On Optimization of CI/MC-CDMA System Through Channel Estimation

Abstract

Multicarrier code division multiple access (MC-CDMA) offers high data rate transmission over radio mobile channel with high user capacity. However, it also suffers from high value of peak-to-average power ratio (PAPR) and multiple access interference. This paper proposes a high user capacity carrier interferometry (CI)/MC-CDMA system with dynamic user allocation scheme. High data rate users are allocated all sub-carriers, while new users are accommodated dynamically to the groups of alternate odd and even subcarriers. This dynamic user allocation is done based on the cross-correlation values among the spreading code patterns which in turn are used for PAPR reduction through phase optimization. An efficient estimation scheme is also suggested for the radio mobile channel modeled as Rayleigh fading. Channel information is then used for receiver performance improvement through weighted subcarrier parallel interference cancelation using artificial neural network. Finally the system is optimized with respect to the number of subcarriers, the number of users and signal-to-noise ratio using genetic algorithms to achieve an acceptable set of values for bit error rate, PAPR and channel capacity. A large set of simulation results are shown to highlight PAPR reduction, efficient channel estimation, improved receiver performance and optimized system design. Simulation is done in an integrated framework of the proposed system with data hiding based image error concealment to highlight the performance gain for real-life image data.

Appendices

Appendix 1

In multicarrier system, the definition of PAPR per discrete-time symbol is given by

$$\begin{aligned} PAPR={\max _{0\le i \le N-1}|S(i)^{2}|\over E[{S(i)}^{2}]} \end{aligned}$$

(30)

where $E[|S(i)|^{2}]$ and $\max _{0\le i \le N-1}|S(i)|^{2}$ denote the average power and the peak power in one symbol interval, respectively. Reduction in PAPR value is possible through the reduction in cross-correlation value among the spreading codes [13]. The reduction in cross-correlation values among the spreading codes for the proposed system is done through the above phase shifts and is supported by the following mathematical expression

$$\begin{aligned} R_{k,j}(\tau )= {1\over 2\varDelta f}{sin\left( {1\over 2} N2\pi \varDelta f \tau \right) \over sin\left( {1\over 2} 2\pi \varDelta f \tau \right) }cos\left( {(N-1)\over 2}2\pi \varDelta f\right) \end{aligned}$$

(31)

where $R_{k,j}(\tau )$ is the cross-correlation between the jth and the kth users and $\tau =\varDelta t_{k}-\varDelta t_{j}=(\varDelta \theta _{k}- \varDelta \theta _{j})/2\pi \varDelta f$ [3].

Appendix 2

Received signal r(t) is first integrated over the bit duration $T_b$ without de-spreading operation as

$$\begin{aligned} r_i=\int _{0}^{T_b}r(t)cos(2\pi \cdot f_{i}t)dt. \end{aligned}$$

(32)

To accomplish the de-spreading operation, $r_{i}$ is multiplied by the jth user’s spreading code and then the real part is taken. This yields the decision statistics for the jth user at the ith subcarrier $r_{i}^{j}$.

MAI estimation and its subsequent cancelation is now done in the respective subcarrier component. Normalized decision statistics for the jth user is defined as

$$\begin{aligned} y_{j}={D^{j}\over {\sum _{i=1}^{N}h_{ik}w_{ij}}} =\alpha _{i}a_{j}+{I_{K}\over {\sum _{i=1}^{N}h_{ik}w_{ij}}}+{N_{J}\over {\sum _{i=1}^{N}h_{ik}w_{ij}}} \end{aligned}$$

(33)

where $I_{K}$ is the interference due to all ‘K’ users except the jth user. Since the proposed method is designed for the large number of users, interference is approximately Gaussian distributed. Total interference power $\sigma _{j}^{2}$ is equal to the sum of the variances of the second and the third terms of (33). Since BPSK modulation is considered, using Bayes’ rule, the conditional bit error probability is as follows:

$$\begin{aligned} P_{e}=P\left[ a_{j}\ne 1/y_{j}\right] = {P\left( y_{j}/a_{j}=-1\right) \over {P\left( y_{j}/a_{j}=1\right) +P\left( y_{j}/a_{j}=-1\right) }}={1\over {1+exp^{\left( 2y_{j}/\sigma _{j}^{2}\right) }}} \end{aligned}$$

(34)

We now analyze mathematically the interference free estimation for the nth bit of the jth user ‘${\hat{a}}_{n}^{j}$’ for the conventional PIC. The expression of the same for the conventional PIC system is

$$\begin{aligned} {\hat{a}}_{n}^{j}=\sum _{i} r_{i,n}-\sum _{k=1,k\not =j}^{K}I_{i,k}=\sum _{i} r_{i,n}-\sum _{k=1,k\not =j}^{K}\alpha _{i}{\hat{a}}_{n}^{k}\rho _{jk} \end{aligned}$$

(35)

where the symbols $r_{i,n}$ represents the resultant received signal at the ith subcarrier corresponding to the nth bit [mathematical form is represented by Eq. (32)]. The symbol $\rho _{jk}$ indicates the cross-correlation between the jth and the kth user’s code patterns that also includes amplitude scaling of the received signal.

Appendix 3

To update the connecting weight for ith component, it can be written as

$$\begin{aligned} d_{i,updated}=d_{i, previous}+\varDelta d_{i} \end{aligned}$$

(36)

Now $\partial E^{j}\over \partial d_{i}$ can be computed using the rule of differentiation as given below

$$\begin{aligned} {\partial E^{j} \over \partial d_{i}}={\partial E^{j} \over \partial V^{j}}{\partial V^{j} \over \partial U^{j}}{\partial U^{j} \over \partial d_{i}} \end{aligned}$$

(37)

Actually $V_j$ is the final output of the neuron obtained after passing through a nonlinear filter, known as activation function. Here we have assumed that the neurons lying on the output layer to have sigmoid transfer function and is written as follows:

$$\begin{aligned} V^{j}={1\over 1+exp^{-\lambda U^{j}}} \end{aligned}$$

(38)