A novel code-based iterative PIC scheme for multirate CI/MC-CDMA communication
- Mithun Mukherjee^{1}Email author and
- Preetam Kumar^{1}
https://doi.org/10.1186/1687-1499-2011-155
© Mukherjee and Kumar; licensee Springer. 2011
Received: 13 April 2011
Accepted: 2 November 2011
Published: 2 November 2011
Abstract
This paper introduces a novel code-based iterative parallel interference cancellation technique (Code-PIC) for the multirate carrier interferometry/multicarrier code division multiple-access (CI/MC-CDMA) system, which supports simultaneous transmission of high and low data rate users. In Code-PIC scheme, multiple-access 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 cross-correlation between users, which significantly reduces the multiple-access interference (MAI) for the desired user. The effect of MAI in CI/MC-CDMA is reduced by giving proper phase shift to different set of users. Improved estimation of MAI in Code-PIC results in lower residual interference after interference cancellation. Simulation results show that Code-PIC scheme offers improved BER performance over AWGN and Rayleigh fading channels compared to Block-PIC and Sub-PIC with reduced latency and complexity.
Keywords
1 Introduction
Multicarrier code division multiple-access (MC-CDMA) system is a promising technique for high-speed 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 multiple-access 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 single-user 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 maximum-likelihood (ML) multiuser detector, the complexity of the detector grows exponentially with the number of users. The iterative expectation-maximization (EM) algorithm enables approximating the ML estimate. EM-based 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 mean-square error (MMSE) has been proposed. A non-linear MMSE multiuser decision-feedback detectors (DFDs) are relatively simple and can perform significantly better than a linear multiuser detector. Multiuser decision-feedback detectors (DFDs) based on the minimum mean-squared 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 pseudo-decorrelator, the group MMSE detector and the pseudo-decorrelating decision-feedback 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 high-speed 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 decision-based 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. Least-squares (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 low-complexity near-optimal ordering MMSE design criteria [13] for efficient decision-feedback 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].
Non-linear 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 MC-CDMA has been proposed in [20].
The effect of MAI that arises from the cross-correlation 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 pseudo-orthogonal users to the existing system [22]. For synchronous CI/MC-CDMA uplink, threshold PIC (TPIC) and Block-PIC [24] have been designed to provide better performance than conventional PIC scheme. Block-PIC significantly outperforms the conventional PIC with a slight increase in complexity. Single user bound with a 1dB off is obtained in Block-PIC at a BER of 1e-03. In [25], subcarrier PIC (Sub-PIC) has been developed for high-capacity CI/MC-CDMA with variable data rates. Although the system capacity has been increased up to three times (i.e., system capacity 3N), higher BER restricts real-time data communication.
This paper attempts to improve the performance of multirate CI/MC-CDMA system by a novel code-based iterative PIC (Code-PIC) scheme. Proper phase shifts between different set of users reduce the effect of MAI. We have shown that BER performance of multirate CI/MC-CDMA 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 slow-frequency selective Rayleigh fading channel. Performance comparisons with Block-PIC and Sub-PIC are also presented in this work.
The paper is organized as follows: System model of CI/MC-CDMA is discussed in Sections 2, and Section 3 describes iterative interference cancellation receiver. In Section 4, multirate high-capacity system is explained. Code-PIC for different user sets is outlined in Section 5. Simulation results are presented in Section 6. Computational complexities of conventional PIC, Block-PIC, Sub-PIC and Code-PIC for multirate CI/MC-CDMA system are evaluated in Section 7. Finally, in Section 8, conclusions are drawn.
2 System model
2.1 Transmitter
2.2 Channel model
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 4-fold 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
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 double-sided power spectral density N_{0}/2.
where y_{ i } is the projected N orthogonal subcarrier component of the received signal r(t).
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 iter-th 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.
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.
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
3.1 Subcarrier PIC (Sub-PIC)
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 Sub-PIC scheme compared to error probability in case of simple matched filter output (Equation (15)).
- i.Dead-Zone 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)
- 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 non-linear parameter λ is selected such that minimum BER can be obtained for iterative IC process. Here, in SDSub-PIC technique, we have considered piecewise linear approximation of hyperbolic tangent as a non-linear 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 high-capacity CI/MC-CDMA with 3N users system is discussed.
4 Multirate high-capacity 3N system
In CI/MC-CDMA system described in Section 2, N length CI codes support N orthogonal users and additional N users are added by pseudo-orthogonal CI codes [21, 22]. To support more users, a high-capacity CI/MC-CDMA system is proposed in [29], where the capacity is increased up to 3N users through the splitting of pseudo-orthogonal CI (PO-CI) codes. As defined earlier, the CI code for k th user (1 <= k <= K) is given by $\left[1,{e}^{j\mathrm{\Delta}{\theta}_{k}},{e}^{2j\mathrm{\Delta}{\theta}_{k}},\dots ,{e}^{\left(N-1\right)j\mathrm{\Delta}{\theta}_{k}}\right]$. 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 PO-CI 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. Non-orthogonal 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 non-contiguous odd-even subcarrier allocation ensures better performance in deep fade as compared to contiguous subcarrier allocation. Proper user allocation algorithm [29] is maintained to minimize the cross-correlation between different user sets. In multirate high-capacity 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
Here, the cross-correlation between j th user in orthogonal group 1 and all the users in group 2 is identical to the cross-correlation 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.
In multipath channel, intercarrier interference (ICI) occurs due to non-orthogonality between subcarrier. So, MAI in multipath fading channel is more than AWGN channel due to ICI.
5 Code-based parallel interference cancellation technique (code-PIC)
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 pseudo-orthogonal CI (PO-CI) codes such that cross-correlation between users from B_{1} and B_{2} group is low. This results in reduced MAI between users.
5.1 Steps involved in Code-PIC scheme
Received signal r(t) is projected onto N orthogonal subcarriers. The initial estimates of all users (1 ≥ k ≥ 3N) are obtained with single-user 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 Code-PIC, 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
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 Code-PIC 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
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 BPSK-modulated synchronous CI/MC-CDMA system with Block-PIC, Sub-PIC and Code-PIC at different signal-to-noise 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 4-fold 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
6.2 Rayleigh fading channel
It has been observed through simulations that for a given BER of about 1e-03, Code-PIC requires 4 iterations, while Block-PIC and Sub-PIC require 8 and 7 iterations, respectively, for 2N system. Also from Figures 6 and 7, it is observed that Code-PIC requires less number of iterations and hence results in reduced latency.
7 Complexity comparison
This section evaluates the computational complexities of conventional PIC [24], Block-PIC [24], Sub-PIC [25] and Code-PIC for multirate CI/MC-CDMA 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].
Complexity per iteration $\left({\mathcal{C}}_{PIC}\right)$ for four PIC schemes
PIC Scheme | Complexity |
---|---|
Conventional PIC | N[(K_{1} + K_{2} + 1)N + 1](K_{1} + K_{2}) |
Block-PIC | N[(log(K_{1} + K_{2}) - 1)N + 1] log(K_{1} + K_{2}) +N[(K_{1} + K_{2} - log(K_{1} + K_{2}) - 1)N + 1](K_{1} + K_{2} - log(K_{1} + K_{2})) |
Sub-PIC | $\left[N\left({K}_{1}+{K}_{2}\right)+1\right]\left(\frac{{K}_{1}}{4}+{K}_{2}\right)+\left[N\left({K}_{1}+1\right)+1\right]\frac{3{K}_{1}}{4}$ |
Code-PIC | $\left[N\left({K}_{1}+{K}_{2}\right)+1\right]\frac{{K}_{1}}{4}+\left[N\left({K}_{1}+1\right)+1\right]\frac{3{K}_{1}}{4}+\left[N\left({K}_{1}+\frac{{K}_{2}}{4}-1\right)+1\right]{K}_{2}$ |
$\left({\mathcal{C}}_{PIC}\right)$ of the 1st iteration for different PIC schemes
PIC | System load | ||||
---|---|---|---|---|---|
1 N 1 N HDR | 1.5 N 1N HDR+0.50N L o DR | 2 N 1N HDR+1N L o DR | 2.25 N 1N HDR+1.25N L o DR | 2.5 N 1N HDR+1.5N L o DR | |
Conventional PIC | 16519168 | 37361664 | 66592768 | 84354048 | 104212480 |
Block-PIC | 22133254 | 32088263 | 59484359 | 76328135 | 95269063 |
Sub-PIC | 363600 | 494688 | 855168 | 1084560 | 1346720 |
Code-PIC | 265280 | 445536 | 658560 | 777360 | 904352 |
8 Conclusion
In this paper, Code-PIC scheme is introduced for multirate CI/MC-CDMA system. The performance is compared with Block-PIC and Sub-PIC 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 Block-PIC and Sub-PIC. In frequency selective channel for 2N multirate system (N = 64), SDCode-PIC ensures SNR gain of 6 dB and 2 dB compared to SDBlock-PIC and SDSub-PIC, respectively, at a BER of 5e-04. From the results, we conclude that Code-PIC is a powerful technique to reduce MAI for multirate CI/MC-CDMA 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 non-ideal channel conditions. The SNR penalty can be reduced further by using suitable error correcting codes.
Declarations
Acknowledgements
The authors would like to thank the anonymous reviewers for their constructive comments.
Authors’ Affiliations
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