# An Adaptive Channel Interpolator Based on Kalman Filter for LTE Uplink in High Doppler Spread Environments

- Bahattin Karakaya
^{1}Email author, - Hüseyin Arslan
^{2}and - Hakan A. Çırpan
^{1}

**2009**:893751

**DOI: **10.1155/2009/893751

© Bahattin Karakaya et al. 2009

**Received: **17 February 2009

**Accepted: **27 July 2009

**Published: **14 September 2009

## Abstract

Long-Term Evolution (LTE) systems will employ single carrier frequency division multiple access (SC-FDMA) for the uplink. Similar to the Orthogonal frequency-division multiple access (OFDMA) technology, SC-FDMA is sensitive to frequency offsets leading to intercarrier interference (ICI). In this paper, we propose a Kalman filter-based approach in order to mitigate ICI under high Doppler spread scenarios by tracking the variation of channel taps jointly in time domain for LTE uplink systems. Upon acquiring the estimates of channel taps from the Kalman tracker, we employ an interpolation algorithm based on polynomial fitting whose order is changed adaptively. The proposed method is evaluated under four different scenarios with different settings in order to reflect the impact of various critical parameters on the performance such as propagation environment, speed, and size of resource block (RB) assignments. Results are given along with discussions.

## 1. Introduction

3GPP Long-Term Evolution (LTE) aims at improving the Universal Mobile Telecommunication System (UMTS) mobile phone standard to cope with future requirements. The LTE project is not a standard itself, but it will result in the new evolved Release 8 of the UMTS standard, including most or all of the extensions and modifications of the UMTS system. Orthogonal frequency-division multiplexing (OFDM) is considered as the strongest candidate of the technology that will be deployed in LTE because of its advantages in lessening the severe effect of frequency selective fading. Since wide-band channels experience frequency selectivity because of multipath effect single-carrier modulations necessitate the use of equalizers whose implementations are impractical due to their complexities. Therefore, OFDM is selected in order to overcome these drawbacks of single-carrier modulation techniques [1]. In OFDM, the entire signal bandwidth is divided into a number of narrower bands or orthogonal subcarriers, and signal is transmitted over those bands in parallel. This way, computationally complex intersymbol interference (ISI) equalization is avoided and channel estimation/equalization task becomes easier. However, orthogonal frequency-division multiple accessing (OFDMA) has a high peak-to-average power ratio (PAPR) because of very pronounced envelope fluctuations, which will decrease the power efficiency in user equipment (UE) and thus decrease the coverage efficiency in uplink for the low cost power amplifier (PA). Moreover, in the uplink, inevitable frequency offset error caused by different terminals that transmit simultaneously destroys the orthogonality of the transmissions leading to multiple access interference [2].

In the literature, various methods are proposed in order to alleviate the aforementioned problems and shortcomings. In order to keep the PAPR as low as possible, single carrier frequency-division multiple access (SC-FDMA) that combines single-carrier frequency-domain equalization (SC-FDE) system with FDMA scheme is introduced. SC-FDMA has many similarities to OFDMA in terms of throughput performance, spectral efficiency, immunity to multipath interference, and overall complexity. Furthermore, it can be regarded as discrete Fourier transform (DFT)—spread OFDMA, where time domain data symbols are transformed into frequency-domain by a DFT before going through OFDMA modulation [2]. Therefore, air interface of Release 8 is being referred to as Evolved Universal Terrestrial Radio Access (E-UTRA) which is assumed to employ SC-FDMA for the uplink and OFDMA for the downlink [3].

To the best knowledge of authors, the very first papers addressing the channel estimation problem in the context of SC-FDMA are [4, 5] both of which consider time-invariant frequency-selective multipath channels, throughout an SC-FDMA symbol. In these papers, zeroforcing (ZF) or minimum mean squared error (MMSE) linear channel estimation methods have been proposed in frequency-domain although they all suffer from ICI, without proposing any cancellation method. Note that, since most of the next generation wireless network standards require transmission in high speed environments, time-variant frequency-selective multipath assumption should be considered rather than time-invariant frequency-selective multipath assumption. However, it is important to note that when the channel is time-variant, the subcarrier orthogonality is destroyed giving rise to ICI due to channel variation within an SC-FDMA symbol.

Even though they are not in SC-FDMA context, there are methods proposed in the literature dealing with ICI mitigation for OFDM-based systems [6–8]. In [6], receiver antenna diversity has been proposed; however, high normalized Doppler spread reduces the efficiency of this approach. In [7], a piece-wise linear approximation is proposed based on a comb-type pilot subcarrier allocation scheme in order to track the time-variations of the channel. In [8] Modified Kalman filter- (MKF-) based time-domain channel estimation approach for OFDM with fast fading channels has been investigated. The proposed receiver structure models the time-varying channel as an AR-process; tracks the channel with MKF; performs curve fitting, extrapolation and MMSE time domain equalizer. In [9], matched filter, LS and MMSE estimator that incorporate decision feedback low complexity time-domain channel estimation and detection techniques are presented for multicarrier signals in a fast and frequency-selective Rayleigh fading channel for OFDM systems. Moreover, polynomial interpolation approaches have been commonly used for channel estimation [10].

In this paper, we focus on a major challenge, namely, the SC-FDMA transmission over time-varying multipath fading channels in very high speed environments, which is regarded as one of the most difficult problems in 3GPP systems. Inspired by the conclusions in [6–9], the signal model in [9] is extended to SC-FDMA systems. A channel estimation algorithm based on Kalman filter and a polynomial curve fitting interpolator whose order is selected adaptively is proposed for LTE uplink systems which include time-varying channels in high speed environments. The variations of channel taps are tracked jointly by Kalman filter in time domain during training symbols. Since channel tap information is missing between the training symbols of two consecutive slots within a single subframe, an interpolation operation is performed to recover it. Hence, the interpolation is established by using a polynomial curve fitting that is based on linear model estimator. The contributions of this study are twofold. (i) The factors which affect the selection of the order of the polynomial curve fitting interpolator are identified; (ii) A procedure that is based on mean squared error (MSE) is developed in order to determine the optimum polynomial order values.

The remainder of the paper is organized as follows. Section 2 outlines the characteristics of the channel model considered along with a discussion that is related to sample-spaced and fractional-spaced channel impulse response concerns. In Section 3, LTE uplink system model is introduced and subcarrier mapping is discussed. In addition, the impact of ICI is formally described for SC-FDMA system. Section 4 provides the details of frequency-domain least squares channel estimation, Kalman filter tracking, and polynomial curve fitting interpolation along with the discussion regarding the selection of its order. Section 5 introduces simulation setups for various scenarios and presents corresponding performance results. Finally, in Section 6, concluding remarks are given along with possible future research directions.

## 2. Channel Model

where denotes the average power of the th path channel coefficient, is the maximum Doppler frequency in Hertz, and represents the complex conjugate operation. The term represents the normalized Doppler frequency; is the sampling period. is the zeroth-order Bessel function of the first kind.

## 3. System Model

where is the sample spaced channel response of the th path during the time sample of th user, is the total number of paths of the frequency selective fading channel, and is the additive white Gaussian noise (AWGN) with .

Because of the term, there is an irreducible error floor even in the training sequences since pilot symbols are also corrupted by ICI. Time-varying channel destroys the orthogonality between subcarriers. Therefore, channel estimation should be performed before the FFT block. In order to compensate for the ICI, a high quality estimate of the CIR is required in the receiver. In this paper, the proposed channel estimation is performed in time domain, where time-varying-channel coefficients are tracked by Kalman filter within the training intervals. Variation of channel taps during the data symbols between two consecutive pilots is obtained by interpolation.

## 4. Channel Estimation

### 4.1. Frequency-Domain Least Squares Estimation

Recall that in (19) some of the subcarriers are left unused for a given user. It is also known that transform-domain techniques introduce CIR path leaks due to the suppression of unused subcarriers [14]. Besides, Kalman filter needs time-domain samples in order to initiate the tracking procedure. However, due to the aforementioned leakage problem, unused subcarriers for a given user will create inaccurate time-domain value. In the literature, the problem has been studied for a single user OFDM system in [15–17]. As mentioned before, leakage problem just affects the initialization of the algorithm therefore we do not focus on the leakage problem and in the subsequent subsection Kalman filtering is introduced along with this inherent leakage problem. By using sophisticated solutions for the leakage problem, initialization of the Kalman can also be improved.

### 4.2. Kalman Filtering

### 4.3. Polynomial Curve Fitting Based on Linear Model Estimator and Order Selection

We now summarize the proposed method for LTE uplink systems.

Step 1.

*Initialization*. Frequency-domain LS estimation to obtain initial tracking parameters for Kalman filter.

Step 2.

*Tracking*. Jointly track CIR taps with Kalman filter employing training sybols.

Step 3.

*Order decision*. Decide the order of the polynomial from the look-up table (i.e., Figure 6).

Step 4.

*Coefficient Estimation*. Compute the polynomial coefficients by applying least-squares approach (30) to the linear model (29) of Kalman estimates and Vandermonde matrix of corresponding time instants.

Step 5.

*Curve Fitting*. Estimate the CIR taps from data symbols by using polynomial coefficients.

## 5. Simulation Results

3GPP channel models which are used in simulations.

Channel model | FS-CIR | 1.4 MHz | 3 MHz | 5 MHz |
---|---|---|---|---|

SS-CIR | SS-CIR | SS-CIR | ||

TUx | 20 | 13 | 17 | 25 |

RAx | 10 | 10 | 11 | 13 |

LTE uplink simulation parameters.

Parameters | 1.4 MHz | 3 MHz | 5 MHz |
---|---|---|---|

Sampling frequency, | 1.92 MHz | 3.84 MHz | 7.68 MHz |

FFT size, | 128 | 256 | 512 |

Maximum available subcarriers, | 72 (6 RB) | 180 (15 RB) | 300 (25 RB) |

Extended CP | 32 | 64 | 128 |

Scenario 1

Scenario 2

Scenario 3

Scenario 4

## 6. Concluding Remarks and Future Directions

Future wireless communication systems such as LTE aim at very high data rates for high mobility scenarios. Since many of these systems have an OFDM-based physical layer, they are very sensitive to ICI. In this study, a channel estimation method is proposed for OFDM-based wireless systems that transmit only block-type pilots (training symbols). In the method proposed, Kalman filter is employed to obtain channel estimates during the training symbols. Next, polynomial curve fitting whose order is adjusted adaptively is applied in order to recover the time-variation of channel taps between training symbols within two consecutive slots in a single subframe. Results show that selecting the order of the polynomial adaptively improves the BER performance significantly. However, as in most of the OFDM-based systems, the method proposed suffers from transform domain techniques as well, since they introduce CIR path leaks due to the suppression of unused subcarriers [14].

This study also reveals that selection of the order of the polynomial used in interpolation depends on many factors such as distance between training symbols in time, maximum Doppler shift, SNR, propagation environment including number of multipath components and delay spread, and so on. However, to the best knowledge of authors, there is no closed-form expression that takes all of the aforementioned factors into account and determines the optimum order value for the interpolation polynomial. In case deriving a closed-form expression is impossible or intractable, generating look-up tables which contain the optimum order values for various scenarios is essential.

The performance of the proposed approach directly related to Kalman filter performance. Specifically for more than one user case Kalman performance will be effected by initialization and the number of parameters to be tracked. Since unused subcarriers increase additional channel impulse response path leakage will degrade the performance of the initialization resulting in overall performance degradation in the proposed approach.

## Declarations

### Acknowledgments

The authors would like to thank WCSP group members at USF for their insightful comments and helpful discussions. The authors would like to acknowledge the use of the services provided by Research Computing, University of South Florida. This work is supported in part by the Turkish Scientific and Technical Research Institute (TUBITAK) under Grant no. 108E054 and Research Fund of the Istanbul University under Projects UDP-2042/23012008, T-880/02062006. Part of the results of this paper is presented at the IEEE-WCNC, USA, March 31-April 3, 2008.

## Authors’ Affiliations

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