Adaptive channel estimation and loading for OFDM based two-way relay systems

Abstract

In this thesis we introduce a low complexity Recursive Least Square (RLS) based Orthogonal Frequency Division Multiplexing (OFDM) channel estimation for two-way relay system. Using the estimate of the channel, a bit and power loading scheme for OFDM based two-way relay system is implemented.

In a wireless communication scenario, the channel frequency response is usually correlated across both time and frequency. Hence an optimal Minimum Mean Square Error (MMSE) estimator for OFDM channel is one which considers the correlation in the dimension of time and frequency. These estimators are known as 2D estimators. Since the channel is time varying and the channel statistics are not available, we implement a 2D-RLS adaptive filter based channel estimator.

The 2D-RLS filter used for channel estimation is based on the principle of fast array based algorithms. The advantage of this algorithm is that it has a computational complexity comparable to that of 2D-Normalized Least Mean Square (2D-NLMS) algorithm while having same convergence rate as the conventional 2D-RLS algorithm. The reason for the low complexity of fast array algorithm is due to the fact that it considers the time shift structure in the input data vector while updating the inverse of covariance matrix. In the case of OFDM channel, this time shift structure is not directly evident. Hence we propose a simple reordering of the input data vector so as to bring in the notion of time shift structure. The adaptive filter so proposed is called Fast Array Multichannel 2D-RLS (FAM 2D-RLS) filter. In order to reduce the number of training symbols, the OFDM adaptive channel estimator is implemented based on the principle of Decision Directed Channel Estimation (DDCE).

The standard literature on adaptive filter usually assumes that the data to be estimated is a scalar quantity while the weight is a vector. But in our proposed OFDM channel estimation method, the data to be estimated is a vector and the weight is a matrix. The steady state analysis of the RLS filter with weight matrix is derived and verified using simulations. The proposed steady state analysis is derived based on the fact that any adaptive filter can be viewed as an iterative equation solver, with RLS algorithm being a special case. Hence this method could be used for deriving the steady state analysis of any adaptive filter algorithm which has a weight matrix.

A two-way relaying scheme is a spectrally efficient relaying scheme. Using FAM 2D-RLS, an OFDM-DDCE is proposed for this relaying scheme. It is observed that even a simple case of relaying involving nodes and relay with single antenna requires the concepts of Multiple Input Multiple Output (MIMO) systems for estimating the channel. The performance of the FAM 2DRLS for estimating pedA, pedB and vehA channel in case of two-way relay are analyzed. The complexity of FAM 2D-RLS can be further reduced, if instead of considering the correlation of the frequency response across all the frequency samples, we consider only a block of the frequency response, i.e the channel frequency response vector is grouped into M subvectors and is estimated using M parallel FAM 2D-RLS filters. This estimation algorithm is called Block FAM 2D-RLS (BFAM 2D-RLS). The computational complexity of BFAM 2D-RLS is lesser compared to that of FAM 2D-RLS by a factor of 1 M . It is observed that even though BFAM 2D-RLS does not consider the correlation across all the frequency response samples, the Mean Square Error (MSE) of the estimate is comparable to that of FAM 2D-RLS. It is also observed that MSE of channel estimation for BFAM 2D-RLS with large M is lesser compared to FAM 2D-RLS for the case of highly frequency selective channels like pedB and vehA.

The capacity and Bit Error Rate (BER) of a communication system can be improved if the modulation scheme and transmitted power is adapted with respect to the variation of the channel. In order to perform adaptive modulation, the channel State Information (CSI) should be available at the transmitting node. In the case of Adaptive OFDM (AOFDM) systems, based on Signal to Noise Ratio (SNR) of each subchannel, power and bit could be assigned. This is known as power and bit loading algorithms. In a two-way relay system, if the channel estimation is performed at the node, the channel response so obtained pertains to that of the overall channel between the two transmitting nodes. In order to implement loading algorithms, the nodes require the CSI of individual channel, i.e channel between source - relay and relay - destination. Since our proposed channel estimation method is implemented in the frequency domain, the individual channel can be easily obtained from the estimated combined channel with a sign ambiguity. The effect of channel estimation error on loading algorithms for two-way relay is also analyzed. All the computer simulations are performed using MATLABR .

As a summary of this section, we point out the unique features of this thesis,

1. A low complexity adaptive filter called FAM 2D-RLS filter is proposed for DDCEOFDM. 2. Steady state equations for RLS filter with matrix weight is derived. 3. FAM 2D-RLS based DDCE-OFDM is implemented for two-way relay systems. 4. Complexity of FAM 2D-RLS is further reduced by BFAM 2D-RLS. 5. A loading algorithm is implemented for OFDM based two-way relay systems. 6. Effect of channel estimation error on loading algorithm for two-way relay system is analyzed.