Channel Estimation Techniques and LTE Terminal Implementation Challenges

Md. Masud Rana

Department of Electronics and Communication Engineering Khulna University of Engineering and Technology

Khulna, Bangladesh. Email: mrana928@yahoo.com

Abstract In this paper least square (LS) and linear minimum mean square error (LMMSE) channel estimation (CE) techniques are presented for long term evolution (LTE) single carrier-frequency division multiplexing (SC-FDMA) systems. The main purpose of LTE is to increases data rate but energy utilization both on the mobile terminal as well as network side is important. For doing this, major challenges for LTE terminal are CE and equalization. This paper discusses the CE techniques and challenges imposed by developments in the LTE terminal implementation. Simulation results shows that the LMMSE CE algorithms outperforms the LS in term of mean square error (MSE) by more than around 3dB. Hence, based on a given LTE systems resources and specifications, a appropriate method among the presented methods can be applied. Keywords: LS, LMMSE, LTE, SC-FDMA.

I. INTRODUCTION

The wireless evolution has been stimulated by an explosive growing demand for a wide variety of high quality of services in voice, video, and data. This rigorous demand has made an impact on current and future wireless applications, such as digital audio/video broadcasting, wireless local area networks (WLANs), worldwide interoperability for microwave access (WiMAX), wireless fidelity (WiFi), cognitive radio, and 3rd generation partnership project (3GPP) long term evolution (LTE) [1], [2]. LTE uses single carrier-frequency division multiple access (SC-FDMA) for uplink transmission and orthogonal frequency division multiple access (OFDMA) for downlink transmission [3], [4]. SC-FDMA utilizes single carrier modulation and frequency domain equalization, and has similar performance and essentially the same overall complexity as those of OFDMA system. These advanced applications in which the transmitted signal disperses over the time and the frequency domains, show the need for highlydeveloped signal processing algorithms. In particular, one of the main challenges in the mobile communication is a wireless channel that suffers from numerous physical impairments due to multipath propagation, interference from other users or layers, and the time selectivity of a channel [5-9].

Many CE techniques have already been proposed for the LTE SC-FDMA systems. The simple least square (LS) algorithm, which is independent of the channel model, is commonly used in CE [10-14]. But the radio channel is time-variant; hence a method has to be found in order to perform estimation in a time-varying channel. The minimum mean-squared error (MMSE) estimate has been shown to be better than the LS estimate for CE in wireless communication systems [15]. The important problem of the MMSE estimate is its high computational complexity, which grows exponentially with inspection samples [16]. In [17], a low rank approximation is applied to a linear MMSE (LMMSE) estimator that employs the correlations of the channel. To further improve the system performance, Wiener estimation has been investigated [18]. Although it exhibits the best performance among the existing linear algorithms, it requires accurate knowledge of second order channel statistics, which is not always feasible at a mobile receiver. Also, this scheme requires higher complexity. This paper outlines the developments of the LTE SC-FDMA systems, and highlights some upcoming challenges, where advanced signal processing could play a important role in resolving them. Specifically, we investigates various types of CE techniques such as LS, and LMMSE CE methods and find out which is the more efficient one. The performance is measured in terms computational complexity, and mean square error (MSE). Simulation results shows that the LMMSE CE algorithms outperforms the existing LS in term of MSE by more than around 3dB. Hence, based on a given LTE systems resources and specifications, a appropriate method among the presented methods can be applied. The rest of the paper is organized as follows. The LS and LMMSE CE methods are describes in section II and its performance are analyzed in section III. In section IV, we highlight the challenges for LTE terminal implementation. Finally, some conclusions are made in section V. The following notations are used in this paper: bold face lower and upper case letters are used to represent vectors and matrices respectively. Superscripts TX

+X denote the transpose and congugate transpose of the X , and I is the identity matrix.

����������� ������������������� ��������������������� ����������������������������������!�"����#��$�����$�"��%�$�&�������

'*+���<�<<�+<'<��=��=>�?J���Q������RRR !<!

II. CE METHODS Pilot estimators are often achieved by multiplexing training sequence into the data sequence. These pilot symbols allow the receiver to extract channel attenuations and phase rotation estimates for each received symbol, facilitating the compensation of channel fading envelope and phase. A general CE procedure for communication system is shown in Fig. 1.

Fig. 1 General CE procedure.

The signal S is transmitted via a unknown time-varying channel w, and corrupted by an additive white Gaussian noise (AWGN) z, before being detected in a receiver. The channel coefficient estw , is estimated using any kind of CE method. In the channel estimator, transmitted signal S is convolved with an estimate of the channel estw . The error between the received signal and its estimate is

- (1)est=e r r

The aim of most CE algorithms is to minimize the MSE, while utilizing as little computational resources as possible in the estimation process.

A. LS Estimation The idea behind LS CE method is to fit a model to measurements in such a way that weighted errors between the estimation and the true model are minimized [14]. The received signal can be written as vector notation as , (2)= +r Sw z

where 1 2 L = [ , ...... ]Tr r r r is the received signal,

1 2 L = diag[s , s ......s ]S is the transmitted signal,

1 2 = [ , ...... ]TLw w ww is the unknown channel

coefficients, and 1 2 = [ , ...... ]TLz z zz is AWGN. The

LS estimate of such a system is obtained by minimizing square distance between the received signal and its estimate as [14]

† = ( - ) ( - ) . (3)j r Sw r Sw

Now differentiate this with respect to w and set the results equal to zero to produce [14]:

-1 +

LS = (\ + ) , (4)w I SS S r where \ is regularization parameter and has to be chosen

such that the resulting eigenvalues are all defined and the matrix -1(\ + )I SS is least perturbed. Here the channel is considered as a deterministic parameter and no knowledge on its noise statistics is needed. The LS estimator is computationally simple but problem is that the inversion of the square matrix turns out to be ill-conditioned (sometime). So, it will need to regularize the eigenvalues of the matrix to be inverted by adding a small constant term to the diagonal [14]. B. LMMSE Estimation MMSE CE method proposes at the minimization of the MSE between the actual and estimated channel impulse response (CIR). The most important problem of the MMSE estimate is its high computational complexity, which grows exponentially with inspection samples [15], [16]. In [17], a low rank approximation is applied to a linear MMSE (LMMSE) estimator that employs the correlations of the channel. The general expression of LMMSE is described as

-1

est LS = ( + _ /SNR) , (5)ww www R R I w

where wwR is the auto-covariance matrix of w, LSw is the channel response in LS estimation, and � is a constant depending on the modulation constellation

2 2k k_ = E[ ] E[ 1/ ]. (6)S S

For QPSK modulation, � is 1[17]. Here, LSw is not very important issue in the matrix computation, the inversion of wwR does not require to be estimated every time the

transmitted sybmols in LSw varies. Also, if signal to

noise ratio (SNR) and wwR are identified earlier or are set to fixed nominal values, the matrix

-1( + _ /SNR)wwR I needs to be computed at once. Under these situation, the estimation requires L multiplications per tone.

III. PERFORMANCE ANALYSIS

A. Computational Complexity The complexity of CE is of crucial importance

especially for time varying wireless channels, where it has to be performed periodically or even continuously. We assume that the evaluation of the scalar addition or subtraction needs L addition and multiplying the scalar by the vector requires L multiplications, and multiplying two matrix need 4L multiplications and 4L-1 additions. Table I summarizes the computational complexity of the different CE methods.

!<?

Table I Complexity of the CE methods

Operation LS CE LMMSE CE Matrix inversion 1 2 Multiplication 11L 17L Addition 11L - 3 17L - 5

We calculate the number of complex addition and

multiplications which are needed to implement the algorithm. It shows that the LS CE algorithm has lower complexity than LMMSE method. For this LMMSE estimator, the main contribution to the complexity comes from the term -1( + _ /SNR)ww wwR R I .

B. MSE Simulation Result In this simulations, we consider a system operating with a bandwidth of 1.25MHz, with a total symbol period of 520{s, of which 10 {s is a cyclic prefix. The entire channel bandwidth is divided into 128 sub-carriers, implemented by 128-point IDFT. Sampling is performed with a 1.92MHz. The data symbol is based on BPSK. In practice, the ideal channel coefficient is unavailable, so estimated channel coefficient must be used instead. The more accurate estimated channel coefficient is, the better MSE performance of the CE will achieve. The performance is measured using MSE between the actual and the estimated channel response. Fig. 2 shows the MSE versus SNR for the different channel estimators. We can see that LMMSE CE can always achieve better performance than LS CE. The main reason is, LMMSE CE method uses channel correlation as well as SNR but the LS CE method does not uses channel correlation. Finally, it concludes that the LMMSE CE method has higher computational complexity and around 3dB better performance compared with the LS CE method.

Fig. 2 MSE of the LS and LMMSE CE methods.

IV. CHALLENGES FOR LTE TERMINAL

IMPLEMENTATION LTE meets the important obligations of next generation mobile communications, but still falls short on some preferred requirements such as cell-edge spectral efficiency in the uplink transmission [19]. LTE implementation poses the following signal processing challenges in terms of performance, cost and power consumption: • Regrettably, the development of data rates is not

matched by advanced in semiconductor structures, terminal power consumption improvements. Therefore, advanced signal processing architectures as well as algorithms are needed to cope with these data rates [19].

• High performance multiput input multiput output (MIMO) receivers such as sphere decoders, maximum likelihood receivers offer substantial system performance gains but enforce an implementation challenge, especially when the high peak data rates are targeted [19].

• LTE utilizes precoding, which requires accurate CE. Advanced methods like iterative decision directed CE and pilot based CE offer system performance improvements, but pose again a computational complexity challenge [19].

• LTE has a large ”toolkit” of MIMO methods and adaptive methods. The choice and combination of the accurate technique in a cell with heterogeneous devices, channel conditions and bursty data services is a challenge [19].

• It is very difficult to implement many antennas in a small hand portable unit. In near future, we need to use wearable antenna on head.

• LTE roll-out will be gradual in most cases- interworking with other standards such as GSM or HSPA is required for a long time. This imposes not only a cost and computational complexity issue. One of the reasons many early 3G terminals had poor power consumption was the need for second generation (2G) cell search and handover in addition to normal 3G operation. Reduced talk-time for dual-mode devices is not suitable [19]. Fig. 3 shows the estimated complexity based on the baseline receiver. Note that the complexity of the LTE receiver grows linearly with respect to system bandwidth and the corresponding maximum nominal throughput. Interestingly, MIMO mode requires less than double the SIMO mode complexity.

0 5 10 15 20 25 30 3510

-5

10-4

10-3

10-2

10-1

100

SNR [dB]

MS

E

LMMSE CE

LS CE

!<*

Fig. 3 Complexity of LTE receiver.

V. CONCLUSION An accurate CE is one of the most important issues for reliable future wireless communication systems such as LTE. In this paper, we briefly insvesteget LS and LMMSE CE techniques for LTE terminal implemtation. Simulations demonstrated that the MSE performance of the LMMSE CE algorithm is at least 3dB better than existing LS estimator. Even though, the LMMSE CE technique requires a little high computational complexity, the advantage in the MSE and convergence towards true channel coefficient may be significantly useful for future mobile communications which allow broadband multimedia Internet access and wireless connection anywhere, and any time. This paper also discusses the challenges imposed by developments in the LTE terminal implementation. Hence, based on a given LTE systems resources and specifications, a appropriate method among the presented methods can be applied.

VI. ACKNOWLEDGMENT The author would like to thanks Prof. Dr. Jinsang Kim. This research work was supported by the Khulna University of Engineering and Technology.

REFERENCES [1] Q. Li, G. Li, W. Lee, M. I. Lee, D. Mazzarese, B.

Clerckx, and Z. Li, “MIMO techniques in WiMAX and LTE: a feature overview,” IEEE Commun. Magazine, vol. 48, no. 5, pp. 86–92, May 2010.

[2] M. Alasti, B. Neekzad, C. J. Hui, and R. Vannithamby, “Quality of service in WiMAX and

LTE networks,” IEEE Commun. Magazine, vol. 48, no. 5, pp. 104–111, May 2010.

[3] Z. Lin, P. Xiao, B. Vucetic, and M. Sellathurai, “Analysis of receiver algorithms for LTE SC-FDMA based uplink MIMO systems,” IEEE Trans. on Wireless Commun., vol. 9, no. 1, pp. 60–65, Jan. 2010.

[4] M. Zhou, B. Jiang, T. Li, W. Zhong, and X. Gao, “DCT-based channel estimation techniques for LTE uplink,” In Proc. Personal, Indoor and Mobile Radio Commun., Sept. 2009.

[5] L. Sanguinetti, M. Morelli, and H. V. Poor, “Frame detection and timing acquisition for OFDM transmissions with unknown interference,” IEEE Trans. on Wireless Commun., vol. 9, no. 3, pp. 1226–1236, Mar. 2010.

[6] M. Morelli, G. Imbarlina, and M. Moretti, “Estimation of residual carrier and sampling frequency offsets in OFDM-SDMA uplink transmissions,” IEEE Trans. on Wireless Commun., vol. 9, no. 2, pp. 734–744, Feb. 2010.

[7] Z. Wang, Y. Xin, G. Mathew, and X. Wang, “Multipath parameter estimation for radio propagation channel measurements with a vector network analyzer,” IEEE Trans. on Vehicular Technology, vol. 59, no. 1, pp. 48–52, Mar. 2010.

[8] J. I. Montojo and L. B. Milstein, “Channel estimation for non-ideal OFDM systems,” IEEE Trans. on Commun., vol. 58, no. 1, pp. 146– 156, Jan. 2010.

[9] M. H. Hsieh and C. H. We, “Channel estimation for OFDM systems based on comb-type pilot arrangement in frequency selective fading channels,” IEEE Trans. on Consumer Electronics, vol. 44, no. 1, pp. 217–225, Feb. 2004.

[10] F. Wan, W. P. Zhu, and M. N. S. Swamy, “A semiblind channel estimation approach for MIMO-OFDM systems,” IEEE Trans. on Signal Process., vol. 56, no. 7, pp. 2821–2834, July 2008.

[11] H. Wu, X. Dai, and H. Zhang, “Semi-blind channel estimation for the uplink of multi-carrier code-division multiple access systems with timing offset,” IET Commun., vol. 3, no. 12, pp. 1832–1842, 2009.

[12] B. Karakaya, H. Arslan, and H. A. Curpan, “An adaptive channel interpolator based on Kalman filter for LTE uplink in high Doppler spread environments,” EURASIP Journal on Wireless Commun. And Networking, vol. 2009, Article ID 893751, 2009.

[13] T. Fusco and M. Tanda, “Blind synchronization for OFDM systems in multipath channels,” IEEE Trans. on Wireless Commun., vol. 8, no. 3, pp. 1340–1348, Mar. 2009.

[14] A. Ancora, C. B. Meili, and D. T. Slock, “Down sampled impulse response least-squares channel estimation for LTE OFDMA,” In Proc. International Conference on Acoustics, Speech,

0 2 4 6 8 10 12 14 16 18 200

1

2

3

4

5

6

7

8

System bandwiudth [MHz]

Com

plex

ity [

Gip

s]

LTE SIMO 16-QAM

LTE MIMO 16-QAM

HSDPA 16-QAM

!<+

and Signal Processing, pp. III–293–III–296, Apr. 2007.

[15] J. J. V. D. Beek, O. Edfors, and M. Sandell, “On channel estimation in OFDM systems,” In Proc. Vehicular Technology Conference, vol. 2, pp. 815–819, Sept. 1995.

[16] M. H. Hsieh and C. H. We, “Channel estimation for OFDM systems based on comb-type pilot arrangement in frequency selective fading channels,” IEEE Trans. on Consumer Electronics, vol. 44, no. 1, pp. 217–225, 1998.

[17] O. Edfors, M. Sandell, J.J. V. D. Beek, S. K. Wilson, and P. O. Borjesson, “OFDM channel estimation by singular value decomposition,” IEEE Trans. on Commun., vol. 46, no. 7, pp. 931– 939, 1998.

[18] L. A. M. R. D. Temino, C. N. I. Manchon, C. Rom, T. B. Sorensen, and P. Mogensen, “Iterative channel estimation with robust Wiener filtering in LTE downlink,” In Proc. Vehicular Technology Conference, pp. 1–5, Sept. 2008.

[19] R. Irmer and S. Chia, “Signal processing challenges for future wireless communications,” In Proc. International Conference on Acoustics, Speech, and Signal Processing, pp. 3625–3628, Apr. 2009.

!<'