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A novel codebased iterative PIC scheme for multirate CI/MCCDMA communication
EURASIP Journal on Wireless Communications and Networking volume 2011, Article number: 155 (2011)
Abstract
This paper introduces a novel codebased iterative parallel interference cancellation technique (CodePIC) for the multirate carrier interferometry/multicarrier code division multipleaccess (CI/MCCDMA) system, which supports simultaneous transmission of high and low data rate users. In CodePIC scheme, multipleaccess interference (MAI) for the desired user is estimated based on the projection of subcarrier and subsequent removal of interference from the received signal depending on specific high or low data rate users. Carrier interferometry (CI) codes are used to minimize the crosscorrelation between users, which significantly reduces the multipleaccess interference (MAI) for the desired user. The effect of MAI in CI/MCCDMA is reduced by giving proper phase shift to different set of users. Improved estimation of MAI in CodePIC results in lower residual interference after interference cancellation. Simulation results show that CodePIC scheme offers improved BER performance over AWGN and Rayleigh fading channels compared to BlockPIC and SubPIC with reduced latency and complexity.
1 Introduction
Multicarrier code division multipleaccess (MCCDMA) system is a promising technique for highspeed communication system due to robustness against intersymbol interference (ISI) over multipath. The capacity of CDMA in cellular and wireless personal communication systems is limited by multipleaccess interference (MAI) due to simultaneous transmission of more than one user. The interference power increases linearly with the number of simultaneous users. To alleviate MAI, several multiuser detection schemes have been proposed in the literature [1]. The conventional detector follows singleuser detection (SUD). In SUD, every user is detected separately in the presence of MAI. Performance improvement is observed with multiuser detection (MUD) schemes, where the information about multiple user is used to detect the desired user. Although notable performance gain is obtained with maximumlikelihood (ML) multiuser detector, the complexity of the detector grows exponentially with the number of users. The iterative expectationmaximization (EM) algorithm enables approximating the ML estimate. EMbased joint data detector [2] has excellent multiuser efficiency and is robust against errors in the estimation of the channel parameters. ML approach requires high computational complexity. To mitigate computational complexity, suboptimal MUD like minimum meansquare error (MMSE) has been proposed. A nonlinear MMSE multiuser decisionfeedback detectors (DFDs) are relatively simple and can perform significantly better than a linear multiuser detector. Multiuser decisionfeedback detectors (DFDs) based on the minimum meansquared error (MMSE) are reported in [3] over multipath. The MMSE adaptive receiver has a much better performance than matched filter receiver with a slightly higher computational complexity. The group pseudodecorrelator, the group MMSE detector and the pseudodecorrelating decisionfeedback detector are proposed by Kapur et al. [4].
Considerable performance improvement can be achieved by the use of interference cancellation (IC) technique. Interference cancellation detector removes interference by subtracting estimates of interfering signals from the received signal. Serial interference cancellation (SIC) has been the active area of research due to its lower complexity compared with other multiuser receiver. SIC [5] removes the interference serially. It is expected that bit error rate (BER) performance improves after each iteration stage of iterative SIC. In highspeed data communications, parallel interference cancellation (PIC) [6] is more preferable due to reduced delay. Hardware complexity is one of the main drawbacks of PIC. Performance analysis of improved PIC has been reported in [7]. However, if some of users' information is wrongly detected, then the estimated MAI increases the interference power resulting in degraded BER performance for desired user. The error propagation can be minimized when hard decision is replaced by soft decision of received bits. Soft decisionbased IC schemes have been proposed by different authors [8–10].
Fast adaptive MMSE/PIC iterative algorithm [11] has been proposed to reduce overhead introduced during the receiver's training period. Leastsquares (LS) joint optimization method [12] is presented for estimating the interference cancellation (IC) parameters, the receiver filter and the channel parameters. Lamare et al. proposed a lowcomplexity nearoptimal ordering MMSE design criteria [13] for efficient decisionfeedback receiver structure along with successive, parallel and iterative interference cancellation structures. Significant performance improvement is obtained with iterative interference cancellation receiver for underloaded CDMA [9, 10, 14, 15].
Nonlinear PIC or SIC performs better compared to other MUD in overloaded system. Suboptimum multiuser detection [16] for overloaded systems has been proposed, but with very specific constraints on the signal set. Multistage iterative interference cancellation has been found suitable in overloaded system [17–19]. Recently, iterative multiuser detection with soft IC for multirate MCCDMA has been proposed in [20].
The effect of MAI that arises from the crosscorrelation between different users' code can be minimized by using Carrier Interferometry (CI) codes [21, 22]. CI codes provide flexible system capacity [23] with good spectral sharing. CI codes of length N can support N simultaneous users orthogonally. User capacity can be increased up to 2N by adding additional N pseudoorthogonal users to the existing system [22]. For synchronous CI/MCCDMA uplink, threshold PIC (TPIC) and BlockPIC [24] have been designed to provide better performance than conventional PIC scheme. BlockPIC significantly outperforms the conventional PIC with a slight increase in complexity. Single user bound with a 1dB off is obtained in BlockPIC at a BER of 1e03. In [25], subcarrier PIC (SubPIC) has been developed for highcapacity CI/MCCDMA with variable data rates. Although the system capacity has been increased up to three times (i.e., system capacity 3N), higher BER restricts realtime data communication.
This paper attempts to improve the performance of multirate CI/MCCDMA system by a novel codebased iterative PIC (CodePIC) scheme. Proper phase shifts between different set of users reduce the effect of MAI. We have shown that BER performance of multirate CI/MCCDMA improves considerably by using subcarrier projection method of the interfering users. Performance for different combination of low and high data rate users is shown over different channel conditions like additive white Gaussian noise (AWGN) and slowfrequency selective Rayleigh fading channel. Performance comparisons with BlockPIC and SubPIC are also presented in this work.
The paper is organized as follows: System model of CI/MCCDMA is discussed in Sections 2, and Section 3 describes iterative interference cancellation receiver. In Section 4, multirate highcapacity system is explained. CodePIC for different user sets is outlined in Section 5. Simulation results are presented in Section 6. Computational complexities of conventional PIC, BlockPIC, SubPIC and CodePIC for multirate CI/MCCDMA system are evaluated in Section 7. Finally, in Section 8, conclusions are drawn.
2 System model
This section describes the model of CI/MCCDMA system considered in the paper. Synchronous CI/MCCDMA system with K users is considered. Each user employs N subcarriers with binary phaseshift keying (BPSK) modulation. CI code [21, 22] of length N for k th user (1 ≥ k ≥ K) corresponds to
where
2.1 Transmitter
The transmitted signal corresponding to n th data symbol of the k th user is
where M is the number of data symbols per user per frame. a_{ k } [n] is n th input data symbol of k th user, which is modeled as a sequence of independent and identically distributed (i.i.d.) random variables taking values from ± 1 with equal probability. {f_{ i } = f_{ c } + i Δf, (i = 0, 1,2, . . . N  1)}is the frequency of i th narrow band subcarrier with center frequency f_{ c } . Δf is selected such that orthogonality between carrier frequencies can be maintained. Typically, Δf = 1/T_{ b } where T_{ b } is bit duration of Nyquist pulse shape p(t). The transmitted signal for K users can be expressed as
2.2 Channel model
The channel is modelled as a slowly varying frequency selective Rayleigh fading channel. It is assumed that every user experiences an independent propagation. Each carrier undergoes a flat fading over entire bandwidth. The frequency selectivity over the entire bandwidth results correlated subcarrier. The correlation between i th subcarrier fade and j th subcarrier fade can be modeled as [26]
where (Δf) _{ c } is the coherence bandwidth. Bandwidth of each subcarrier is chosen to be less than (Δf)_{ c }, i.e., 1/T_{ b } ≪ (Δf) _{ c } < BW, where BW is the total bandwidth of the transmission. For multipath frequency selective channel, we have assumed 4fold Rayleigh fading [21, 24], i.e., BW/(Δf) _{ c } = 4.
The transfer function of the channel of the i th subcarrier for k th user is ξ_{i,k}= α_{i,k}. exp(β_{i,k}), where α_{i,k}and β_{i,k}are complex channel gain and carrier phase offset for i th subcarrier of k th user, respectively.
2.3 Receiver
The received signal r(t) can be written as
where β_{i,k}is random carrier phase offset uniformly distributed over [0, 2π] for k th user in i th subcarrier. Rician amplitude distribution can be applied for α_{i,k}in indoor data communication, where line of sight (LOS) components in received signal can be found. Rayleigh fading would be more appropriate in long distance wireless communication where LOS is hardly possible. For channel model, each resolvable multipath component is assumed to follow Rayleigh fading characteristics. The advantage of using orthogonal code vanishes when multipath fading paths are assumed. η(t) represents AWGN with zero mean and doublesided power spectral density N_{0}/2.
The received signal r(t) is projected on N orthogonal subcarriers and is despread using k th user's CI code. The i th subcarrier component of received signal r(t) can be written as
where y_{ i } is the projected N orthogonal subcarrier component of the received signal r(t).
The decision variables for k th user at different subcarriers may be expressed as
where {r}_{i,iter}^{k} is decision variable for i th subcarrier of k th user at iterth iteration stage.
where * denotes the complex conjugate and η_{ i } is Gaussian random variable with zero mean and variance of N_{0}/2. E_{ b } is the transmitted bit energy and {\xe2}_{k}^{\left(iter\right)} is the estimated data of k th user at iterth iteration stage. {\widehat{\beta}}_{i,m} is the estimate of the phase for i th subcarrier of m th user. For synchronous transmission, {\widehat{\beta}}_{i,m}={\beta}_{i,k} is assumed. Further, it is assumed that the received power of every user is same.
When y_{ i } is multiplied by k th user's spreading code,
Taking the real part of X _{ k },
where
I_{ k } is the MAI experienced by k th user due to (K  1) users. Multiplication of noise (η_{ i } ) by the user's spreading code (exp(j(i Δθ_{ k } ))) does not change the noise distribution. So, additive noise term N_{ k } is zero mean Gaussian random variable with variance of N_{0}/2 for k th user.
The average bit error probability for k th user is given by
The average BER of all users is given by
From the Equation (15), it is clear that if probability of noise and interference term is higher than \sqrt{\frac{2{E}_{b}}{{N}_{0}}}, then BER tends to increase. So, cancellation of interference is necessary to obtain a lower bit error probability. This motivates the need for interference cancellation technique.
3 Iterative interference cancellation receiver
In this section, conventional PIC structure is discussed. The estimated interference due to (K  1) users is directly subtracted from r(t) for the desired k th user. The improved received signal {\widehat{r}}_{k}^{iter}\left(t\right) of k th user may be written as
where {\u015d}_{m}^{iter}\left(t\right) is the estimated signal at iterth iteration for the m th user. {\u015d}_{m}^{iter}\left(t\right) can be written as,
3.1 Subcarrier PIC (SubPIC)
In SubPIC, the received signal is projected on N orthogonal subcarrier, and the interference due to other users is subtracted at subcarrier level. Using Equations (7) and (17), the received signal of k th user after orthogonal projection is given as:
where {\u0177}_{i} is the projected N orthogonal subcarrier component of {\widehat{r}}_{k}^{iter}\left(t\right). When {\u0177}_{i} is multiplied by k th user's spreading code,
Taking the real part of {\widehat{X}}_{k}^{iter},
where {\widehat{\mathbf{I}}}_{k}^{iter} is the estimated MAI experienced by k th user due to (K  1) users at iterth iteration.
So, received data of k th user at iterth iteration can be given as
The average bit error probability in SubPIC for k th user is given by
The interference term is reduced by the cancellation of estimated interference. From the above Equation (24), it is clear that the bit error probability becomes low in SubPIC scheme compared to error probability in case of simple matched filter output (Equation (15)).
Again, {\widehat{\mathbf{Z}}}_{k}^{iter} can be written as
where
The term {\mathbf{W}}_{k}^{iter} stands for the residual or uncancelled interference that arises due to imperfect cancellation. In iterative receiver structure, {\mathbf{W}}_{k}^{iter} is reduced after every iteration stages. For initial estimations, after forming the decision variables r^{k} , minimum meansquare error combiner (MMSEC) is employed to make decision in an AWGN channel [27]. Also, in slowfrequency selective channel, the performance of MMSEC is a good solution [28]. MMSEC exploits diversity of frequency selective channel to minimize intercarrier interference (ICI). Y_{ k } can be written as {\mathbf{Y}}_{k}={\mathbf{r}}^{k}\stackrel{\u0304}{\omega} for {\xe2}_{k}^{0}\left[n\right], where \stackrel{\u0304}{\omega} is the weight vector of the combiner [27]. The decision of k th user at iter^{th} iteration becomes
The scheme represented by Equation (27) is referred as hard decision PIC (HDSubPIC) [25]. The BER performance of SubPIC improves significantly by taking soft estimation of the interfering users. In soft decision SubPIC (SDSubPIC), the estimation of the received data is performed by taking soft decisions using nonlinear function [17]. The soft decision of X_{ k } is given by {\stackrel{\u0303}{x}}_{k}=\varphi \left({\mathbf{Y}}_{k}{\widehat{\mathbf{I}}}_{k}^{iter}\right), where ϕ(x) is the nonlinear function. Different types of nonlinearities like deadzone nonlinearities, hyperbolic tangent and piecewise linear approximation of hyperbolic tangent can be used for ϕ{(x)}.

i.
DeadZone Nonlinearity:
\varphi \left(x\right)=\left\{\begin{array}{cc}\hfill \mathsf{\text{sgn}}\left(x\right)\hfill & \hfill \mid x\mid \phantom{\rule{2.77695pt}{0ex}}\ge \lambda \phantom{\rule{2.77695pt}{0ex}}\hfill \\ \hfill 0\hfill & \hfill \mid x\mid \phantom{\rule{2.77695pt}{0ex}}<\phantom{\rule{2.77695pt}{0ex}}\lambda \hfill \end{array}\right.(28)
If λ = 0 then it becomes similar to hard decisionbased estimation in Equation (27).

ii.
Hyperbolic Tangent:
\varphi \left(x\right)=\left\{\begin{array}{cc}\hfill \mathsf{\text{sgn}}\left(x\right)\hfill & \hfill \mid x\mid \phantom{\rule{2.77695pt}{0ex}}\ge \phantom{\rule{2.77695pt}{0ex}}\lambda \hfill \\ \hfill tanh\left(x\u2215\lambda \right)\hfill & \hfill \mid x\mid \phantom{\rule{2.77695pt}{0ex}}<\phantom{\rule{2.77695pt}{0ex}}\lambda \hfill \end{array}\right.(29) 
iii.
Piecewise linear approximation of Hyperbolic Tangent: In piecewise linear approximation, for all iteration the function ϕ{(x)} can be written as
\varphi \left(x\right)=\left\{\begin{array}{cc}\hfill \mathsf{\text{sgn}}\left(x\right)\hfill & \hfill \mid x\mid \phantom{\rule{2.77695pt}{0ex}}\ge \phantom{\rule{2.77695pt}{0ex}}\lambda \hfill \\ \hfill x\u2215\lambda \hfill & \hfill \mid x\mid \phantom{\rule{2.77695pt}{0ex}}<\phantom{\rule{2.77695pt}{0ex}}\lambda \hfill \end{array}\right.(30)
The nonlinear parameter λ is selected such that minimum BER can be obtained for iterative IC process. Here, in SDSubPIC technique, we have considered piecewise linear approximation of hyperbolic tangent as a nonlinear function of soft decision IC process. In the last stage of iteration, the final decision is made by hard detector, {\xe2}_{k}\left[n\right]=\mathsf{\text{sgn}}\left\{{\mathbf{Y}}_{k}{\widehat{\mathbf{I}}}_{k}^{iter}\right\}. In the next section, multirate highcapacity CI/MCCDMA with 3N users system is discussed.
4 Multirate highcapacity 3N system
In CI/MCCDMA system described in Section 2, N length CI codes support N orthogonal users and additional N users are added by pseudoorthogonal CI codes [21, 22]. To support more users, a highcapacity CI/MCCDMA system is proposed in [29], where the capacity is increased up to 3N users through the splitting of pseudoorthogonal CI (POCI) codes. As defined earlier, the CI code for k th user (1 <= k <= K) is given by \left[1,{e}^{j\mathrm{\Delta}{\theta}_{k}},{e}^{2j\mathrm{\Delta}{\theta}_{k}},\dots ,{e}^{\left(N1\right)j\mathrm{\Delta}{\theta}_{k}}\right]. This code is divided into odd and even parts. Further, orthogonal subcarriers are also divided into odd and even parts. The odd/even partitioning of POCI and odd/even separation of available subcarriers are useful in adding extra users and hence the system capacity.
In multimedia communication, users transmit at variable data rate. In this paper, different data rate users are broadly grouped into high data rate users (HDR) and low data rate users (LoDR). HDR users are assigned by N contiguous subcarriers. Nonorthogonal odd/even subcarriers with odd/even CI code are allocated to LoDR users. In multipath fading channel, if some of the subcarriers are passed through deep fade, then other subcarriers are used to ensure low BER. The noncontiguous oddeven subcarrier allocation ensures better performance in deep fade as compared to contiguous subcarrier allocation. Proper user allocation algorithm [29] is maintained to minimize the crosscorrelation between different user sets. In multirate highcapacity system model, there are five user sets.
U_{1} : assigned normal CI; transmit through all subcarriers
U_{2}: assigned odd CI codes; transmit through odd subcarriers
U_{3}: assigned even CI codes; transmit through odd subcarriers
U_{4}: assigned odd CI codes; transmit through even subcarriers
U_{5}: assigned even CI codes; transmit through even subcarriers
The transmitted signal for multirate highcapacity system can be expressed as
It is assumed that HDR users transmit data at 'q' times higher than LoDR users. The angles ΔΦ_{1}, ΔΦ_{2}, ΔΦ_{3} and ΔΦ_{4} are phase shift for the different LoDR sets (U_{ i } , i = 2, 3, 4, 5) with respect to HDR users assigned by normal CI codes. Different angles are shown in Figure 1.
These phase angles are chosen such that the interferences between different sets is reduced. Let us assume that R_{1,2}(j, k) represents the crosscorrelation between j th user in group 1 and k th user in group 2.
Here, the crosscorrelation between j th user in orthogonal group 1 and all the users in group 2 is identical to the crosscorrelation between (j + 1)th user in orthogonal group 1 and all the users in group 2. The total numbers of users in group 1 and group 2 are K_{1} and K_{2}, respectively.
Let R_{1,2}(j) is the total crosscorrelation between j th user and all the users in group 2.
In CIbased system, R_{1,2}(j) = R_{1,2}(j + 1), i.e., every user in one set has same total crosscorrelation from users of the other set. If both sets have same number of users, i.e., K_{1} = K_{2}, then the total crosscorrelation between j th user in orthogonal group 1 and all the users in group 2 is identical to the crosscorrelation between k' th user in orthogonal group 2 and all the users in group 1. Total crosscorrelation between group 1 and group 2 can be written as
If K_{1} = K_{2} = N, then R_{1,2} becomes
Let {R}_{{U}_{x},{U}_{y}}\left(j,k\right) refers to crosscorrelation between j th spreading sequence in U_{ x } user set and k th spreading sequence in U_{ y } user set. For real signal, the expression is
Total crosscorrelation between j th user and all the user of U_{2} set becomes
where {K}_{{U}_{x}} represents total number of users in U_{ x } set. In general,
and
So, total crosscorrelation between j th user in U_{1} set and all the users in other set is given by
From Equation (44), it is clear that the users of the same set of subcarrier used by U_{1} user set create interference to the j th user of U_{1}. set. Assuming orthogonality is maintained in subcarrier, there is no crosscorrelation between [U_{2}, U_{4}] set and [U_{2}, U_{5}] set. U_{2} and U_{3} user sets are using different set of subcarriers that is utilized by U_{4} and/or U_{5} sets. In same subcarriers, the crosscorrelation between two different user set is minimized by proper phase separation described in Equation (32). For U_{2} user set, all users from U_{1} set and U_{3} user create interference on odd subcarrier. Then, total interference for j th user in U_{2} user is obtained by
In multipath channel, intercarrier interference (ICI) occurs due to nonorthogonality between subcarrier. So, MAI in multipath fading channel is more than AWGN channel due to ICI.
5 Codebased parallel interference cancellation technique (codePIC)
As discussed in Section 4, there are two groups of users, B_{1} and B_{2}, based on data rates where U_{1} ∈ B_{1}, U_{2,3,4,5} ∈ B_{2} and U_{2} ∩ U_{3} ∩ U_{4} ∩ U_{5} = ϕ. The users of B_{1} group utilize N available subcarriers, and B_{2} users employ alternate odd/even subcarrier. Users in B_{2} group are assigned pseudoorthogonal CI (POCI) codes such that crosscorrelation between users from B_{1} and B_{2} group is low. This results in reduced MAI between users.
The estimated interference is cancelled out using a codebased PIC (CodePIC) scheme. Steps involved in CodePIC scheme is described next with a simplified structure shown in Figure 2.
5.1 Steps involved in CodePIC scheme
Received signal r(t) is projected onto N orthogonal subcarriers. The initial estimates of all users (1 ≥ k ≥ 3N) are obtained with singleuser detector (SUD). In multistage iterative receiver, all users from a selected group are detected first. After that, all users from the next groups are selected. In CodePIC, MAI is reduced using the following steps at a given iteration:
step 1: At the first stage of iterative receiver, the group of desired user (say j th user) is identified.
step 2: If the desired user belongs to B_{2} group (LoDR), then signal components for B_{1} users are reconstructed and projected onto N subcarriers. Now, the MAI due to all B_{1} users is estimated on i th subcarrier. Estimated interference is subtracted from the received signal. After that, steps 3 and 4 are performed.
OR
If the desired user group is B_{1}, then to obtain the decision on odd subcarrier, reconstructed signals of U_{2} and U_{3} are considered; otherwise, for even subcarrier operation, reconstructed signal of U_{4} and U_{5} users are projected on i th subcarrier. MAI due to B_{2} group is estimated and subtracted from the received signal component at subcarrier level. Step 4 is performed for all users of B_{1} group.
step 3: The subcarrier set (i th subcarrier) of j th user is identified. If the subcarrier set is odd subcarrier, then signal components due to U_{2} and U_{3} set are reconstructed; otherwise, U_{4} and U_{5} users are considered. Then, the code pattern (ODD CI or EVEN CI) of j th user is also detected. If the code pattern is ODD CI, then reconstructed signal components of U_{3} or U_{5} user sets (depends on which user set is selected based on i th subcarrier set) are projected on the i th subcarrier; otherwise U_{2} or U_{4} user sets are projected. MAI due to projected user sets is estimated and subtracted from the received signal.
step 4: The received signal component consists of users of only j th user set. The interference due to other users of j th user set is estimated and subtracted to obtain improved decision via decision combiner for j th user. This step is repeated for all users of j th user set.
These steps are performed for all users of the selected group. Next, we discuss the decoding of B_{1} and B_{2} users in 5.2 and 5.3 subsection, respectively.
5.2 Decoding of B_{1}users
For a given desired user from B_{1} group, MAI is caused due to all users from B_{1} group and the users of B_{2} who use same subcarrier of B_{1} group. The estimated MAI of k th user due to other (K  1) users at 'iter' iteration stage \left({\widehat{\mathbf{I}}}_{k}^{iter}\right) may be expressed as
and
where {\xe2}_{k}^{iter}, {\xce}_{k\left({U}_{i}\right)}^{iter} and {\xce}_{k\left({U}_{i},{U}_{j}\right)}^{iter} are the estimated data of k th user, total estimated MAI for U_{ i } user set and MAI due to U_{ j } user set for the U_{ i } user set, respectively, at 'iter' iteration stage. We assumed that HDR users transmit data at 'q' times higher than LoDR users. While calculating {\xce}_{k\left({U}_{1}\right)}^{iter} for n th bit, {\xce}_{k\left({U}_{1},{U}_{i}\right)}^{iter}, (i = 2, 3, 4, 5) remains same for taking the decision of all consecutive 'q' number of bits. So, time and complexities become less in CodePIC technique. The major drawback of this type of technique is that if one of the bits of LoDR is wrongly estimated, then it can effect 'q' number of HDR bits. Error propagation can be minimized if hard decision is replaced by soft decision of received data bits [7, 10, 17]. In the last stage of iteration, the final decision is made by hard detector, {\xe2}_{k}=\mathsf{\text{sgn}}\left\{{\mathbf{Y}}_{k}{\widehat{\mathbf{I}}}_{k}^{iter}\right\}.
5.3 Decoding of B_{2}users
Let us take U_{2} user set as one of the desired user set of B_{2} group. Only odd subcarriers of the available subcarriers are used by U_{2} set. So, the users who use odd subcarrier create interference on U_{2} set. All B_{1} users are nonorthogonal to set B_{2} users. Interference due to HDR users can be written as
In B_{2} group, only U_{2}, U_{3} users utilize odd subcarriers. There is no interference due to U_{4}, U_{5}, assuming proper orthogonality maintained in subcarrier. {\xce}_{k\left({U}_{2}\right)}^{iter} can be written as
This proper estimation and subtraction of MAI from the received signal improves the system performance. MAI experienced by other users set can be obtained in similar way.
6 Simulation results
This section demonstrates the BER performance comparison of BPSKmodulated synchronous CI/MCCDMA system with BlockPIC, SubPIC and CodePIC at different signaltonoise ratios (SNR) using Monte Carlo simulations in MATLAB. Both hard and soft decisions of received data bits are used to estimate the MAI. Perfect channel estimation and synchronization are assumed at the receiver. No forward error correcting code is employed for data transmission. For multipath frequency selective channel, we have assumed 4fold Rayleigh fading [21]. It is also assumed that HDR users transmit data at 4 times higher than LoDR users. In the next subsection, results over AWGN channel are presented and then the results over Rayleigh fading channel are reported.
6.1 AWGN channel
Figure 3 illustrates the performance of SDCodePIC technique for 2.5 user multirate system with 64 HDR users and 96 LoDR users. Number of subcarriers (N) is 64. From the figure, it is clear that BER performance improves by increasing the number of iterations. The estimated MAI becomes closer to actual MAI as number of iterations increases. So, the residual part of MAI ({\mathbf{I}}_{k}{\widehat{\mathbf{I}}}_{k}^{iter}) becomes less. Subtraction of estimated MAI results in the improvement in BER performance. After 5th stage of iteration, a BER of 1.3e03 is obtained at 10 dB SNR. Bit error probability of 6.7e04 is observed after 8th iteration, at same SNR. After a certain number of iterations, the residual interference cannot be removed further. So, BER performance remains almost same for higher number of iterations. From the simulation, the performances of 8th and 10th stages are almost same. So, for 2.5N user multirate system, the number of iterations is fixed at 8 without increasing latency and complexities involved in higher stage of iterations.
The performance comparison of SDCodePIC and SDSubPIC scheme is evaluated in Figure 4 for 2.5N multirate system (N HDR users and 1.5N LoDR users). A total of 160 users (64 HDR + 96 LoDR) are transmitting data at two different data rates over AWGN channel. In SDSubPIC, estimation of the interference for desired user is done without considering interference from other user group. So, large number of iteration stages is required to cancel interference to achieve allowable BER. In SDCodePIC, the interference is estimated based on the knowledge of desired user group and interfering user group. So, the improved estimation ensures less number of iteration to get same BER performance or even better than SDSub PIC. From the figure, it is clear that the performance of SDCodePIC after 5th stage is better than that of the 8th stage of SDSubPIC over an AWGN channel. A SNR gain of 1.5 dB is obtained in SDCodePIC compared to SDSubPIC at a BER of 2e03 after 8th stage of iteration.
In Figure 5, the results are reported for evaluating the effect of adding users more than N (K > N), i.e., overloading in multirate CI/MCCDMA system. The number of high data rate (HDR) users is fixed at 64. The interference effect on high data rate users due to LoDR group is observed in this figure. For 96 LoDR users (1.5N LoDR), the interference due to LoDR is more than 76 LoDR (1.2N LoDR) user system. The average BER of 2.5N (1N HDR + 1.5N LoDR) and 2.2N (1N HDR + 1.2N LoDR) user multirate systems are 6.2e04 and 4.5e04, respectively, at 10 dB SNR using SDCodePIC after 8th iteration over AWGN. System is also tested with 70 LoDR (1.1N) users with subcarrier (N) = 64. At 10 dB SNR, the BER reduces to 3e04 after same iteration over an AWGN channel. The degradation in SNR is 2.3 dB compared to single user bound over AWGN channel at a BER of 3e04. A SNR gain of 0.8 dB is obtained in 2.1N system compared to 2.2N user system at a BER of 6e04. The gain in SNR is 1.3 dB in 2.1N user system compared to 2.5N user system at 7e04 BER.
6.2 Rayleigh fading channel
In Figure 6, the performance of CodePIC is compared with BlockPIC [24] and SubPIC [25] for 2N system with hard decisions. 64 (1N) HDR users, 32 LoDR (N/2) users (using odd subcarrier) and 32 LoDR (N/2) users (using even subcarrier), i.e., a total of 128 users transmit data simultaneously. After 10th stage of iteration, a BER of 7.3e04 is obtained at 25 dB SNR with BlockPIC. In SubPIC, a BER of 4e04 is observed at 25 dB SNR. But, in CodePIC, only after 6th iteration, BER of 3e04 is observed. From the figure, it is clear that CodePIC provides a performance gain of about 4 dB and 2 dB compared to BlockPIC and SubPIC, respectively, at a BER of 1e03 with reduced number of iterations.
Figure 7 illustrates the performance comparison between three soft decisionbased PIC schemes. At 25 dB SNR, a BER of 5.6e05 is obtained using SDCodePIC after 8th iteration compared to 5e04 and 2e04 for SDBlockPIC and SDSubPIC, respectively, after 9th iteration. From the result, it is clear that soft decisionbased CodePIC (SDCodePIC) performs significantly better than soft decisionbased SubPIC (SDSubPIC) [30] and soft decision based BlockPIC (SDBlockPIC) with less number of iterations. From the figure, it is clear that SDCodePIC performs better than SDBlockPIC and SDSubPIC with reduced complexity.
It has been observed through simulations that for a given BER of about 1e03, CodePIC requires 4 iterations, while BlockPIC and SubPIC require 8 and 7 iterations, respectively, for 2N system. Also from Figures 6 and 7, it is observed that CodePIC requires less number of iterations and hence results in reduced latency.
7 Complexity comparison
This section evaluates the computational complexities of conventional PIC [24], BlockPIC [24], SubPIC [25] and CodePIC for multirate CI/MCCDMA system over AWGN channel. Computational complexity per bit period of PIC algorithm is computed in terms of number of HDR users (K_{1}), number of LoDR users (K_{2}), number of available subcarriers (N) and number of iterations (num _iter) [31]. We define the complexity unit as one real multiplication or one signed addition. More complex operation like division is considered as multiplication operation [32]. It is also assumed that the sgn(.) operation and binary comparison require no additional computational complexity [32].
In multirate CI/MCCDMA, it is assumed that there are K_{1} HDR users and K_{2} LoDR users (K_{1} + K_{2} ≥ 3N). The number of LoDR users in U_{ i } , (i = 2,3,4,5) set equals to K_{2}/4. In a given bit period, the total computational complexity of multistage PIC detector can be expressed as
where {\mathcal{C}}_{\mathsf{\text{PIC}}} is the complexity of one iteration for the hard decision PIC, and {\mathcal{C}}_{x} is additional computation required for soft decision PIC technique (equals to zero if only hard decision is used). Table 1 shows the {\mathcal{C}}_{\mathsf{\text{PIC}}} of one iteration for the four PIC schemes.
In conventional PIC, computation complexity is N[K_{1} + K_{2} + 1)N + 1] (K_{1} + K_{2}) per iteration for (K_{1} + K_{2}) users. From Table 2 and Figure 8, it is observed that complexity of BlockPIC is almost same as conventional PIC, which is also reported in [24]. In SubPIC, MAI is estimated and subtracted at subcarrier level. So, computational complexity is reduced compared to BlockPIC and conventional PIC schemes. In CodePIC, computation required to estimate the MAI is significantly reduced by the proper selection of the interfering user sets. This further simplifies the subtraction of MAI. Hence, the computation complexity CCCC is significantly less for CodePIC compared to other schemes. It is also observed from Table 2 that for a given system load, complexity of CodePIC is significantly less than conventional PIC and BlockPIC. Further, it is observed from Figure 8 that the complexity of CodePIC is comparable to SubPIC up to a system load of about 1.5N and for higher loads CodePIC outperforms SubPIC.
8 Conclusion
In this paper, CodePIC scheme is introduced for multirate CI/MCCDMA system. The performance is compared with BlockPIC and SubPIC with hard and soft estimates of received data bits over AWGN and frequency selective Rayleigh fading channels. The proposed scheme provides significant performance improvement with less complexity and reduced latency compared to PIC schemes like BlockPIC and SubPIC. In frequency selective channel for 2N multirate system (N = 64), SDCodePIC ensures SNR gain of 6 dB and 2 dB compared to SDBlockPIC and SDSubPIC, respectively, at a BER of 5e04. From the results, we conclude that CodePIC is a powerful technique to reduce MAI for multirate CI/MCCDMA system over frequency selective channel with overloaded condition. It will be interesting to evaluate the performance of this scheme under imperfect timing and frequency synchronization over nonideal channel conditions. The SNR penalty can be reduced further by using suitable error correcting codes.
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Mukherjee, M., Kumar, P. A novel codebased iterative PIC scheme for multirate CI/MCCDMA communication. J Wireless Com Network 2011, 155 (2011). https://doi.org/10.1186/168714992011155
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DOI: https://doi.org/10.1186/168714992011155
Keywords
 Interference Cancellation
 Additive White Gaussian Noise Channel
 Soft Decision
 Parallel Interference Cancellation
 Data Rate User