Channel Quality Indicator Estimation for OFDMA Systems in the Downlink

Abdel-Majid MOURAD, Loïc BRUNEL, Akihiro OKAZAKI, and Umer SALIM

Mitsubishi Electric - Information Technology Centre Europe B.V. (ITCE) 1, Allée de Beaulieu - CS 10806 - 35708 Rennes - FRANCE

Abstract - This paper investigates the problem of

Channel Quality Indicator (CQI) estimation in the context of OFDMA systems in the downlink. The problem of CQI estimation is addressed for SINR-based CQI forms. In this paper, we present a technique for instantaneous SINR estimation which consists in using the channel estimator already present at the receiver to obtain the useful signal levels and signal regeneration (SR) estimator to get the level of interference plus noise. We show that SR estimator has an error floor caused by channel estimation errors, and then we introduce a compensation factor ρ in order to remove this error floor. The compensation factor ρ is defined as the ratio between the variance of channel estimation errors and the level of interference plus noise at the input of the channel estimator. Thanks to the compensation factor ρ, we achieve a gain of about 1 dB in term of RMSE for CQI estimation over a wide range of CQI values.

Keywords – OFDMA, link adaptation, CQI estimation,

channel estimation, signal regeneration.

I. INTRODUCTION A radio communication system is generally composed of

multiple layers, each responsible of fulfilling some specific functionalities. The first layer, called physical layer or layer 1 (L1), is responsible of transmitting the binary information from a transmitter to a receiver through a radio channel. The L1 algorithms are designed in a manner to ensure robustness against the signal distortions caused by the propagation and interference conditions of the channel. Depending on the channel conditions, different sets of L1 algorithms can be employed resulting in different transmission qualities and spectral efficiencies. The set of L1 algorithms employed is referred to as the L1 mode. The second layer called data link layer or layer 2 (L2) is responsible of allocating the radio resources to the users and of controlling their Quality of Services (QoS). The L2 mechanisms are designed in a manner to optimize the utilization of the radio resources while fulfilling the users’ QoS requirements [1]. The radio resources generally include time slots, frequency sub-carriers, spreading codes, and antennas, and they are allocated by the so-called scheduling mechanism. The QoS requirements are usually given in terms of latency, error rates, and throughput. The control of the users’ QoS requirements is achieved by the retransmission scheme like hybrid automatic repeat request (H-ARQ) and the link adaptation schemes like adaptive modulation and coding and power control [2]. The main purpose of link adaptation is to select the transmission powers

and L1 modes that are best suited to the channel conditions and to the QoS requirements of the active users.

In order to enable for adequate decisions on the selection of L1 modes, link adaptation mechanisms require knowledge of the transmission quality over the channel conditions of the desired user. The transmission quality is generally reflected by the frame error probability conditioned on the particular realization of the channel. However, such information cannot be directly accessible, hence arises the need to define another measure that is accessible and that maps directly to the frame error probability [3][4][5]. This accessible measure is widely called as channel quality indicator (CQI). In the literature, we can find several CQI forms almost all making use of some performance metrics, such as the signal to interference plus noise ratio (SINR). The most commonly used forms follow the concept of effective SINR introduced by [6]. The most famous ones are the geometric mean effective SINR [3], the exponential effective SINR [7] and the mutual information exponential effective SINR [8].

In the state of the art, the CQI forms are established and their performances are evaluated under the assumption of perfect knowledge of the SINR metrics [4][8]. Furthermore, the link adaptation mechanisms are evaluated by assuming first that the CQI form chosen enables accurate prediction of the frame error probability and second that CQI estimation is free from errors. The assumption of error free CQI estimation is not realistic, and when accounting for CQI estimation errors, some conclusions on the CQI performance and on the efficiency of link adaptation may become greatly biased and erroneous. This study aims at figuring out the problem of CQI estimation and pointing out some techniques for solving this problem with good accuracy. It is a first step to answer the essential question of quantifying the impact of CQI estimation errors on the efficiency of link adaptation mechanisms.

This study considers the Orthogonal Frequency Division Multiple Access (OFDMA) system, which is a combination of OFDM multi-carrier modulation with FDMA multiple access. Recently, OFDMA system has been chosen in standardization by 3GPP for the downlink of beyond 3G systems [9].

The rest of this paper is organized as follows. Section II describes the system model. Then, in Section III, we state the problem of CQI estimation and present performance analysis with enhancement. Next, Section IV shows numerical results and Section V draws conclusions and presents perspectives.

II. SYSTEM MODEL We consider the OFDMA system in the downlink, where a

base station (BS) transmits a data frame to its K active user equipments (UEs). The BS allocates different groups of sub-carriers called resource blocks (RB) to the different UE so that there is no intra-cell interference. We assume that each RB carries Nd data symbols and Np pilot symbols. The pilot symbols are reference symbols known to the receiver. We denote by u the index of the desired UE and c(u) the index of its c-th allocated RB. Also, we denote by rc,n

(u) the n-th symbol received by u-th UE within c-th RB. This received symbol has the following form:

( ) ( ) ( ) ( )uncnc

unc

unc wsar

u

,,,, +=

(1)

Where ac,n(u), sc,n

(u), and wc,n(u) denote respectively the

amplitude of the useful signal, the useful signal and the noise plus interference signal received by u-th UE at n-th position within c-th RB.

The instantaneous SINR received by u-th UE at n-th position within c-th RB is given by:

( )( )

( )2,

2,

, ucw

uncu

nc

aS

σ=

(2)

Where σw,c(u)2 denotes the variance of the interference plus

noise {wc,n(u)} received by u-th UE within c-th RB.

For the CQI form, we choose to follow the widespread concept of effective SINR [6], which gives the CQI as a function of the instantaneous SINR corresponding to data positions. This can be written for c-th RB and u-th UE as:

( ) ( ) ( )( )uNc

ucc

uc d

SSfCQI ,1, ,,…=

(3)

The function fc is referred to as the compression function since it compresses the Nd SINR values into one scalar CQI value. Several compression functions have been proposed in the literature with different accuracy and complexity [3][4][7][8]. In this study, we choose the most famous exponential effective SINR proposed by [7]:

( )( )

−−= ∑

=

sN

n

unc

s

uc

SN

CQI1

,exp1logβ

β

(4)

Where β is a parameter that is specific to the L1 mode [7].

III. CQI ESTIMATION The main concern of this study is to define a procedure for

estimating the CQI and to point out the key factors that impact CQI estimation accuracy. For the sake of generality, we aim at defining an estimation procedure that is common to all SINR-based CQI forms. Hence, our problem becomes that of estimating the instantaneous SINR over a given RB. As shown in (2), the instantaneous SINR depends on the useful signal amplitude and on the level of interference plus noise. An estimate of the useful signal amplitude is available thanks to pilot-aided channel estimation [10][11].

A. Interference plus noise level estimation The received symbols contain not only interference plus

noise but also transmitted symbols {sc,n(u)} (see (1)). In the

ideal case of exact knowledge of signal amplitudes {ac,n(u)}

and transmitted symbols {sc,n(u)}, the level of interference plus

noise can then be directly estimated as:

( ) ( ) ( ) ( )∑=

−=sN

n

unc

unc

unc

s

ucw sar

N 1

2,,,

2,

1σ̂

(5)

In (5), the signal of interference plus noise is first regenerated by subtracting from the received symbols the useful signal symbols {ac,n

(u)sc,n(u)}. Assuming sufficiently

large number of symbols Ns available, the law of large numbers (LLN) is then applied to calculate the level of interference plus noise. This estimator is commonly referred to as signal regeneration (SR) estimator [13][14].

In practice, the useful signal amplitudes {ac,n(u)} are not

exactly known but they are estimated through pilot-aided channel estimation. For the transmitted symbols {sc,n

(u)}, they are exactly known if they are pilot symbols and can be estimated through hard or soft demodulation if they are data symbols. For data symbols estimation, even if it is less accurate, hard demodulation is preferred to soft demodulation because of its much lower complexity. Recall that with hard demodulation, the data symbol estimate is given by:

( )( )

( ) ( ) 2,,, ˆminargˆ dard unc

unc

d

unc

u−=

Α∈ (6)

Where A(u) is the alphabet associated with the modulation scheme used by the BS for desired u-th UE. From (6), we note that channel estimation accuracy has also an impact on data estimation accuracy.

If we assume accurate estimation for {ac,n(u)} and {sc,n

(u)}, the interference plus noise level can then be estimated from (5) by replacing the exact values {ac,n

(u)} and {sc,n(u)} by their

estimated values. Thus, we have:

( ) ( ) ( ) ( )∑=

−=sN

n

unc

unc

unc

s

ucw sar

N 1

2,,,

2, ˆˆ1σ̂

(7)

B. Performance analysis and enhancement In order to analyze the performance of SR estimator in (7),

we consider the following model for channel estimation errors [12]:

( ) ( ) ( )unc

unc

unc aa ,,,ˆ ε+=

(8)

Where εc,n(u) is the channel estimation error associated with

the useful signal amplitude ac,n(u) and it is generally assumed to

be independent of ac,n(u) and to follow a zero mean complex

valued white Gaussian process of variance σε,c(u)2.

Assuming first exact knowledge of symbols {sc,n(u)}, by

making use of the channel estimation error model in (8) we can show that the interference plus noise level estimate always overestimates its exact value:

( ) ( ) ( ) ( )

( ) ( )2,

2,

21

2,,,

2,

1ˆ

ucw

ucw

N

n

unc

unc

unc

s

ucw

s

wdN

σσσ

εσ

ε ≥+≈

+−= ∑=

(9)

Now, if we consider hard demodulation errors for data estimation, someone may think at first glance that the performance will become worst than with exact data in (9). But unexpectedly, this may not be true. Indeed, because of minimization criterion in (6), the interference plus noise level estimate with hard demodulated data is always less than with exact data. Thus, the estimate with hard demodulated data is an underestimate of (9), which in turn is an overestimate of the exact value. The estimate with hard demodulated data may therefore get closer to exact value than with exact data.

Assuming the same level of interference plus noise over the pilot symbols used for channel estimation and the data symbols, we can assert that a direct relationship exists between the level of interference plus noise and the channel estimation accuracy. In order to take this into account, we introduce the ratio ρ between the variance of channel estimation errors σε,c

(u)2 and the level of interference plus noise σw,c

(u)2. Using ratio ρ, a more accurate estimate of the level of interference plus noise can then be obtained from (9) as:

( ) ( ) ( ) ( )∑=

−+

=sN

n

unc

unc

unc

s

ucw sar

N 1

2,,,

2, ˆ1

11~

ρσ

(10)

In (10), the ratio ρ compensates for the overestimation caused by channel estimation errors in (9). Thus, with exactly known data symbols, (10) can achieve better performance. However, with hard demodulated data, data estimation errors are no longer beneficial since underestimating (10) always persists but thanks to ρ, (10) does no longer overestimate the exact value.

The factor ρ mainly depends on the performance of channel estimator. It can be derived from theoretical analysis or computer simulations of the channel estimator performance. In the ideal case of perfect channel estimation, ρ is equal to 0.

IV. PERFORMANCE EVALUATION

A. OFDMA context The parameters for downlink OFDMA system are mainly

taken from [9]. Table 1 summarizes the most relevant parameters considered for performance evaluation. As given in Table 1, a sub-frame spans 14 OFDM symbols with 600 sub-carriers available in each OFDM symbol. Pilots for channel estimation are contained in the 1st, 5th, 8th and 12th OFDM symbols with a sub-carrier spacing between adjacent pilots equal to 6. Data symbols are therefore contained within 10 OFDM symbols. A RB has 12 sub-carriers and lasts all along the 14 OFDM symbols. It has Np = 2*4 = 8 pilots for channel estimation and Nd =12*10 = 120 data symbols.

Channel estimation is performed by Wiener filtering in the frequency dimension and then by linear interpolation along the time dimension. A localized transmission is assumed in the

sense that the sub-carriers of a RB are adjacent. The channel model is ITU vehicular A for urban environments and the interference plus noise is assumed to follow an AWGN model.

System bandwidth 10 MHz Sub-carrier spacing 15 KHz Sampling frequency 15.36 MHz FFT size 1024 # of available sub-carriers 600 # of guard interval samples 72 Size of sub-frame 14 OFDM symbols Sub-frame duration 1 ms OFDM symbols containing pilots 1st, 5th, 8th, 12th Spacing between adjacent pilots 6 sub-carriers # of sub-carriers per RB 12 Transmission mode Localized Modulation scheme QPSK Exponential effective SINR β = 2 Channel estimation Wiener filtering # of coefficients for Wiener filter 10 Channel model ITU vehicular A Interference plus noise model AWGN

Table 1: OFDMA system parameters [9].

B. Numerical results Figure 1 depicts the root mean square error (RMSE)

between exact interference plus noise level (dB) and estimated level (dB) versus the signal to interference plus noise ratio (SIR) (dB). Three scenarios are considered: scenario 1 - perfect channel estimation and perfect data estimation, scenario 2 - real channel estimation and perfect data estimation, and scenario 3 - real channel estimation and hard data estimation. We take Ns = 16 symbols for the level of interference plus noise estimation, which is reasonable for scenarios assuming perfect data estimation (e.g. pilots).

In Figure 1, we can first see that in scenario 1, RMSE is not 0 but constant of nearly 1 dB due to the low number of 16 symbols considered when applying LLN for calculating the level of interference plus noise. Obviously, this RMSE decreases when the number of symbols Ns increases.

In scenario 2, we can observe constant RMSE of about 2.7 dB. When the SIR increases, someone may expect that as channel estimation accuracy increases, RMSE should decrease and converge to scenario 1. But unexpectedly, the RMSE keeps slightly constant. This is because the RMSE is function of the relative value of estimated level to exact level of interference plus noise, and this relative value is almost constant because the ratio ρ between the variance of channel estimation errors and exact interference plus noise level is almost constant (see 9). This observation justifies our choice of the constant ratio ρ to compensate the errors caused by channel estimation errors.

In scenario 3, we can see that up to 2.5 dB SIR the RMSE decreases when SIR increases and then it starts increasing and converges to scenario 2. The convergence with scenario 2 for high SIR values can be straightforwardly understood because data estimation errors become negligible. On the other hand, the fact that with data estimation errors we have a lower RMSE than with free data estimation errors is justified by our remark done in section III.B. Indeed, as discussed in III.B, with hard demodulation, we get an underestimate of the estimate obtained in scenario 2, which in turn is an overestimate of the exact value. Thus, sometimes the underestimate of the overestimate gets closer to exact value. This also justifies the existing of an optimal point of 2.5 dB SIR which RMSE is minimum. At this point, underestimation of the overestimation is the closest to the exact value.

Figure 1: RMSE vs. SIR (dB) for scenarios 1, 2 and 3 without compensation (ρ = 0).

Figure 2 shows the RMSE (dB) of interference plus noise level versus SIR (dB) in both scenarios 2 and 3 with compensation factor ρ = 0 (no compensation) and ρ = -2 dB. As we can see from Figure 2, applying (10) with ρ = -2 dB improves the performance of SR estimator in scenario 2 of about 1.3 dB. In scenario 3, we can see that performance are less accurate than in scenario 2 in the region of low SIR level because of data estimation errors. Here, data estimation errors are no longer beneficial because ρ removed the overestimation caused by channel estimation errors when the transmitted symbols are known.

Figure 3 shows the RMSE between exact CQI (dB) and estimated CQI (dB) versus SIR (dB) in scenarios 2 and 3 with compensation factor ρ = 0 (no compensation) and ρ = -2 dB. We also show the reference scenario of real channel estimation and perfect estimation of the interference plus noise level. In the reference scenario, we can observe continuous decrease of RMSE with respect to SIR. This is because channel estimation accuracy improves when SIR increases. Note that for high SIR values, unlike scenario 1 (see Figure 1), the RMSE falls below 1 dB. This is because in

this reference scenario, we assume perfect estimation of the level of interference plus noise.

Figure 2: RMSE vs. SIR (dB) for scenarios 2 and 3 with compensation factor ρ = 0 and ρ = -2 dB.

Figure 3: RMSE vs. SIR (dB) for scenarios 1, 2 and 3 with compensation factor ρ = 0 and ρ = -2 dB.

In scenario 2, we can see that without compensation (ρ = 0), the RMSE stabilizes at about 3 dB in the range medium to high SIR and thus we recognize the error floor caused by channel estimation errors on SR estimator (see scenario 2 in Figure 1). In the range of low SIR, we can see a strange phenomenon with scenario 2 better than the reference scenario which is free from interference plus noise level estimation errors. This can be justified by the correlation that exists between the useful signal level estimation errors and the interference plus noise level estimation errors. This correlation is due to the use of channel estimates in the estimation of both. Thus, because of this important correlation in the range of low SIR where the channel estimation errors are too high, the interference plus noise estimations errors become beneficial to CQI estimation, which is observed in Figure 3.

In scenario 3 without compensation (ρ = 0), we can see that it converges to scenario 2 (ρ = 0) in the range of high SIR where data estimation errors are less frequent. In the range of

-5 0 5 10 15 200

0.5

1

1.5

2

2.5

3

3.5

4

SIR (dB)

RM

SE

(dB

)

Scenario 1

Scenario 2Scenario 3

-5 0 5 10 15 200

0.5

1

1.5

2

2.5

3

3.5

4

SIR (dB)

RM

SE

(dB

)

Scenario 1

Scenario 2 - ρ = 0

Scenario 3 - ρ = 0

Scenario 2 - ρ = -2 dB

Scenario 3 - ρ = -2 dB

-5 0 5 10 15 200

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

SIR (dB)

RM

SE

(dB

)

Reference scenario

Scenario 2 - ρ = 0

Scenario 3 - ρ = 0

Scenario 2 - ρ = -2 dB

Scenario 3 - ρ = -2 dB

low SIR, the estimation errors of interference plus noise level become beneficial to CQI estimation as explained previously, and therefore, scenario 2 which has more interference plus noise level estimation errors than scenario 3 performs better in term of RMSE for CQI estimation.

With compensation (ρ = -2 dB), we can see that in scenario 2, we get much closer to the reference scenario than without compensation (ρ = 0). We also recover the gain of about 1 dB (see scenario 2 in Figure 2) achieved in term of RMSE for interference plus noise level estimation.

Figure 4: RMSE vs. CQI (dB) for scenarios 1, 2 and 3 with compensation factor ρ = 0 and ρ = -2 dB.

Figure 4 shows the RMSE of CQI (dB) versus the exact CQI (dB) in the scenarios 2 and 3 without compensation (ρ = 0) and with compensation (ρ = -2 dB). We also show the reference scenario. Here, each CQI value comes from the combination of different levels of interference plus noise and useful signal. For instance, a low CQI value comes not only from low level of interference plus noise but also from low level of useful signal. In Figure 4, we have the same behavior of RMSE curves than in Figure 3 but the gain achieved in term of RMSE for interference plus noise level estimation thanks to compensation factor affects a wide range of CQI values (gain of about 1 dB in scenario 2 for CQI > 2.5 dB). This is because high level of SIR where channel estimation accuracy is good and where the gain achieved by compensation is high not only affects high CQI values but also lower CQI values.

V. CONCLUSIONS This study considered the problem of SINR-based CQI

estimation for OFDMA systems in the downlink. The SINR estimation is done by using the channel estimator to obtain the useful signal level and the signal regeneration (SR) estimator to obtain the level of interference plus noise. SR estimator makes use of the estimates of transmitted symbols and their associated channel estimates to regenerate the interference plus noise signal.

We showed that SR estimator overestimates the exact level of interference plus noise and has an error floor. To compensate for the error floor caused by channel estimation

errors, we introduced the compensation factor ρ defined as the ratio between the variance of channel estimation errors and the level of interference plus noise at the input of the channel estimator. By using the compensation factor ρ, SR estimator was shown to achieve better performance in term of RMSE for interference plus noise level. The gain achieved by the compensation factor ρ is found to be about 1 dB in term of RMSE of for CQI estimation and this for a wide range of CQI values (CQI > 2.5 dB).

Future work will be devoted to quantify the impact of CQI estimation errors on the efficiency of link adaptation.

VI. REFERENCES [1] J. Zander and S. Kim. Radio Resource Management for

Wireless Networks. Artech House Publishers, 2001. [2] M. Assaad and D. Zeghlache. TCP Performance over

UMTS-HSDPA Systems. Auerbach Publications, 2006. [3] H. Holma. A Study of UMTS Terrestrial Radio Access

Performance. Ph.D. thesis, Helsinki University of Technology, Oct. 2003.

[4] A.-M. Mourad. On the System Level Performance of MC-CDMA Systems in the Downlink. Ph.D. thesis, ENST Bretagne, Jan. 2006.

[5] M. Lampe et al. Misunderstandings about Link Adaptation for Frequency Selective Fading Channels. Proceedings of IEEE PIMRC, Sep. 2002.

[6] S. Nanda and K. M. Rege, Frame Error Rates for Convolutional Codes on Fading Channels and Concept of Effective Eb/N0. IEEE Transactions on Vehicular Technology, Vol. 47, No. 4, Nov. 1998.

[7] 3rd Generation Partnership Project (3GPP). System Level Evaluation of OFDM – Further Considerations. TSG-RAN, WG1 #35, R1-031303, Nov. 2003.

[8] K. Brueninghaus et al. Link Performance Models for System Level Simulations of Broadband Radio Access Systems. Proceedings of IEEE PIMRC, Sep. 2005.

[9] 3rd Generation Partnership Project (3GPP). Physical Layer Aspects for Evolved UTRA. TSG-RAN, WG1, TR 25.814 V 1.0.3, Release 7, May 2006.

[10] M. Ergen et al. Channel estimation techniques based on pilot arrangement in OFDM Systems. IEEE Transactions on Broadcasting, Vol. 48, No. 3, Sep. 2002.

[11] P. Hoeher et al. Two-Dimensional Pilot-Symbol-Aided Channel estimation by Wiener Filtering. Proceedings of IEEE ICASSP, Apr. 1997.

[12] T. Sälzer et al. Influence of System Load on Channel Estimation in MC-CDMA Mobile Radio Communication Systems. Proceedings of IEEE VTC, May 2001.

[13] L. Husson et al. Estimation of Noise and Interference Power for Transmissions over Rayleigh Fading Channels. Proceedings of IEEE VTC, May 2001.

[14] H. Xu et al. A Novel SNR Estimation for OFDM. Proceedings of IEEE VTC, May 2005.

[15] S. M. Kay. Fundamentals of Statistical Signal Processing: Estimation Theory. Prentice Hall, 1993.

-5 0 5 10 150

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

CQI (dB)

RM

SE

(dB

)

Reference scenario

Scenario 2 - ρ = 0

Scenario 3 - ρ = 0

Scenario 2 - ρ = -2 dB

Scenario 3 - ρ = -2 dB