Performance Analysis of Llr Combining Harq for Mimo

2010 International Symposium on Intelligent Signal Processing and Communication Systems (lSP ACS 2010) December 6-8, 2010

PERFORMANCE ANALYSIS OF LLR COMBINING HARQ FOR MIMO SYSTEMS IN MOBILE WIMAX

Rahmat Mulyawan1, Fifin Nugroho2, Riris Nov/, Felis Dwiyasa2, Trio Adiono1

lInstitut Teknologi Bandung (ITB), Indonesia. Tel/Fax: +62-22-250-6280 [email protected], [email protected]

2Xirka Silicon Technology, Indonesia. PhonelFax: +62-22-2014189/+62-22-2014253 {fifin.nugroho, riris.novi, felis.dwiyasa}@xirkachipset.com

ABSTRACT

The use of hybrid automatic-repeat-request (HARQ) with multi-antenna systems (MIMO) promises high throughput with high reliability in broadband wireless communication systems. One of the combining methods in MIMO-HARQ is by directly optimizing the log-likelihood ratio (LLR) values instead of compensating the multiple signal-tointerference-and noise power ratios (SINRs) as in conventional combining method. The problem of this approach is that the receiver complexity is significantly increased along with the order of the modulation used. This paper proposed simplified implementation of the MIMO-HARQ with LLR combining method under the IEEE 802.l6e Mobile WiMAX system. Proposed scheme are verified using ITU-B Pedestrian and ITU-A Vehicular channel model with various modulation order. Simulated packet error rate (PER) results show that the simplified method paired with CTC has greater performance, yet lower complexity, compared to original direct method paired with CC.

1. INTRODUCTION

Hybrid ARQ (HARQ) systems incorporate both channel coding and an ARQ system to achieve high throughput and high reliability, which are the key properties of channel coding and an ARQ systems, respectively [1]. Instead of discarding the previously received signals that are detected to contain errors as in ARQ systems, HARQ systems further enhance their performances by combining all the received signals to decode the transmitted message. There are two popular types of HARQ: HARQ with Chase combining (HARQChase) [2] and HARQ with incremental redundancy (HARQ-IR) [1]. In HARQ-Chase, the transmitter sends a message that is coded by both error-detection coding, such as Cyclic Redundancy Check (CRC), and channel coding.

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Then, the receiver decodes the message and detects any error in the CRC. If an error is detected, the receiver requests the transmitter via feedback channel to retransmit the message using the same modulation-and-coding scheme. Although the same signal vector is retransmitted, it differs from the received signal vector from the previous one because of time diversity. After combining the new received signal vectors with the old one, the receiver decodes the combined transmitted message. This procedure repeats until no error is detected after combining all the received signal vectors.

Retransmission (same Packet Data)

I Retransmission

+

� � L-----5ave to 8uffer---------- + Soft

eRG failed eRG succeded

Fig. 1. HARQ-Chase

I ACK

HARQ-IR works in a similar way to HARQ-Chase except that HARQ-IR uses different modulation and coding schemes for retransmissions, providing flexibility and more robust throughput, but the receiver complexity


becomes higher in return [3]. Therefore, HARQ-Chase is more widely used in wireless communications systems, including systems based on the IEEE 802.16e Mobile WiMAX [4] because it can be easily implemented and provides a good operating point in the tradeoff between throughput and reliability.

Combining schemes for MIMO with HARQ-Chase proposed in [5] works in a fundamentally different way than conventional receiver design. Instead of utilizing receive filter to maximize the SINRs, it directly optimize the parameter most-closely related to the decoding performance, i.e., the log-likelihood ratio (LLR), which is widely-used soft-bit information metric. The decoding performances are then analyzed by comparing the LLR values, which makes this method also known as HARQ with LLR combining.

This paper proposed simplified implementation of the MIMO-HARQ with LLR combining method under the Mobile WiMAX system. Proposed scheme are verified using ITU-B Pedestrian and ITU-A Vehicular channel model in various modulation order. Simulated packet error rate (PER) results will be presented for each scenario.

2. SYSTEM ARCHITECTURE

We employ IEEE 802.l6e MIMO system that employs NT transmit antennas and NR receive antennas, thereby using NT spatial streams. In this paper we use NT = NR = 2 as in Mobile WiMAX System Profile [6], but this

scheme can be extended to arbitrary NT and NR.

o '" o +

� o

a �� r� . 8 0" ::;;0 �

-- Fading Channel + AWGN -

Fig. 2. MIMO-HARQ in IEEE 802.16e Mobile WiMAX

We will focus the analysis in the receiver, mainly

MIMO HARQ Decoder. If N transmissions has occurred for the same transmit message, then the relationship between the transmitted signal vector and the received signal vector at the i-th transmission is

�i=!:fJ.b.+1!i' i=I, ... ,N (1)

and its conditional probability distribution function is

P (�i 1!:fJ., b.) = n!R exp ( - 11�i -!:fJ.b. 11 2) (2)

where �i denotes the NR x 1 received signal vector, !:fJ. is

NR X NT channel response matrix, b. is NT X 1

transmitted signal vector, and 1!i denotes NR x 1 additive

white Gaussian noise (A WGN) vector at time i which is assumed to be Li.d. and zero-mean circularly symmetric

complex Gaussian (ZMCSCG) with covariance bvR• 3. MIMO-HARQ DECODER

Our system uses MIMO Spatial Multiplexing (Matrix

B) with HARQ-Chase with Maximum Likelihood (ML) decoder. The receiver can be extended to be used with linear equalizer such as ZF or MMSE [7] but will results in suboptimal performance [8].

A. HARQ Combining Scheme After the (N - 1) transmission, the receiver stores the

values of Euclidean distance II�N _liN!112 in the buffer

for every received vector estimation g, and combine these

values with the new Euclidean distance calculated in the N transmission. DLC scheme acts as a big ML decoder, fully

using all the relevant information, i.e., �i and !:fJ. for all

i = 1, ... , N. Therefore, the DLC scheme has the optimal decoding performance. However, directly implementing the original DLC scheme proposed by [5] imposes prohibitively high computational complexity because it involves a division, summations of exponential functions, and logarithmic operations per each LLR value.

(3)

The complexity can be reduced by using max-Iog

MAP approximation [10]: 10gLi exp ai � maxiai , at the expense of some degradation in decoding performance. The resulting LLR for hi is

(4)

Combining of the LLR can also be done in the symbol

level by using extended version of MRC scheme in

MIMO to HARQ, known as Symbol Level Combining

(SLC) [9]. Similar to DLC scheme, we can use

approximation to calculate the LLR,

(5)


1 - N H , -- 2 ( N H ) where !:f.N = Li=I!:L!:L and �N = !:Lv Li=l!:L �i . Furthermore, this approach not only simplifies LLR calculation but also reduces the complexity of the SLC

_ 1 scheme by removing the needs to calculate H- 2, the

square root inverse of combined channel matrix [5]. Another method to combine LLR is done in bit level or

Bit Level Combining (BLC). This method is practically

simpler to implement and provides flexibility to be used in

HARQ-IR. But it suffers from slight performance

degradation because it neglects the fact that the same

transmit signal vector is repeatedly reused, contrary to

DLC schemes. We can derived the BLC scheme from

DLC scheme by interchanging the order of summation

and minimization and further simplify the algorithm using

the approximation that we have used before. The LLR of

BLC then becomes

LLR��prox). ::::: L7=1 [ ming(o)e x�O) {11�i -!:Ls.(O) 112} ming(l)e x[t) {l1�i -!:LS.(I) In ] (6)

B. Performance Gap As stated previously, the simplification of LLR

combining algorithm can lead to some performance

degradation compared to the direct method. We measure

this gap in CTC in various modulation to verify that the

performance gap can be negligible compared to CTC's

coding gain. The results is shown in Table 1.

Table 1. Proposed vs Direct LLR calculation (CTC-1I2)

Modulation Avg. Performance Degradation 4-QAM 0.1 dB

16-QAM 0.15 dB 64-QAM 0.2 dB

C. Computational Complexity The conventional LLR combining scheme directly

calculate LLR from (3) and use Convolutional Coding

(CC), which is popular channel coding scheme with low

complexity implementation. The use of approximation as

we described in previous analysis will cause performance

degradation, especially in the channel decoder output. To

overcome this, we applied Convolutional Turbo Coding

(CTC) which has higher complexity but offers better

decoding performance and more robust to suboptimal

decoding implementation [10]. CTC is also a mandatory

feature for WiMAX System Profile Certification Test

[11]. The comparison of direct implementation with CC

and simplified implementation with CTC, both using

memory order M = 2 [13], is presented below.

Table 2. Complexity of LLR combining (direct) with CC

Convolutional Coding (CC) with Viterbi

Process # Equivalent Addition

Branch Metric Calc 6(2AM)

Path Metric Calc 4(2AM)

Hard Decision 3 Overall Complexity 10(2J\M)+3

HARQ LLR Combining (direct)· per Nt Symbol processed


Distance Calculator 10K+3 Normalization 2

Constellation LUT 12

QR-Decomposition 45 (SLC only)

Direct LLR Combining with CC M = 2

Total Operation 43 + l17 + 10K)Nt 4-QAM; K = 4; Nt = 2 157 1

16-QAM; K = 16; Nt = 2 I 397

64-QAM; K = 64; Nt = 2 113571

Table 3. Complexity of LLR combining (proposed) with CTC Convolutional Turbo Coding (CTC) with Max-Log-MAP


Branch Metric Calc 12(2AM)

Path Metric Calc (BWD) 4(2AM)

Path Metric Calc (FWD) 4(2AM)

Soft Decision 8(2AM)-3

Overall Complexity 28(2AM)-3

HARQ LLR Combining (simplified)' per Nt Symbol processed


Distance Calculator 16

Normalization 2

Constellation LUT 12

QR-Decomposition 45 (SLC only)

Simplified LLR Combining with CTC M - 2 -Total Operation 109 + l3Q}Nt

4-QAM; K = 4; Nt = 2 169 I 16-QAM; K = 16; Nt = 2 169 I 64-QAM; K = 64; Nt = 2 I 169

4. SIMULATION RESULTS

In this chapter, we will compare the performance of direct and simplified implementation of the LLR combining HARQ. We consider parameters as in Table 3 for our simulations, assuming perfect channel estimation and synchronization in the receiver.

Table 5. IEEE 802.16e Simulation Parameter

Parameter Values FFT Size 1024

Cyclic Prefix 1/8 Frame Duration (TOO) 5ms

Sampling Factor 28/25 Subcarrier Spacing 102.86IJ s (10.93 kHz)

Carrier FreQuencv 2.3 GHz

Packet Size 84 Byte

Channel Speed ITU-B Pedestrian 3 km/hr

ITU-A Vehicular 60 km/hr

Fig. 3 depicts packet error rate (PER) against SNR

performance in low mobility (Pedestrian-B) for 64-QAM


and high mobility (Vehicular-A) channel for 4-QAM and

16-QAM modulation. The simplified implementation

results will be shown in solid lines and direct

implementation results in dotted lines.

Q)

iii cr

e w Q; -'" u '"

a.

4-QAM Veh-A 60kmlhr 10

° ....,----_1*---,

10

, , • , ,

• , , , �

2 3 4 5 6 SNR (dB)

16-QAM Veh-A 60kmlhr 10

° r---------,

dt \ \ \\ " " \, " " "

\� EB

10·3

,-�_�_�_-, 10 12 14 16

SNR (dB)

64-QAM Ped-B 3kmlhr

16 18 20 22 SNR (dB)

-e- Simple DLC+CTC

-t-- Simple SLC+CTC

---A- Simple BLC+CTC

--8-- Direct DLC+CC

--8- Direct BLC+CC

-+- Direct SLC+CC

Fig. 3. Comparison of HARQ Implementation Results

In 4-QAM modulation, PER around 1 % or 10-2 is

achieved by the simplified DLC scheme when SNR is 3

dB in high mobility. To achieve the same PER, the direct

DLC with CC needs 5 dB SNR. The trends continue in

higher modulation, for example 16-QAM, when PER less

than 10-2 is achieved when SNR is 11 dB and 16 dB by

simplified and direct method, respectively. The SNR

margin is mainly created by CTC implementation as

channel decoder. Not only compensate the performance

gap of the simplified scheme, CTC also give better

performance, although increase complexity in return. This

paradox is carefully exploited by the proposed simplified

scheme, which has significant advantage along with

increasement in modulation order.

By using direct implementation scheme, the DLC and

SLC can achieve same performance results, while BLC

has significant performance gap as previously analyzed in

chapter III. However, the case is slightly different in

simplified implementation scheme. Because of the

approximation, the performance of DLC and SLC is not

exactly the same, while the performance gap of BLC is

smaller than when direct implementation is used. In all

cases, the best performance is given by the DLC scheme,

followed by the SLC and BLC scheme. Nevertheless, the

SLC still has advantage in terms of buffer size [5] and

BLC can also be used for HARQ-IR. Therefore, the best

implementation scheme still depends on how the systems

will be deployed.

5. CONCLUSION

This paper proposed simplified implementation of

MIMO-HARQ with LLR combining method. With simple

approximation and by using Convolutional Turbo Coding

(CTC) as channel coding scheme, the proposed scheme

can achieve better results in term of packet error rate than

direct implementation scheme using Convolutional

Coding (CC). The proposed scheme also has lower

complexity, especially in large modulation size such as

16-QAM and 64-QAM. Better results theoretically can be

achieved with pairing CTC with direct implementation of

the LLR combining. But it is not practical because the

complexity of receiver will be increased significantly, thus

making the proposed scheme becomes better choice for

implementation.

REFERENCES

[1] S. Lin, D. J. Costello. Jr., and M. 1. Miller, "Automaticrepeat-request error-control schemes," IEEE Commun. Mag., vol. 22, Dec. 1984.

[2] D. Chase, "Code combining - a maximum-likelihood decoding approach for combining an arbitrary number of noisy packets," IEEE Trans. Commun., May 1985.

[3] D. Toumpakaris, J. Lee, A. Matache, and H. Lou, "Performance of MIMO HARQ under receiver complexity constraints," IEEE GLOBECOM, 2008.

[4] IEEE Std 802.l6-2004/Corl-2005,Amendment 2, Feb. 2006. [5] E. Jang, 1. Lee, H. Lou, and J. M. Cioffi, "On the combining

schemes for MIMO systems with hybrid ARQ," IEEE Transactions on Wireless Communications, Feb. 2009.

[6] WiMAX Forum™ Mobile System Profile, 2008. [7] A. Paulraj, R. Nabar, and D. Gore, Introduction to Space

Time Wireless Communications, Cambridge Press. 2003. [8] E. N. Onggosanusi, A. G. Dabak, Y. Hui, and G. Jeong,

"Hybrid ARQ transmission and combining for MIMO systems," in Proc. IEEE International Conference on Communications 2003, May 2003.

[9] J. Lee, D. Toumpakaris, E. W. Jang, H. Lou, and 1. M. Cioffi, "Transceiver design for wireless systems via MIMO Hybrid ARQ," IEEE Communications Magazine, vol. 47, pp. 32-40, Jan. 2009.

[10] A. Salbiyono, et. aI., "CTC Decoder for Mobile WiMAX with HARQ Support," Proc. The 5th International Conference TSSA, 2009.

[11] A. Vasquez, E. Antelo, "Implementation of Exponential Function in Floating Point Unit," Journal of VLSI Sig. Processing, Springer, 2003.

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Performance Analysis of Llr Combining Harq for Mimo