CCI CANCELLATION USING KF IN FADED MIMO CHANNELS

Multi input multi output system (MIMO) has become a viable option to meet the demand of high data rate wireless communication. But MIMO system performance is severely affected by the presence of co-channel interference (CCI). CCI cancellation in MIMO channel therefore is a challenging area of research. This paper provides a Kalman Filter based CCI cancellation approach. In the severely faded Rayleigh channel in coded MIMO set-up, experimental results show that Kalman filter based approach for CCI cancellation provides satisfactory results and can thus prove to be a reliable CCI cancellation technique in future. KeywordsCo-channel interference, MIMO, STBC, Rayleigh Fading


I. INTRODUCTION
In recent years, researchers have found that substantial amount of performance gain of transmitted and receive diversity can be achieved by using multiple antennas. Multiple-Input Multiple-Output (MIMO) system. MIMO technology is a part of many high data rate wireless communication systems. It increases capacity and performance of wireless links. This is generated by the transmitreceive diversity inherent in MIMO technology. Space-time block code (STBC) is a method usually employed into MIMO wireless communication systems to improve the reliability of data transmission using multiple antennas. The use of STBC with diversity gains derived from MIMO setup provide improved performance in faded wireless channels.
Co-channel interference (CCI) in wireless channel is a degrading phenomenon. It is more so with MIMO systems and the capacity of such systems is limited considerably by the presence of CCI. Therefore, CCI cancellation is challenging area and continues to attract research. The receiver design which could effectively remove the CCI and give a satisfactory receiver performance is a pertinent problem.
Many methods of CCI cancellation in MIMO domain have been proposed. In paper [2], STBC is used to combat CCI. A minimum mean square error (MMSE) and maximum a-posteriori (MAP) receiver design was proposed in [3]. In [6], maximum likelihood (ML) estimate of channel using training sequence are studied assuming temporally and spatially white noise.
In the present work, we study channel estimation and data detection of coded MIMO system with two CCI sources under fading in an interference limited environment using recursive Kalman Filter (KF). We specially use an application specific KF for a coded -MIMO set-up which cancels CCI successfully. The paper is organised as follows. Section II introduces basic theoretical notions regarding the model. Section III describes the system Model. Experimental details and stimulated results are included in Section IV. Section V contains the conclusion of the work.

II. BASIC THEORTICAL NOTIONS
The use of STBC and MIMO has proven to be an effective combination. This section provides a brief description of STBC, CCI, Rayleigh fading and related channel aspects considered for the work.
A .Rayleigh Multipath Fading Channel-The propagation environment for any wireless channel is either indoor or outdoor may be subject to LOS (Line-of-Sight) or Non LOS (NLOS). A probability density function of the signal received in the LOS environment follows the Rician distribution, while that in the NLOS environment follows the Rayleigh distribution. In mobile radio channels, Rayleigh distribution is commonly used to describe the statistical time varying nature of the received envelope of a flat fading signal or the envelope of an individual multipath component [1].

B. Space-Time Block Code (STBC)-
In general multiple antennas are used to achieve spatial diversity and to achieve time diversity the transmission is repeated n times. Scope of diversity is expanded by using multiple antennas at both the receiver and transmitter. The capacity of multi-antenna systems far exceeds that of a single antenna system and capacity grows at least linearly with the number of transmit antennas as long as number of received antenna is greater than or equal to number of transmit antennas. STC were first introduced by Vahid Tarokh, Nambi Seshadri and Robert Calderbank from AT&T research labs in 1998 as a novel means of providing transmit diversity for the multiple antennas fading channel. These STCs achieve significant error rate improvements over single-antenna systems. Their original scheme was based on trellis codes but the simpler block codes were utilised by Siavash Alamouti [14], and later Vahid Tarokh, Hamid Jafarkhani and Robert Calderbank [15] to develop STBCs. STC involves the transmission of multiple redundant copies of data to compensate for fading and thermal noise in the hope that some of them may arrive at the receiver in a better state than others C. Co-channel interference (CCI)-MIMO architectures are useful for combined transmit receive diversity. For its parallel mode of transmission, MIMO system offer high data rate in narrow bandwidth .MIMO system is characterized by multiple antenna elements at the transmitter and receiver, have demonstrated the potential for increased capacity in rich multipath environments. A MIMO system input-output relationship can be written as ..,N denoting the transfer function between the jth transmit and ith receive antenna respectively. Propagation related variations modeled by Rayleigh, ITU pedestrian and vehicular channels and Rician distribution can be included in matrix H.

Fig1: A generic MIMO scheme with interferer
Considering the presence of CCI, the expression (4) can be modified as below: where P is constant interference power, L is the number of interferer, hi(k) is the channel vector of the ith interferer and rest of the terms as described with reference to equa (1).A generic set-up depicting a MIMO arrangement with certain no of interferer is shown in Fig 1. Here propagation taking place through channel H while interference signal si(k) reach the receiver end through another set of channel taps denoted by .Receiver receives the CCI affected signal.
D. Kalman Filter-In 1960, R.E. Kalman published his famous paper describing a recursive solution to the discrete data linear filtering problem. The Kalman filter is a set of mathematical equations that provides an efficient computational (recursive) means to estimate the state of a process, in a way that minimizes the mean of the squared error. The filter is very powerful in several aspects: it supports estimations of past, present, and even future states, and it can do so even when the precise nature of the modelled system is unknown [8]. Kalman Filter estimation is quite common in the literature at least for single user channel. In [9] and [10] the KF is used for tracking MIMO channels based on a low order autoregressive (AR) model. However, exact modelling of fast time varying channel with a low order model is impossible since the AR functions are irrational and higher order statistics are needed.
Process to be estimated: The Kalman filter estimates the state xЄR n of a discrete-time controlled process that is governed by the linear stochastic difference equation The random variables w k and v k represent the process and measurement noise respectively. They are assumed to be independent of each other, white, and with normal probability distributions ( ) (0, ), p w N Q  The a priori state estimate at step k is defined as ˆn k x    given knowledge of the process prior to step k, and ˆn k x   to be a posteriori state estimate at step k given measurement z k . a priori and a posteriori estimate errors are The a priori estimate error covariance is then and the a posteriori estimate error covariance is [ ] An a posteriori state estimate ˆk x can be computed as a linear combination of an a priori estimate ˆk x  and a weighted difference between an actual measurement z k and a measurement prediction The difference k k z Hx   is called the measurement innovation, or the residual. The n × m matrix K is chosen to be the gain or blending factor that minimizes the a posteriori error covariance.
The specific equations for the time and measurement updates are presented in Table 1. After each time and measurement update pair, the process is repeated with the previous a posteriori estimates used to project or predict the new a priori estimates [8].

III. SYSTEM MODEL
We have considered in our setup, multiple single-user links with two CCI sources. We assume the desired user has 2 transmit antennas, the two other interfering user has 2 transmit antennas each, and there are 2 receive antennas of the desired user. Here, we have used STBC before transmission. Figure .3. Transmitter and receiver structure of co-channel interference setup.
The system model for CCI set up in wireless communication is depicted in Figure 3.The received signal at the Receiver 3 is a complex signal with CCI content. This signal is estimated with the KF and the original signal is recovered approximately in the receiver.
The state space equations for tracking the MIMO channel can be expressed as: where h is the channel tap, A is a time-varying transition matrix, C is the observation matrix and v is the measurement noise vector. On the receive antenna, the noise n has the Gaussian probability density function with with µ hi,j = 0 and σ h 2 i,j = No/2. A first-order Auto-Regressive (AR) model provides a sufficient model for time varying channels. Therefore, A can be a diagonal matrix of autoregressive model factor α, where The KF expression for MIMO channel is divided into two parts. First part is the predictor and the second part is the update is given as where, R v = βI and β is a covariance of the noise vector v. The K matrix is called the Kalman gain and the P matrix is called the estimation error covariance. Alamouti's transmit diversity space-time coding scheme relies on the availability of accurate channel state information (CSI) at the receiver. However, motion between the transmitter and the receiver results in a change in the propagation path and channel uncertainties become prevalent. To eliminate this problem, Kalman filter is used to estimate the channel.

IV. EXPERIMENTAL RESULTS
In this section, simulation results are presented. In this work, range of signal to noise ratio (SNR) considered is −10 to 10 dB. The channel experienced by each transmit antenna is independent from the channel experienced by other transmit antennas. For the transmit antenna, each transmitted symbol gets multiplied by a randomly varying complex channel matrix hi,j . As the channel under consideration is Rayleigh, the real and imaginary parts of hi,j are Gaussian distributed. of hi,j having mean µh = 0 and variance σh2 =1/2.
The channel experienced between each transmit to the receive antenna is randomly varying in time. The performance of the Kalman estimator proposed here performed satisfactorily and is better than of some similar works already reported in severely faded environments over the range of SNR −10 to 10 dB. The components of the system and channel parameters during the work are summarized in Table  II.

STBC DECODING Alamouti
The performance of the channel estimator based on Kalman filter is tested through simulations for CCI affected signal. It is seen that the estimated component nearly matches the original signal. This is observed in Figure 4. The plot shows the estimated values nearly matches the original value for up to sample no 40. But for other values there are fluctuations due to variations in the channel.  Gain is shown in the Figure 6.It is approaching the value 0 which satisfactorily show the CCI is well cancelled by the Kalman Filter. From Figure 5, we see that the estimation process fluctuates upto around 40 samples but beyond that it stabilizes. The estimate nearly matches the desired value. It means that beyond the 40 samples, the proposed approach cancels CCI better. CCI is a vital problem in the MIMO channel. In this work Kalman Filter is used to estimate the signal from the MIMO set-up filled with CCI. We specially used an application specific KF for a coded MIMO set-up which cancels CCI successfully. It shows successful recovery of the required data with around 40% of available data. The performance of the STBC coded set-up is found to be better compare to the uncoded form.