; with K ¼ 10; SNRi¼ 0 dB;
Finally, the convergence behaviour of the proposed PA receiver is compared with the optimal, MMSE and MOE receivers. The results given in Figure 10 show that the proposed receiver with
1=5 pilot symbols converges in about Ns¼ 100 data symbols, and is only 1:3 dB away from the
optimal receiver. On the other hand, the MMSE receiver using full pilot symbols offers nearly the optimal performance, but degrades significantly if only 1=2 pilot symbols are available.
0 0.1667 0.3333 0.5 0.6667 0.8333 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 Output SINR (dB)
Normalized frequency offset (|∆f1Ts|)
Optimal (Ideal) Proposed PA (1/5) MMSE (Full) MMSE (1/2) MOE (Blind)
Figure 6. Receiver output SINR versus normalized frequency offset Df1Ts; with K ¼ 10; SNRi¼ 0 dB;
NFR ¼ 10 dB; Ns¼ 100; J ¼ 3 and P ¼ 5: -10 -8 -6 -4 -2 0 2 4 6 8 10 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 Output SINR (dB) Input SNR (dB) Optimal (Ideal) Proposed PA (1/5) MMSE (Full) MMSE (1/2) MOE (Blind)
Figure 7. Receiver output SINR versus input SNR, with K ¼ 10; NFR ¼ 10 dB; Ns¼ 100; Df1Ts¼ 1=6; J ¼ 3 and P ¼ 5:
Again, the reasons for the significant discrepancy between the proposed and MMSE receivers with a low pilot symbol ratio is that the proposed receiver cancels the MAI before channel and frequency offset estimation, whereas the MMSE receiver estimates the channel and frequency offset in the presence of strong MAI.
0 2 4 6 8 10 12 14 16 18 20 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 Output SINR (dB) NFR (dB) Optimal (Ideal) Proposed PA (1/5) MMSE (Full) MMSE (1/2) MOE (Blind)
Figure 8. Receiver output SINR versus NFR, with K ¼ 10; SNRi¼ 0 dB; Ns¼ 100; Df1Ts¼ 1=6; J ¼ 3 and P ¼ 5: 2 4 6 8 10 12 14 16 18 20 22 24 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 Output SINR (dB) Number of Users (K) Optimal (Ideal) Proposed PA (1/5) MMSE (Full) MMSE (1/2) MOE (Blind)
Figure 9. Receiver output SINR versus user number K; with SNRi¼ 0 dB; NFR ¼ 10 dB; Ns¼ 100; Df1Ts¼ 1=6; J ¼ 3 and P ¼ dðK 1Þ=2e:
5. CONCLUSION
A decision aided CDMA receiver with partially adaptive interference suppression is proposed for downlink mobile satellite communications in the presence of frequency offset. The new receiver is developed with the following procedure. First, blind adaptive correlators are constructed at different fingers based on the GSC scheme to collect multipath signals and suppress strong interference. For reduced complexity implementation, partial adaptivity is incorporated into the GSC based on the Krylov subspace technique, leading to an efficient algorithm without the need of matrix inversion. Second, pilot symbols assisted frequency offset estimation, channel estimation and RAKE combining give the estimate of signal symbols. Finally, for further performance enhancement, an iterative decision aided scheme is introduced which reconstructs and subtracts the signal from the GSC input data. This effectively eliminates the performance drop due to finite data samples effect. Simulation study shows that the proposed partially adaptive CDMA receiver is very robust to frequency offset, and can achieve nearly the same performance of the optimal MSINR and MMSE receivers under severe system conditions. The main advantages of the proposed receiver over others lie in a lower implementation complexity and overhead for pilot symbols.
ACKNOWLEDGEMENTS
This work was sponsored jointly by the Ministry of Education and National Science Council, R.O.C, under the Contract 89-E-FA06-2-4
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Optimal (Ideal) Proposed PA (1/5) MMSE (Full) MMSE (1/2) MOE (Blind)
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AUTHORS’ BIOGRAPHIES
Gau-Joe Lin was born in Chyayi, Taiwan, R.O.C. on March 28, 1963. He received the BSEE degree from Chung Cheng Institute of Technology, Taoyuan, Taiwan, in 1986, and the MSEE degree from National Sun Yat-Sen University, Kaohsiung, Taiwan, in 1991. Currently he is working toward the PhD degree in the Department of Communication Engineering at National Chiao Tung University, Hsinchu, Taiwan. From 1986 to 1989 and 1991 to 1999, he was in the C3I department at Chung Shan Institute of Science and Technology, Taoyuan, Taiwan. His research interests include multiuser detection, communication signal processing, and smart antennas.
Ta-Sung Lee was born in Taipei, Taiwan, R.O.C. on October 20, 1960. He received the BS degree from National Taiwan University, Taipei, Taiwan, in 1983, the MS degree from the University of Wisconsin, Madison, in 1987, and PhD degree from Purdue University, W. Lafayette, IN, in 1989, all in electrical engineering. From 1987 to 1989, he was a David Ross Graduate Research Fellow at Purdue University. In 1990, he joined the Faculty of National Chiao Tung University (NCTU), Hsinchu, Taiwan, where he currently holds a position as Professor in the Department of Communication Engineering. From 1999 to 2001, he was Managing Director of the Communications and Computer Training Program of NCTU. His present research interests include advanced signal processing and MIMO techniques for wireless communications.
Dr. Lee is a member of Phi Tau Phi Society of R.O.C., and recipient of 1999 Young Electrical Engineer Award of the Chinese Institute of Electrical Engineers and 2001 NCTU Teaching Award.
