A novel initialization scheme for a constant modulus algorithm RAKE (CMA-RAKE) receiver for frequency-selective fading asynchronous code-division multiple access (CDMA) channels is proposed. The solutions from the minimization of the constrained minimum output energy (CMOE) criterion are adopted as the initialization of the subsequent CMA receivers. The proposed receiver is proven to be near-far resistant at different levels of near-far problems. Simulations confirm the superiority of the receiver over the existing RAKE receivers in terms of signal-to-interference plus noise (SINR) ratio over a wide range of near-far situation

Jonathon Chambers (1251609)

Peerapol Yuvapoositanon (7207325)

English

Loughborough University Institutional Repository

   This item was submitted to Loughborough’s Institutional Repository (https://dspace.lboro.ac.uk/) by the author and is made available under the following Creative Commons Licence conditions.      For the full text of this licence, please go to: http://creativecommons.org/licenses/by-nc-nd/2.5/  International Symposium on Signal Processing and its Applications (ISSPA), Kuala Lumpur, Malaysia, 13 - 16 August, 2001. Organued by the Dept. of Microelectronics and Computer Engineering, VTM, Malaysia and Signal Processing Research Centre, QVT, Australia A CMOE-CMA RAKE RECEIVER STRUCTURE FOR NEAR-FAR FREQUENCY-SELECTIVE FADING CDMA CHANNELS Peerapol Yuvapoositanon and Jonathon A.  Chambers Signal and Image Processing Group, Department of and Electronic and Electrical Engineering, University of Bath, Bath BA2 7AY, United Kingdom Email: eeppay@bath.ac.uk ABSTRACT A novel initialization scheme for a constant modulus algo- rithm RAKE (CMA-RAKE) receiver for frequency-selective fad- ing asynchronous code-division multiple access (CDMA) chan- nels is proposed. The solutions from the minimization of the con- strained minimum output energy (CMOE) criterion are adopted as the initialization of the subsequent CMA receivers. The proposed receiver is proven to be near-far resistant at different levels of near- far problems. Simulations confirm the superiority of the receiver over the existing RAKE receivers in terms of signal-to-interference plus noise (SINR) ratio over a wide range of near-far situations. 1. INTRODUCTION In wideband CDMA systems, a RAKE receiver is used to gather signal energies at different chip delays by coherently combining the outputs from a bank of correlators or arms. However, the con- ventional RAKE receiver is susceptible to the near-far problem: the situation where interfering users are stronger than the desired user. In [l], the conventional RAKE structure is maintained but the correlators are replaced by the near-far resistant .constrained minimum output energy (CMOE) detectors developed in [2].  This receiver is called the decorrelating RAKE (D-RAKE) receiver due to the decorrelating nature of the CMOE detectors. The perfor- mance in terms of the mean-square error (MSE) of the D-RAKE receiver is shown to be superior to that of the single-arm CMOE detector [2]. The idea of replacing the correlators in the conventional RAKE receiver with adaptive CMA equalizers is proposed in [3] by as- suming knowledge of the correct timing of the desired user. After convergence, the MSE performance of the CMA-RAKE receiver is shown to be better than that of the D-RAKE receiver [I]. How- ever, the CMA-RAKE receiver (and any receiver using the con- stant modulus stochastic gradient (CM-SG) criterion) is suscep- tible to misconvergence in the near-far situation due to its multi- modal cost surface. Unless a prewhitening process is employed, the solution is likely to be dominated by the stronger interfering solutions and results in failure to successhlly retrieve the desired transmissions [4]. In this paper, we propose an initialization scheme for the CMA- RAKE receiver by using the solution from the minimization of the This workwas supported by the Mahanakom University of Technology, Bangkok, Thailand. 0- 7803-6703-0/01/$10.00 82001 IEEE CMOE criterion (CMOE-CMA RAKE) for frequency-selective fad- ing asynchronous CDMA channels. The signal-to-interference plus noise ratio (SNR) is used as a performance measure for the de- sired solution. It is shown from the simulations that for different levels of near-far problems, the SINR performance of the CMOE- CMA RAKE receiver is improved upon that of the D-RAKE [I] and CMA-RAKE receivers [3]. The SINR of the CMOE-CMA RAKE receiver is shown to be maintained for the different levels of near-far situations. 2. SYSTEM MODEL For the real system model from Honig et al. [5], the baseband re- ceived signal for a K-user asynchronous CDMA channel is de- fined as m K  i=-m k = l  where Ak represents the received amplitude of the Lth user. The data bits b k [ i ]  are independent identically distributed (i.i.d.) and assumed to be drawn from the finite alphabet (-1, +l}. The sym- bol period is denoted by T. The spreading (or signature) waveform of the kth user C k ( t )  is Lc-dimensional and has unit energy prop- erty, i.e., l)ck1)' = 1 and,.rk E [O,T) are the relative offsets of the asynchronous signals at the receiver. The zero mean additive white Gaussian channel noise u(t) has power spectral density d. The amplitude Ak and delay Q can be incorporated in the chan- nel response hk(t) and the spreading code sequence c(t) can be replaced with the discrete-time combined code-channel response Le-1 gk[n] = C k [ i ] h k [ n  - i ] ,  (2) a=o where ck [a]  is the ith element of the code vector for the kth user c k  = ( c k [ O ] ,  . . . ,c[Lc - l ] ) T  and the received signal r ( t )  in (1) can be wntten in the discrete-time vector form K K r[n] = r k b ]  + Vi.] = Gkbk[n] + v[n], (3) where Gk is the combined code-channel response matrix of the kth user and bk[n] = ( b k [ n ] ,  bk[n - 11,. . . , bk[n - Lb + k = l  k = l  418 Authorized licensed use limited to: LOUGHBOROUGH UNIVERSITY. Downloaded on January 12, 2010 at 11:18 from IEEE Xplore.  Restrictions apply. International Symposium on Signal Processing and its Applicaiions (ISSPA)). Kuala Lumpur, Malaysia, I3 - I6 August, 2001. Organized & the Dept:of Microelectronics and Computer Engineering, UTM, Malaysia and Signal Processing Research Centre, QUK Australia and V[n] = (V[n],V[n - I],... ,V[n - Lb 4- with L b  = L + L h - l  L. 1. Note that Gk = CkHk, (4) where the code matrix cn: and the channel matrix H k  are - l1 . where the channel response vector for the kth user has length Lh. i.e., hk = (h[Lh - 11,. . . , The elements of the Lf x L b  combined code-channel matrix G k  are derived from (2): gk(Lc - 1) . ' .  gk(LbLc - 1) Gk=( gk (L c  :- 2) . . . gk(LbLc - 2) ) .  (7) gk(Lc'-Lf) " '  gk(Lbic -Lf) We can represent (3) as , r[n] = Gb[n] + v[n], (8) where B = (GI Gz . * .  G K )  representing the overall combined code-channel matrix and b[n] = (bT[n] , bz[n] , . . . , bz[n])T the overall data vector. Finally, we introduce the LbK x 1 com- bined code-channel-equalizer (system) response vector as s[nl = W'[.lG, (9) where ~ [ n ]  is the Lf  x 1 weight vector of an equalizer at time n. 3. COMBINED STRUCTURE OF CMOE AND CMA FOR RAKE RECEIVER Initialization is probably the most influential factor that controls the convergence behaviour of CMA [6], [7]. Therefore, to achieve reliable reception for a CMA receiver in near-far situations, an ini- tialization technique which is robust to near-far environments is required. The CMOE criterion is preferable in interference sup- pression especially in severe near-far situations due to its decor- relating nature [5], [2]. We propose a novel initialization scheme for the CMA receivers in the RAKE receiver structure with the so- lution derived from the minimization of the CMOE criterion that satisfies the sufficient conditions stated in [6] and, with more ex- tended results, in [7]. 3.1. Admissibility of CMOE as an  initialization scheme for a CMA equalizer It has been shown in [7] that in multiuser systems the initial kur- tosis condition of outputs is not the sole indicator that controls the CM-SG convergence as claimed in [6]. It is the SINR condition that is more restrictive and computing SINR is more appropriate when sample size is restricted to be small [7]. Therefore, in this paper we then concentrate on finding the initial estimator by the solution derived by minimizing the MOE criterion that satisfies the minimum requirement to the SINR condition. We define the minimum and maximum (normalized) kurtoses of the interference signals without the assumption of zero inter-symbol interference (ISI) as The minimum SINR at delay v for non-Super-Gaussian signals for the lcth user is verified to be [7] 3 and pmU = 5. with ng repre- where pmin = senting the (normalized) kurtosis of Gaussian signals. It has been I -I. f i # - I .  shown that if SINR!Yk'(y[n]) > SINR,$)n,v, the estimator will of- fer the estimates of the source k with delay v. Lemma I: For the CM estimator wk which is initialized by the weight vector fk which minimizes the CMOE criterion at the SINR greater than the minimum SINR, i.e., . W r n i t )  ._ - fk[n] s.t. SINRik'(y[n]) > (12) then the W k  will preserve the estimates for the desired user k at delay v. 3.2. CMOE-initialized CMA RAKE receiver structure As in .the case of the D-RAKE MOE receiver, the CMOE-CMA PAKE structure tries to collect the energies of the signals of the other paths. We introduce a constrained MOE initialization part for CMA. Firstly, we adopt the constraint proposed by Tsatsanis [2] which is shown to be f&Ck = (0,. . . ,o ,  ; ,o,.  . . , O )  2 17. (13) This corresponds to the Zth position of the rays. Denote the output energy of the Ith detector as I J i A E b  = f Z I R f k . l ,  (14) where R = E{r[n]rT[n]}. We desire to minimize J!iE in order to suppress the energy of interference by By taking the instantaneous value of the autocorrelation matrix R, the adaptation rule for the Ith CMOE detector of the kth user be- comes [ l ]  fk,I[n + 11 = fk,l[n] - pcma,In~,r[n]rT[n]fk,l[n], (16) where pcma,l is the stepsize of the lth detector and II&, = I - Ck (CECk)-.'CT denotes the projection matrix onto the nullspace of Ck. The initialization of the lth detector is f;fl""' = CLlr, (17) Authorized licensed use limited to: LOUGHBOROUGH UNIVERSITY. Downloaded on January 12, 2010 at 11:18 from IEEE Xplore.  Restrictions apply. International Symposium on Signal Processing and its Applications (ISSPA), Kuala Lumpur, Malaysia, 13 - 16 August, 2001. Organized by the Dept. of Microelectronics and Computer Engineering, UTM, Malaysia and Signal Processing Research Centre, QUT, Australia where C: is the pseudo-inverse of Cf. As shown in [2], the Ith detector in ck whose delay corresponds to that of the dominant path can be identified by using the maximum MOE criterion after the convergence of all L, detectors. The estimated MOE of the Zth detector is where yk,1[72] = f&[n]r[n], V l  E ( I , .  . . , L,}  denote the output signals of the Ith arm at time n and Nt is the sample size of the data symbols. We determine the first arm by that which gives the maximum output energy The set of weight vectors of all arms of the RAKE structure can be constructed as (fk,r[n], VZ E (1 , .  . . L a } }  where La denotes the number of arms and La can be set to be much less than L, since the long delay paths usually correspond to small energies of the received signals. To guarantee convergence to the desired user solution as stated in Lemma 1, we initialize the first arm (I = 1) of the CM equalizers with the weight vector of the first arm of the CMOE detectors at the first symbol (Y = 1) with the minimum SINR. For a system with sub-Gaussian signals with none of the interference signals bearing kurtosis less than that of the desired user, the minimum SINR,i,,, is 3.8 dB, i.e., where N., is the time to adopt the solution derived by the mini- mization of the CMOE criterion to initialize the CM eqodizer for the first arm. By CMA algorithm, for real signals, the criterion minimizes the following cost [8] where Z k , l  = wc,lr is the output symbol of the Zth equalizer for the kth user and the dispersion constant ' y k J  defines the gain of the Ith CMA equalizer. The gain of each arm depends on the channel response at the corresponding delay, i.e., 'ykJ = hE[I]. From the construction of the D-RAKE receiver, the outputs of the Zth arm are shown to be Yk,l[n] = h k [ l ] b k [ n ]  -k ek.l[n], (22) where e&,! [n] denotes the effective noise. This enables us to ap- proximate the magnitude of the channel coefficient at the lth delay. Since E{b:} = 1 and ek,l[n] << hk[I]b&[n], we can approximate the gain TkJ, VI E (1, . . . , La}, by where Nt is the sample size ofthe data symbols and N, is acheived in (20). The adaptation rule for the CM-RAKE receiver is wk.l[n -k 11 = wk,l[n] - clcma,lr[n]%k,l[n]ek,l[n], (24) where p-,~ is the stepsize and ek , l [n]  = ~ : , ~ [ n ]  - 'yk,l  is the error signal for the Ith arm of the kth CMA equalizer. After con- vergence, the arm outputs will be coherently combined to enhance the SINR by a coherent combiner which is essentially the prin- cipal eigenvector of the sample autocorrelation of the outputs of all arms zk[n] = (zk,l[n] , .. . , ?&,L,[n])T. The structure of the CMOE-CMA RAKE receiver is shown in Fig. 1. Fig. 1. The CMOE-CMA RAKE receiver. 4. SIMULATIONS We considered a 10-user (K = 10) symbol.asynchronous sys- tem and we assumed without loss of generality that the first user was the user of interest with unity power. We used Gold codes with processing gain Le = 31 for the spreading codes of all users. User delays n were uniformly distributed over [0, 3Tc) and then kept fixed. The propagation channels are bandlimited with root- raised-cosine pulse shaping with excess bandwidth 0.2. The num- ber of multipath rays was four where the last three rays were uni- formly distributed in delay over [0, 52'') with standard deviation of 0.4. The channel length was 5T' and assumed to be the same for all users. The background noise was zero-mean AWGN with SNR=PO dB (referenced to the desired user). The performance measure was the average SMR in dB which is given by [SI where rr)[n] are the transmitted signals of the first user as de- scribed in (3) and r denotes the index of a particular run. All SIR plots were averaged over 100 Monte-Carlo runs (R = 100). For all receivers, the number of arms was three (La = 3) and the receiver length was chosen to be twice that of the spread- ing gain (215,). We compare the SINR performances of the pro- posed CMOE-CMA RAKE receiver with the D-RAKE CMOE receiver [ l ]  and the CM-RAKE receiver [3] in near-far environ- ments. For a relatively high near-far level 4 = -lo&, Vk = (2, . . . ,9}) as demonstrated in Fig. 2, the proposed CMOE-CMA receiver is shown to exhibit the best SINR performance while the CMA-RAKE receiver performs better than the D-RAKE. Note that the CMA-RAKE receiver in [3] assumes exact knowledge of the correct timing of the desired user. If this is not the case, the kurtosis-based initialization scheme may be used as in [4]. How- ever, a large number of samples is required to achieve reliable esti- mates of the kurtoses. The benefit of employing the RAKE struc- ture is also demonstrated as the SINR performance of the CMOE- CMA RAKE receiver is improved from that achieved by the sin- gle ( 1 st) arm CMOE-CMA receiver. In Fig. (3), it is shown that the SINR levels of the CMOE-CMA RAKE receiver is maintained over a wide range of the near-far situations. This confirms the near- far resistance of the proposed receiver. The comparison of the sys- tem responses of each arm at initial state 4:; and at steady-state (after convergence) d) at 4 = -10 dB, are shown in Fig. 4. The corresponding initial SINRs for the Ith arm are 7,6 and 5 dB for 1 = 1, 2 and 3 respectively. After all CMA equalizers con- ' ' h  * h  420 Authorized licensed use limited to: LOUGHBOROUGH UNIVERSITY. Downloaded on January 12, 2010 at 11:18 from IEEE Xplore.  Restrictions apply. International Symposium on Signal Processing and its Applications (ISSPA)). Kuala Lumpur. Malaysia, 13 - 16 August, 2001. Organized b the Dept. of Microelectronics and Computer Engineering, UTM, Malaysia and Signal Processing Research Centre. QUT, Australia Fig. 2. The SINR performance of the CMOE-CMA-RAKE re- ceiver compared with that of the D-RAKE receiver [ I], the CMA- RAKE receiver [3] and the single (1st) arm CMOE-CMA receiver at 4 = -10 dB. Note the SINR improvement of the CMOE- CMA RAKE receiver over the single-arm CMOE-CMA receiver. Ab 2L ” ” ” ” ’ 0 -2 -4 -e a -10 -12 -14 -10 -18 -20 A:I< Ida) Fig. 3. Comaparison of the SINR performance at different near- far levels. Note the near-far resistance of the CMOE-CMA RAKE receiver over a wide range of near-far levels. verge, the steady-state system reponses 4’) are shown in Fig. 4 (b), (d), and (f). It is confirmed that the first user is preserved at the correct delay by the non-zero gains of 4;) at Y = 1 while the interference is further suppressed by CMA. 5. CONCLUSIONS The minimization of the CMOE criterion is adopted as an ini- tialization scheme for a CMA-RAKE receiver for asynchronous CDMA systems. It is confirmed by simulations that the CMOE- CMA RAKE receiver is near-far resistant as long as the initial- ization satisfies the minimam SINR requirement. The RAKE re- ceiver structure is used for combining the desired signal energies at different chip delays. The SINR performance is shown to be improved after coherently combining the outputs from all of the receiver arms. 6. REFERENCES [I]  H. Liu and K. Li, “A decorrelating RAKE receiver for CDMA communications over frequency-selective fading channels,” Fig. 4. Comparison of the initial and steady-state system responses ofeach arm at 3 = -10 dB. The initial system responses of each arm, q:;, are shown in subfigure (a), (c) and (e) for 1 = 1, 2 and 3 respectively. After equalization, the steady-state system responses, qii), are shown in subfigure (b), (d) and (f). A= Ab IEEE Trans. Commun., vol. 47, no. 7, pp. 1036-1045, 1999. M. K. Tsatsanis, “Inverse filtering criteria for CDMA sys- tems,” IEEE Trans. Signal Processing, vol. 45, no. I, pp. M. Torlak and B. L. Evr.is, “A self-recovering RAKE receiver for asynchronous CDMA systems,” in Proc. Int. Conj Acous- tics, Speech and Signal Processing, Istanbul, Turkey, 2000, P. Schniter and C. R. Johnson Jr., “Minimum-entropy blind ac- quisitiodequalization for uplink DS-CDMA,” in Proc. Aller- ton ConJ: on Communications, Control, and Computing, Mon- ticello, IL, 1998, pp. 401-410. M. L. Honig, U. Madhow, and S .  Verdu, “Blind adaptive mul- tiuser detection,” IEEE. Trans. Inform. Theory, vol. 41, pp. 944-966, 1995. Y. Li and Z. Ding, “Convergence analysis of finite length blind adaptive equalizers,” IEEE Trans. Signal Processing, vol. 43, no. 9, pp. 2120-2129, 1995. P. Schniter and C. R. Johnson Jr., “SINR-based sufficient con- ditiions for CMA desired-user-lock,” in Proc. IEEE WCNC, New Orleans, 1999, vol. 2, pp. 814-818. D. N. Godard, “Self-recovering equalization and carrier track- ing in two-dimensional data communication systems,” IEEE Trans. Commun., vol. 28, pp. 1867-1875, 1980. 102-1 12, 1997. vol. 5 ,  pp. 2869-2872. 42 1 Authorized licensed use limited to: LOUGHBOROUGH UNIVERSITY. Downloaded on January 12, 2010 at 11:18 from IEEE Xplore.  Restrictions apply. 

A CMOE-CMA RAKE receiver structure for near-far frequency selective fading CDMA channels

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A CMOE-CMA RAKE receiver structure for near-far frequency selective fading CDMA channels

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