Improved Cooperative CDMA Using Blind Adaptive Interference Cancellation Indu Shakya, Falah H.Ali, Elias Stipidis Communications Research Group Department of Engineering and Design University of Sussex Brighton,UK Email:{i.l.shakya, f.h.ali, e.stipidis}@sussex.ac.uk

Abstract— In this paper, we introduce blind adaptive interference cancellation for a practical uplink CDMA effected by multiple access interference (MAI) in cooperative communications systems scenario. During the collaboration phase, each paired users exchange their data to communicate with the base-station by using their own and pairing users’ channels to achieve the spatial diversity. The base-station performs ranking of users’ power and detects the strongest using the successive interference cancellation (SIC) principle to gradually remove MAI from the desired signals. The proposed scheme uses an improved SIC which performs adaptive despreading to form better estimates of users’ data and then uses blind MAI estimation and cancellation by making use of the despreader weights to minimize the residual MAI. Simulation results show that the scheme achieves better diversity gain and allows much higher number of users to share the same bandwidth compared with conventional cooperative schemes.

I. I NTRODUCTION Recently, cooperative communication has emerged as an interesting approach to improve the link performance of wireless networks by sharing the antennas and other resources among the users [1], [2], [3], [4], [5], [6], [7], [8]. It becomes more useful particularly for the mobile users, which can not due to their size and power limitations, employ more than one antenna to communicate with other users or basestation. The paper by Sendonaris et. al. [1] considered user cooperation assuming orthogonal user channels in multiuser communications for CDMA system. However, in practice MAI almost always exists and must be removed if the system performance is to be improved. The performance of a single user with relay assisted diversity in uplink CDMA under different propagation environments is investigated in [9]. It is shown that the conventional matched filter (MF) detection which ignores the presence of MAI, fails to attain full diversity gain. An improved receiver that suppresses MAI before signal combining from relays are shown to achieve performance very close to perfect cooperation. However, the scheme only considered a single user system with multiple relays assisting the user for achieving the diversity. A new scheme combining user cooperation a SIC under practical uplink CDMA is described in [8]. Where the SIC used the correlator output for MAI estimation and cancellation [10]. This has shown to provide improved BER and achievable rate compared with a

SIC only and cooperative MF schemes under moderate system loading conditions and with nearfar users. It is well known that the conventional SIC using correlators suffers from imperfect MAI estimation problem as system loading increases. This causes error propagation to later users’ detection stages and the SIC may perform even worse than without cancellation [11]. This problem can be alleviated to great extent by improved SIC design that uses constant modulus (CM) property of user transmitted signals to blindly suppress MAI while estimating desired user’s signal at the despreader output. Furthermore it uses a simple gradient descent based adaptive algorithm to update the estimates blindly within the SIC process [12] and referred to here as BA-SIC. The proposed scheme employs the BA-SIC within the cooperation diversity system framework of uplink CDMA. As will be shown later, it improves the system performance considerably compared with conventional cooperative schemes. The paper is organized as follows. In section II, the system model is presented. The proposed cooperative transmission scheme is described in section III and the operation of the conventional Cooperative SIC is described in section IV. The Cooperative BA-SIC scheme is described in section V. Section VI shows the BER simulation results and comparisons. Finally the paper is concluded in section VII.

II. S YSTEM M ODEL AND A SSUMPTIONS A typical multiuser communication scenario of an uplink synchronous CDMA with a pair of cooperating users {1, 2}, .., {k, i}, .., {K − 1, K} and the base-station receiver {d} system employing the proposed cooperative scheme is shown in Figure 1. A common multiple access channel (MAC) with BPSK modulated user signals with fading and AWGN is assumed. To gain clear insight into the impact of cooperation on multiuser SIC reception under MAI conditions, there are some assumptions made in this paper. These assumptions are used for all the cooperative techniques (CBA-SIC, C-MF and C-SIC) used here in this paper for comparisons and are listed below: 1) The cooperating pair of users are chip synchronized before they start to cooperate and transmit each others’ data.

Extension to asynchronous case should be possible with a little modification to the scheme. 2) The amount of interference from non paired user nodes to the cooperating pair of users is small and can be treated as background noise. This may be easily justified due to uniform distribution of users within the coverage of a typical cellular system. Therefore, the cooperating user nodes see much less interference from other users compared to the base-station receiver, which is usually placed in the center of a cell to be able to transmit and receive to/from all users more efficiently. 3) The pairing users are assumed to know the phases of their transmit channels such that during transmission, their signals are multiplied with appropriate phase offsets for coherent combining at the base-station receiver [1].

a binary sequence taking values [−1, +1] with equal probabilities, p(t) is rectangular pulse with P∞ period Tb . The spreading sequence is denoted as ck (t) = n=−∞ ck (n)p(t−nTc ) with antipodal chips ck (n) of rectangular pulse shaping function p(t) of period Tc and R T normalized power over a symbol period is equal to unity 0 b ck (t)2 dt = 1. The spreading factor is N = Tb /Tc and v(t) is the AWGN with two sided power spectral density N0 /2. The received composite signal at the base-station receiver d from all users’ transmissions during the first period is rd (t) and from that of the partnering users’ in the second period is rd0 (t) and can be written as: rd (t)= rd0 (t)=

K X

gkd (t)sk (t) + v(t)

k=1 K X

(2) gid (t)si (t) + v(t)

i=1,i6=k

Fig. 1.

Cooperation scenario between pairs of users

In the proposed cooperative CDMA uplink system, during the first symbol period, the users transmit their own data using their originally assigned spreading sequences. At the same time, the users that are pairing with transmitting users receive and decode the transmitted signals. During the second period, the pairing users forward the decoded data using the spreading sequences of their partners. Without loss of generality and for the sake of ease in presentation, we proceed our analysis for {k, i} pair of users. It is easy to understand that the same cooperation scenario applies to all other pairs of cooperating users. The signals received at the cooperating pairs {k, i} at the first period can be written as: p ri (t)= Pk gki (t)bk (t)ck (t) + vi (t), p (1) rk (t)= Pi gik (t)bi (t)ci (t) + vk (t), where, Pk is the signal power, g(t) = αk (t)ejπφ(t) is the complex fading channel between the users with amplitude 2 α(t) P∞ and phase φ(t) components with variance σ , bk (t) = b (m)p(t − mT ) is the data signal, where bk (m) is b m=−∞ k

√ where sk (t) = Pk bk (t)ck (t) is the transmitted signal of k th user. The model of signal si (t) transmitted during the second period is exactly the same as above but they are originated from the i, i 6= k user using k th user’s estimated data b0k (t) using their own channels gid (t) = αi (t)ejπφid (t) . The signal model described above applies to all pairs of cooperating users with appropriate modifications. The cooperative scheme performs satisfactorily when the inter-user channel gains are higher or at least equal to that of the respective transmit channels of the users to the destination (base-station in this work) [13]. Assuming average noise variance of the users and the base-station receivers are equal, the relative signal to noise ratio (SNR) gain in dB of inter-user channels βk , βi compared to the respective transmit channels of the users to the base-station can be shown as βk =

2 2 σki σik , β = i 2 2 σkd σid

(3)

2 2 2 2 where, σki , σik and σkd , σid are the variances of interuser channels gki , gik and the users’ channels to the base-station receiver gkd , gid , respectively. Symmetry of inter-user channels i.e. gki = gik , ∀k assumed here is 2 2 reasonable as in [1]. In the near far condition, σkd 6= σid and hence βk 6= βi with nearfar ratio being defined as 2 2 Ω = max{σjd }/σkd , j ∈ {1, 2, ., i, ., K}, j 6= k.

III. M ULTIUSER C OOPERATIVE T RANSMISSION S CHEME Based on the system model, a signalling structure of the proposed scheme with two users spanned over two consecutive symbol periods is shown in (4). The same signalling structure applies to all other consecutive periods. When appropriate, the signals are presented in vector form and indices denoting time dependance are dropped. A single cycle of cooperative

transmission scheme can also be written as p p sk = Pk gk bk ck , Pk gk b0i ci | {z } | {z } first period second period p p si = Pi gi bi ci , Pi gi b0k ck ) | {z } | {z } first period second period

(4)

In the first period, the users transmit their signals as shown in equation (4). Due to the broadcast nature of the channels, the signals are simultaneously received both at the cooperating users and at the base-station receiver. At the same time, the received signals are independently processed at the users’ receivers. For handling these operations, it is assumed that full duplex capabilities or echo cancellation technique [13] is available. The received signals at the cooperating pairs at this period are given in (1). The detection of signals at each other user node is performed by first obtaining the soft estimates of the signals by despreading the received signal with the known spreading sequence. For example the k th user this is given by Z Tb 1 rk ck , ∀k (5) zk = Tb 0 Then, by performing channel phase correction and taking the sign of the real part of the signal zk , the estimate of the k th user’s transmitted signal b0k is obtained h  i ∗ b0k = sgn < zk gik (6) where, sgn{.}, <{.} and {.}∗ denote sign, real and complex conjugation operation, respectively. During the second period, the cooperating users simply forward the detected data of the partners b0k to the basestation receiver using the their partners spreading sequences ck . It should be noted that the estimated data may not be identical to the transmitted of the originating users due to the detection errors in (5) and (6). The accuracy of detection and thus error performance improvement of the system due to cooperation depends on the relative SNR gains of the inter-user channels gki and gik to their respective transmit channels to the base-station receiver gkd and gid . The processes (5) and (6) are performed at all pairs of mobile nodes each acting both as a user and a partner.

power estimates of the users are generated at the output of the corresponding users’ matched filters and the one with the maximum is selected, given by ( Z ) 1 Tb rd ck , 1 ≤ k ≤ K zmax = max (7) Tb 0 In the second period the estimate of the strongest user obtained from the first period denoted by index k −→ {max} is generated from the output of bank of MF as follows: Z 1 Tb 0 0 rd cmax , (8) zmax = Tb 0 The estimated signals of the user from the two periods is maximum ratio (MRC) combined to form a final decision statistic Zmax . Note that other combining methods such as equal gain combining (EGC), minimum mean square error combining (MMSEC) [14] are equally applicable for the diversity combining and may have significant effect the system performance. For the MRC, the combined signal can be shown as follows: 0 Zmax = zmax α ˆ max + zmax {ˆ α}0max

(9)

where, α ˆ max and {ˆ α}0max are amplitudes of estimated strongest user in first period and belong to the user’s and it’s partner’s channel, respectively. Finally, the hard decision of data of the user with index k = max is performed from the SIC stage as follows: h i ˆbk = sgn <{Zmax } (10) The C-MF scheme uses the processes above (7)- (10) only and performed for all K users. Note that power ordering shown in (7) does not effect the detection performance of MF based receivers. The C-SIC reuses the estimated signal 0 to remove of the strongest user in a given stage zmax , zmax it’s MAI. For this purpose the cancellation process now has to be applied to both the received signals from the first and second periods for improving the estimation of weaker users signal that follows the same processes (7) - (10). The estimates of the user’s signal in the first and second period zmax and 0 are separately spread using the spreading sequence of zmax the detected user with index k = max and subtracted from the respective received signals rd (t) and rd0 (t) to obtain less interfered received signals as follows

IV. C OOPERATIVE MF (C-MF) AND SIC (C-SIC) S CHEMES

rd = rd − zmax ck 0 r0d = r0d − zmax ck

During both the first and second period of the cooperation scheme, the base-station receiver processes the received signals to perform detection of users’ data. The C-SIC receiver performs the detection of user signals based on order of their estimated strength using the principle of SIC. The C-MF is obtained when there is only despreading and data detection is used i.e. no cancellation is performed. In the first period the signal estimation of the strongest among the users is carried out, followed by the cancellation of its MAI contribution from the remaining composite received signal. The relative

The processes (7) - (11) are repeated until all users’ data signals are detected.

(11)

V. C OOPERATIVE B LIND A DAPTIVE SIC (CBA-SIC) The performance of conventional SIC degrades significantly under high system loading due to biased estimates of linear correlators used. In view of the performance limitations of the conventional SIC and the problem of inaccurate MAI estimation and cancellation, it is desirable to generate some

adaptive despreader weights that do not allow a decision statistic zk to revert it’s sign when the presence of MAI tends to do so. The CM algorithm (CMA) is a simple algorithm that attempts to maintain constant modulus of the signals at the output [15], [16], [17] and it’s complexity is only O(N ) computation per symbol per user, where N is the length of the despreader weight vector. An adaptive despreader using the CM criterion is shown in Figure 2. Provided that the CM algorithm is fast enough to track the changes in MAI power variations and the corresponding weights are selected, the decision error due the MAI effects can be eliminated. Practical CM algorithms however may not perform perfectly and there are bound to be some inevitable misconvergence problems. However, the useful properties of the CMA is exploited within the adaptive despreaders and suitably implemented within SIC in [12] also referred to here as Blind Adaptive SIC (BA-SIC). In the sequel, the BA-SIC algorithm embedded within the cooperative diversity system i.e. CBA-SIC is proposed and evaluated.

and summed over the symbol period given by zk (m) = {rk (m)}T wk (m) zk0 (m) = {r’k (m)}T w’k (m)

(12)

The CM criterion JCM can be written as minimization of the following cost function n o2 (13) JCM = E zk (m)2 − γ where, E{.} is the expectation operator, γ is the dispersion constant, which is equal to unity for binary phase shift keying (BPSK) signals. The instantaneous error signal ek (m) is calculated as ek (m) = zk (m){zk (m)2 − γ} e0k (m) = zk (m){zk0 (m)2 − γ}

(14)

The estimated gradient vector of the error signal is then calculated by ∇k (m) = rk (m)ek (m) ∇0k (m) = r’k (m)ek (m)

(15)

Using the gradient of (15), the weight vector at next symbol wk (m + 1) is updated as follows wk (m + 1) = wk (m) − µ∇k (m) w0k (m + 1) = w0k (m) − µ∇0k (m)

(16)

where, µ is the step-size usually chosen as a small number [18] is used to adapt elements of the weight vector to minimize the cost function (13). The output signals zk (m) and zk0 (m) are combined with MRC using amplitude estimates α ˆ k (m) and α ˆ i (m). The combined signal is delivered to the decision making process to perform hard decision h  i ˆbk (m) = sgn < zk (m)ˆ αk (m) + zk0 (m)ˆ αi (m) (17)

Fig. 2.

CMA-aided despreading process of BA-SIC

At the first symbol period, the weights of the despreaders are initialized with user’s spreading sequence wk (1) = ck and w0k (1) = ck , respectively. Without loss of generality, it is assumed that the first user (strongest among K users) to be detected is user 1. Similarly next strongest user is assigned an index as user 2 and so on. At the first stage, the received signal can be expressed as rd (m) = r1 (m) and r’d (m) = r’1 (m), respectively, where r1 = [r1 (1), r1 (2), .., r1 (N )]T . The remaining composite signal after cancellation at k th stage for the detection of the user’s and it’s cooperating pair signals are expressed as rk+1 (m) and r’k+1 (m), respectively. Below, the diversity combining, detection and interference cancellation procedures for k th stage is described. At k th stage, the decision statistic zk (m) is obtained by multiplying chips of rk (m) with the vector of weights wk (m) = [wk (mN + 1), wk (mN + 2), .., wk (mN + N )]T

The cancellation process also requires amplitude estimation of the detected user signal and spreading. For this purpose, scaling factors α ˜ k (m) are first obtained using the despreader weights and the known spreading sequence as follows c˘k (m) w ˘k (m) c˘k (m) α˜0 k (m) = 0 w ˘k (m) α ˜ k (m) =

(18)

where, c˘k (m) =

N 1 X |ck (mN + n)| N n=1

w ˘k (m) =

N 1 X |wk (mN + n)| N n=1

w ˘k0 (m) =

N 1 X 0 |w (mN + n)| N n=1 k

(19)

are the mean amplitude of user’s spreading sequence chips and the mean of the weight vector updated by the CM algorithm,

respectively. The estimated symbol is then scaled with it’s new amplitude estimate α ˜ k (m) and spread to generate the cancellation term as follows xk (m) = α ˜ k (m)zk (m)ck (m) 0 ˜ x’k (m) = α k (m)z 0 k (m)ck (m)

(20)

The remaining composite signal after the interference cancellation is rk+1 (m) = rk (m) − xk (m) r’k+1 (m) = r’k (m) − x’k (m)

(21)

The processes (12)-(21) are repeated for each stage until the weakest user is detected. VI. S IMULATION R ESULTS AND C OMPARISONS

suppressing and canceling MAI, improves the amplitude and data estimates of users’ and that of cooperative signals, much improved BER at high system load is expected. As expected, the proposed technique shows noticeable improvement in the error performance compared to the Cooperative SIC (C-SIC) receivers under the same system settings as the βk increases: for example, a SNR gains of ≈ 2 dB for a BER of 10−3 can be seen here. The BER performance of the proposed CBA-SIC is shown in Figure 4 and compared with C-SIC for system loading of K = 6 − 24 users under fixed Eb /N0 = 20 dB. The degree of cooperation is quantified by the relative SNR gains of interuser channels to the transmit channels of the respective users i.e. βk . The CBA-SIC shows a superior BER performance under high system loading conditions, which is expected due to improved estimation of users’ data signals and amplitudes of the blind adaptive approach to MAI cancellation.

Fig. 3. Performance of Cooperative BA-SIC in flat Rayleigh fading channel with K=20, Gold sequence, N=31

Fig. 4. BER performance vs. number of users of Cooperative BA-SIC in flat Rayleigh fading channel with Eb /N0 = 20dB, Gold Sequence, N=31

A baseband model of K user synchronous uplink DSCDMA system with BPSK modulation and short binary Gold sequences of length N = 31 is used. All the uplink and interuser channels are assumed to be Rayleigh flat fading with normalized Doppler shift fd Tb = 0.003 and a small step size of µ = 0.0001 is assumed in the adaptive algorithm. The system using different cooperative schemes is simulated in MATLAB using 20000 Rayleigh faded symbols for each user for obtaining the average BER of users and 40000 symbols for each user in the case of BER calculation for the weakest user. In Figure 3, BER simulation results of the proposed Cooperative BA-SIC (CBA-SIC) system is plotted under system loading of K = 20 users. The BER of Non cooperative SIC and C-SIC under the same system conditions are also shown. The CBA-SIC that uses blind adaptive approach for

The impact of nearfar conditions on the BER of CBA-SIC is shown in Figure 5. System loading of K = 6 − 24 is considered, where the desired weakest user has unity power while all other users’ signals are received at power level uniformly distributed between 0 − 10 i.e. Ω = 10 dB. The Eb /N0 of the desired weakest user is assumed to be 20 dB. The step-size of adaptive algorithm is set as µ = 0.0001 Ω . The BER of the user is plotted against different system loading i.e. the number of users and also under different ratio of inter-user channel SNR gains βk . It can be observed that the performance of CBA-SIC is robust in nearfar conditions and high system loading of up to 18 users. The performance of C-SIC shows similar gain, however the degradation in BER starts with much lower system loading of 12 users compared with CBA-SIC. Also it is noted that C-SIC does not benefit much from strong channel SNR of the partners’ compared with

CBA-SIC. The reason for this is the conventional SIC while removes part of MAI also suffers from unreliable estimation of weaker users’ signals and hence only the fraction of diversity gain achieved. The results for CBA-SIC and C-SIC on the other hand are in strong contrast with Cooperative MF (C-MF) detection technique, where the BER of weakest user degrades rapidly even under very small number of users.

Fig. 5. BER performance vs. number of users of Cooperative BA-SIC in flat Rayleigh fading channel with nearfar condition (10dB), Eb /N0 of the weakest user=20dB, Gold Sequence, N=31

VII. C ONCLUSION We proposed a new Cooperative BA-SIC scheme to improve the performance of uplink CDMA. It is noted that the improved MAI estimation and cancellation performance of the BA-SIC provides higher number of users to enjoy the cooperative diversity gains than that with a conventional SIC. Also it is noted that the nearfar effects can provide more improved BER under low system loading conditions. Future work will constitute theoretical analysis of achievable rates and evaluation under frequency selective fading channels.

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