Channel Estimation using Least Mean Square (LMS) Algorithm for LTE-Advanced

JOURNAL OF COMPUTING, VOLUME 3, ISSUE 12, DECEMBER 2011, ISSN 2151-9617 https://sites.google.com/site/ https://sites.google.com/site/journalofcomputing journalofcomputing WW.JOURNALOFCOMPUTING.ORG

102

Channel Estimation using Least Mean Square (LMS) Algorithm for LTE-Advanced LTE-Advanced Saqib Saleem, Qamar-ul-Islam

Abstract:

For IMT-Advanced’s high data rate requirement requirement for the internet and multimedia services, 3GPP has proposed evolved version of LTE, known as LTE-Advanced. To achieve the targets for next generation mobile communications systems, the following systems enhancements are proposed in Rel-10: Carrier Aggregation, Co-ordinated Multipoint Transmission and Reception (CoMP), Relaying Capability, Advanced MIMO techniques and Heterogeneous Networks. In order to achieve high spectral efficiency and high cell edge throughput, Channel State Information (CSI) is desired to be known as the both ends of transceiver. Channel can be estimated in time-domain and frequency-domain. For multiantenna transmission systems under high mobility conditions when channel is fast fading frequency selective, channel needs to be estimated at each instance. Under these situations, adaptive algorithms can be used to have knowledge of channel. In this paper, the behavior of Least Mean Square (LMS) algorithm is determined and the evaluation parameters used are number of channel taps and CIR samples of the channel. Monte-Carlo Simulations are carried for the performance and complexity comparison of LMS-based channel estimation for MIMO-OFDM system.

Keywords: MIMO-OFDM, LMS, CIR Samples, Channel Taps, LTE, IMT-Advanced

——————————  —————————— 1 INTRODUCTION

For 4G’s IMT‐Advanced system’s requirements, e.g. less energy consumption per bit per bit transmission, all over the world service provisioning, flexible usage of frequency‐ bands, common network architecture, interworking with the existing 2G and 3G radio access networks [1] 3GPP made a core network consisting of evolved packet core (EPC), E‐UTRA and E‐UTRAN, which is generally known as LTE‐Advanced. By using the system requirements as given in TR 25.912 and TR 25.913, a peak data rate of 326.4 Mbps for MIMO and 100 Mbps for SISO system can be achieved by using 64 QAM modulation technique for DL data transmission. But for UL case 86.4 Mbps data rate can be achieved by using 64 QAM and 57.6 Mbps for 16 QAM and for QPSK, maximum data rate supported can be 50 Mbps in case of SISO system model [2]. As compared to HSPA, spectral efficiency of LTE‐ Advanced is 3‐4 tim times es greater for DL and 2‐3 times for UL. In Rel‐10, mobility support for 350‐500 Km/hr and control plane latency less than 5 ms are under consideration. [3].

44

———————————————— 

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Saqib Saleem is with Institute of Space Technology, Islamabad. He is currently working as Lecturer in Department of Electrical Engineering. His areas of interest are Channel Estimation, Spectrum Sensing, LTE-Advanced. Dr. Qamar-ul-Islam is also with Institute of Space Technology, Islamabad. He is currently working as Head of Department of Electrical Engineering.

In order to make LTE‐A competitive of IMT‐A, the following new techniques are proposed: the requirement of 100 MHz bandwidth MHz bandwidth for 1 Gbps can be can be achieved by carrier‐aggregation of contiguous and non‐contiguous band, to achieve optimized diversity gains by using MIMO and beam‐steering techniques, a cell with six sectors, each sector having four antennas is preferred as compared to a cell with three sectors and each sector having eight antennas, for soft‐ handovers the macro‐diversity can be can be achieved by achieved by co‐ operative MIMO to increase or decrease the system capacity, coverage‐area can be increased with minimizing interference by using relay which can decode the data before transmission [4]. To eliminate the inter‐symbol interference caused by multi‐path fading channels, equalizers are used which depend on the channel impulse response (CIR) knowledge. Three kinds of channel estimation techniques are proposed in [5,6,7]. In first technique, channel can be estimated by using time‐domain statistics of the slow varying channel under low mobility conditions. Least Square Error (LSE) and Linear Minimum Mean Square Error (LMMSE) algorithms can be used for estimating channel. LSE has less complexity than LMMSE due to the matrix inversion and dependency on channel statistics but the performance of LMMSE is better. DFT method can be used as channel estimator in frequency‐domain. Under non‐integer multipath delays, DCT technique can be used to avoid the high


frequency component. The complexity of frequency‐ domain estimator can be reduced by neglecting the components having values less than the noise by using a windowing function on DFT‐CE. By considering the channel as first order AR process, adaptive filtering schemes can be used for channel estimation. In [7], Kalman filtering based channel estimator is optimized for different channel filter lengths and multi‐paths. In this paper, LMS algorithm is used for time‐varying channel and performance and complexity is analyzed for varying channel impulse response samples and the multi‐paths for different MIMO systems according to LTE‐Advanced. The paper is organized as follows: Physical Layer of LTE‐A is explained in Section II and LMS channel estimation algorithm is given in Section III with the simulation results given in next section. In last section conclusions are drawn.

2 PHYSICAL LAYER OF LTE-ADVANCED

Physical signals generated by Layer 1of LTE‐A are used for following purposes: synchronization, cell identification, channel state estimation. Reference Signals (RS), also known as pilot signals, are used to detect any variation in amplitude and phase of the received signal [1]. In LTE‐A, for DL the multiple access technique used is OFDMA OFDMA and SC‐FDMA is used for UL, both for FDD and TDD modes. Irrespective of different multiple access techniques used, LTE‐A uses same frame structure for UL and DL. Frame used for FDD mode is of 10 ms duration containing 10 sub‐frames. For UL and DL same frame frame structure is followed. For TDD mode, Sub‐frame 0 and 5 are allocated only for DL transmission while sub‐ frame 2 is used for UL transmission purposes. Pilot signals, DwPTS for DL and UpPTS for UL, are transmitted in sub‐frame 1 [8]. For DL sub‐frame, OFDM symbol symbol can be can be generated by generated by [1]

 

   ,   





For UL, the SC‐FDMA signal can be can be generated by generated by

 

    .    ,     ,    

In LTE‐A, the data transmission can be by up to four layers for UL and eight layers for DL case. For two antenna transmission scheme, 3 bit pre‐coding codebook is used for data multiplexing for UL while 6 bit pre‐coding codebook is used for four transmit antennas [8]. To achieve UL transmit diversity, Single Antenna Port Mode is defined for PUCCH, PUSCH and SRS transmissions. For UL control channel with two transmit antennas, the transmit diversity can be achieved by Spatial Orthogonal Resource Transmit Diversity (SORTD) while for PUSCH, OFDM signal pre‐coded using DFT technique is used. For LTE‐A, two reference signal are used for UL : Demodulation Reference Signal (DRS) and Sounding Reference Signal (SRS). DRS is pre‐coded but SRS is not pre‐ coded [2]. UL power control is used to reduce the interference under slow varying channels and to lessen the path loss. In DL multiuser multiuser MIMO techniques are supported without the configuration of RRC. The reference signals supported in DL are used for PDSCH demodulation and Channel State information (CSI) estimation. 3 LMS BASED CHANNEL ESTIMATION

To avoid the matrix inversion, involved in LSE and LMMSE [18], LMS algorithm can be used to solve Wiener‐Holf equation, which may or may not require a priori statistical information of the channel and data. A summary of LMS algorithm is given as follows 1‐ 2‐

,

 ,

LSE method is applied to get the initialized, , used for first iteration. After finding the filter co‐efficients, the channel estimation becomes estimation becomes

 ,             ,   

    

CP+ N)T s . Where T s is symbol duration Where 0 ≤ t < (N CP CP C P N and is cyclic prefix length. is resource atom for OFDM symbol and carrier frequency.

103

Where

,   ,  ,   1 … ,  1  1    Where LMS filter has length M.


 iteration, the error is given by given by   ,   ,  4 From this error, co efficients can be can be updated by updated by  ∗     1     ,   Where the value of step size parameter  depends on 3‐

104

At

By increasing CIR samples from 5 to 10, the complexity increases 20%. While further increase of CIR samples to 20, there is 60% increment in complexity. The combined effect of SNR and CIR ‐ ‐ samples on performance is shown in Figure 3. MSE for different MIMO schemes is shown in Figure 4. The ‐ performance is better for system than the correlation between correlation between the data. and 4 systems. Irrespective of CIR samples, low order MIMO scheme results in better performance. 5‐ After up‐dating the co‐efficients. The weighted‐ MSE behavior MSE behavior remains same for CIR samples less than error is given by given by 5, after that the performance degrades, almost linearly for increasing CIR samples.

22

 4

33

      

4

MSE v/s CIR Samples of LMS Estimator for 2 x 2 Sys tem

x 10

4 SIMULATION RESULTS

Monte‐Carlo Simulations for different MIMO systems employing OFDM as modulation and demodulation techniques are carried out. FFT size of 128‐point and channel length of 64 with CP length of 16 is taken in this system. The performance comparison of LMS channel estimator as a function of CIR samples for different SNR values is shown in Figure 1. From Figure 1, it is clear that for any channel length, the performance is better under low SNR operating conditions. As we go on increasing CIR samples, MSE also increases. So for better performance, less number of CIR samples for low SNR values are are preferred. The effect of channel filter length on MSE for different LMS estimators is shown in Figure 2. We note that performance remain same for LMS and Leaky‐LMS estimators for all CIR samples. The complexity of LMS estimator as a function of CIR samples is given in Table 4.6.

LMS Leaky-LMS

2.2

2

1.8 E S M

1.6

1.4

1.2 10

20

30 40 CIR Samples

50

60

Fig.2 MSE vs CIR Samples for different LMS Estimators

MSE v/s SNR v/s CIR Samples of LMS EStimator for 2 x 2 System 4

x 10 4

12

MSE v/s CIR Samples of LMS Estimator for 2 x 2 System

x 10

12

10

SNR =5 dB

10

SNR =10 dB SNR =15 dB

8


8

E S M E S M

6

6

4

4

2

2

0 25 20 15 10

0 0

5 10

20

30 40 CIR Samples

50

60

Fig.1 MSE vs CIR Samples for LMS Estimator

70

SNR

0

20

40

60

CIR Samples

Fig.3 MSE vs SNR vs CIR Samples for LMS Estimator

80


105

TABLE 1: COMPLEXITY COMPARISON OF LMS ESTIMATOR FOR DIFFERENT MIMO SCHEMES CIR Samples ( ) ( )

2 2 

LS-LMS 68.65 80.045 106.23

5 10 20

3  3 

LMMSE-LMS 180.6 178.83 286.16

LS-LMS 147 176.6 238

4 4 

LMMSE-LMS 395 440.8 525

LS-LMS 260 453 470

TABLE 2: COMPLEXITY OF LMS ESTIMATOR FOR DIFFERENT CHANNEL TAPS FOR Channel Taps Time ( ) 5 255.2 10 269.6 20 321.4



Figure 5 shows the performance of LMS for the cases when initially channel estimator is LS and LMMSE. The performance of LMMSE‐LMS is better than LS‐ LMS because LMS because in first technique, second order channel statistics are exploited due to which this method results in more complexity as given in Table 4.7. By increasing CIR samples from 5 to 10 in LMMSE LMMSE‐LMS, the complexity increases by 8% while in LS‐LMS this increment was 20%. While the increment in complexity is 18.91% when increasing CIR samples from 5 to 20 but in case of LS‐LMMSE it was 60%. Table 1 also demonstrates that for 5 CIR samples the complexity increases by increases by 167 167% % in case of LMMSE ‐LMS as compared to LS‐LMS. While for 10 CIR samples, this increment is 140% and this value reduces to 96% for 20 CIR samples. So the larger the number of CIR Samples, the increment will be less for LMMSE ‐LMS scheme than that of LS‐LMS. The computational time for different MIMO systems for both LMMSE ‐LMS and LS‐LMS schemes is shown in Table 1. More computational time results for higher order MIMO schemes e.g. scheme results in 115% more computational time for both LS‐LMS and LMMMSE ‐ LMS cases as compared to . While for , the increment is almost 290%. The performance as a function of channel taps for LMS is shown in Figure 6.

33

22

44

TABLE 3: COMPLEXITY OF LMS ESTIMATOR FOR DIFFERENT MIMO SCHEMES Channel Taps ( ) ( ) ( ) 5 258 260.6 467 10 291 269 526 20 340 470 565

2 2  3 3  3  4 4

2 2

(

)

LMMSE-LMS 705.5 753 1100

SYSTEM

By increasing the channel taps, the performance also goes on degrading for all SNR values. So for better for better performance and less complexity, small number of channel taps are proposed, as for large number of channel taps not only the performance degrades but complexity also increases as given in Table 2. The increment increment of channel taps value from 5 to 10 results in 5% more computational time while 20 channel taps gives 26% more complexity. . Performance as a function of SNR and channel taps is shown in Figure 7. The performance for different MIMO systems as a function of channel taps is shown in Figure 8. The low order MIMO systems give better performance for all channel taps. For less order MIMO scheme, the effect of increasing the channel taps on performance is not so significant as for case but as we increase the order of MIMO system, the performance degrades, degrades, almost, as a linear function of increasing channel taps.

22

x 10

4

MSE v/s CIR Samples of LMS Estimator for 2 x 2 System

5.74 2 x 2 System 3 x 3 System 4 x 4 System

5.72

5.7

E 5.68 S M

5.66

5.64

5.62 2

4

6

8

10 12 CIR Samples

14

16

18

20

Fig.4 MSE vs CIR Samples for different MIM O Schemes


x 10

5

complexity. To achieve the data rate targets of a wireless communication system through channel feedback, LMS channel estimator is optimized for a system with channel filter length of 5‐10 CIR Samples and channel taps less than 10 for both optimized optimized performance and complexity.

MSE v/s CIR Samples of LMS Estimator for 2 x 2 System LS-LMS

1.038

106

LMMSE-LMS

1.036 1.034 1.032 E S M

1.03

MSE v/s SNR v/s Channel Taps of LMS EStimator

1.028 1.026

x 10 1.024

6

14

1.022

12

1.02 5

10

15 CIR Samples

20

25

10 8

Fig.5 MSE vs CIR Samples for LS-LMS

E S M

6 4

14

x 10

6

MSE v/s Channel Taps of LMS Estimator for 2 x 2 System

2 80

SNR =5 dB

0 25

SNR =10 dB

12


60 20

SNR =25 dB

10

40 15

10

20 5

0 Channel Taps

SNR 8

Fig.7 MSE vs SNR vs Channel Taps for LMS Estimator

E S M

6

16

4

5

MSE v/s Channel Taps of LMS Estimator for different MIMO Systems

14

2

0

x 10

12 0

10

20

30 40 Channel Taps

50

60

70

2 x 2 System 4 x 4 System

10

Fig.6 MSE vs Channel taps for LMS and LMMSE-LMS LMMSE-LMS Estimator

3 x 3 System

E S M

8

6

5 CONCLUSION

Small length of channel filter is preferred not only for better performance but also for less complexity for low SNR values and for low order MIMO systems. If complexity can be compromised then performance can be made even better by taking the initially estimated channel using LMMSE method. Similar to channel filter length, less number of channel taps not only gives better performance but also less

4

2

0

10

20

30 40 Channel Taps

50

60

70

Fig. 8 MSE vs Channel Taps for different MIMO Schemes


REFERENCES [1] [2]

[3]

[4]

[5]

[6]

[7]

[8]

3GPP, TS 36.211 V0.1.2. (2006‐11), ” Physical Channels and Modulation(Release 8)”. Available: www.3gpp.org 3GPP, TR 36.814 V9.0.0. (2010‐03), ” E‐UTRA, Further advancements for E‐UTRA Physical Layer Aspects (Release 9)” .Available: www.3gpp.org 3GPP, TS 36.912 V9.2.0 (2010‐03), ” Feasibility Study for Further Advancements for E‐UTRA (LTE‐ Advanced)(Release 9)”.Available: www.3gpp.org 3GPP, TS 36.913 V9.0.0. (2009‐12), ”Requirements for further advancements for E‐UTRA (LTE‐Advanced) (Release 9)”.Available: www.3gpp.org Saqib Saleem, Qamar ‐ul‐Islam, ”Optimization of LSE and LMMSE Channel Estimation Algorithms based on CIR Samples and Channel Taps”, IJCSI International Journal of Computer Science Issues Vol. 8 Issue.1,pp.437‐443, 443, January January 2011 Saqib Saleem, Qamar ‐ul‐Islam, “LMS and RLS Channel Estimation Algorithms for LTE‐Advanced”, Journal of Computing, Computing, Vol.3, Issue.4, pp.155‐163, April 2011. M.A.Mohammadi,M.Ardabilipour,”Performance Comparison of RLS and LMS Channel Estimation Techniques with Optimum Training Sequences for MIMO‐OFDM Systems”, 978‐1‐4244‐1980 ‐7, IEEE 2008 Seongwook Song, Andrew C.Singer and Koeng‐Mo Sung,”Soft Input Channel Estimation for Turbo Equalization”, IEEE Transaction on Signal Processing, Vol.52, No.10,October 2004

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Channel Estimation using Least Mean Square (LMS) Algorithm for LTE-Advanced

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