On Pilot Design for Interference Limited OFDM Systems K. Prasanth, M.S. Padmanabhan, R. Vinod, Kiran Kuchi, J Klutto Milleth Centre of Excellence in Wireless Technology, India [email protected], [email protected], (padmanabhan,kkuchi,klutto)@cewit.org.in

Bhaskar Ramamurthi Indian Institute of Technology Madras [email protected]

Abstract—Modern cellular networks are inherently interference limited, and therefore, pilot design is extremely important to the overall system performance. The pilots have to be carefully arranged and modulated to track the fading channel as well as to suppress the interference efficiently. 4G wireless systems based on OFDMA use pilot design strategies that can be classified as ’Data on Pilot’ and ’Pilot on Pilot’. In this paper, a ’Null on Pilot’ scheme that uses null tones and pilot tones to avoid most of the interference on the pilots is considered. Various design aspects of these three pilot schemes are discussed in detail. The channel estimation, interference covariance estimation, link performance with different interference profiles, and system throughput are analyzed and compared with these pilot schemes. It is shown that the popular approach of ’Data on Pilot’ scheme is inferior to the other two approaches in exploiting the post-processing SNR gain of MMSE interference suppression receivers. The performances of ’Null on Pilot’ and ’Pilot on Pilot’ are quite similar.

I. INTRODUCTION Reuse-1 cellular systems use the same frequency band in all the cells and sectors. When systems such as IEEE 802.16m [1] and 3GPP LTE-A [2] are deployed using reuse-1, they will be heavily limited by co-channel interference (CCI). This predominantly limits cell- edge throughput, and hence reduces the overall system throughput. These systems also use link adaptation as a mechanism to improve the system throughput. Pilot design is of foremost importance in constructing the receiver as well as obtaining the channel quality indicator (CQI) for link adaptation. The use of MMSE interference suppression receivers can significantly improve the performance of such systems. The two commonly used pilot design strategies in MIMOOFDM systems are ’wideband common pilots’ and ’narrowband dedicated pilots’. In a system with common pilots that are not precoded with the user-specifc precoding matrix, any user can use all the pilots spread over the entire band to estimate the raw MIMO channel. This also implies that in a precoded system with common pilots, the user must know the precoding matrix to reconstruct the effective precoded channel as seen by the user data. However in a dedicated pilot system, the This work was funded in part by the COMET K2 Center Austrian Center of Competence in Mechatronics (ACCM). The COMET Program is funded by the Austrian Federal government, the Federal State of Upper Austria and the Scientific Partners of ACCM.

pilots are precoded with the user-specific precoding matrix and effective channel can be estimated from these pilots without the knowledge of the user-specific precoding matrix. Dedicated pilots, though it precludes wideband channel estimation, is a flexible way of supporting several MIMO modes. 4G wireless systems such as 802.16m and LTE-A are supporting the dedicated pilot design. Based on the interference seen on the received pilots, the dedicated pilot design strategies can be classified into • Pilot-on-Pilot (PoP): pilots collide with pilot tones of interferers • Data-on-Pilot (DoP): pilots collide with data tones of interferers • Null-on-Pilot (NoP): pilots collide with null tones of interferers In this paper, the above mentioned pilot design strategies are investigated in the context of MMSE interference suppression receiver for a single stream transmission system. II. S YSTEM D ESCRIPTION A reuse-1 OFDM based cellular system with Nt transmit and Nr receive antennas are considered. The transmission will be a single stream in which the same symbol is transmitted in all the Nt transmit antennas. The Nr dimensional received vector at the receiver on each resource element is modelled as y = hx +

N X

g i xi + n

(1)

i=1

where a resource element is a single subcarrier in an OFDM symbol in which a symbol is transmitted, h is desired channel vector, gi is the channel vector of the ith co-channel interferer among the N dominant interferers. The rest of the interferers, and the thermal noise are modelled as AWGN vector n with covariance matix Rnn = N0 I. All the vectors are of dimension Nr . The MMSE interference suppression receiver for this system is given by x ˆmmse = wmmse y (2) wmmse = hH (hhH + Rin )−1

(3)

where Rin =

N X

gi gi H + N0 I

(4)

i=1

and the post-processing SNR of the MMSE receiver is given by γ = hH Rin −1 h (5) For link adaptation, the receiver estimates a CQI which is further used to select the modulation and coding scheme (MCS) that provides a target block error rate. The best link adaptation mechanism should use the post-processing SNR as the CQI, since it captures the interference cancellation as well as the diversity combining capabilities of the receive filter. The performance of the MMSE receiver and link adaptation is highly dependent on the quality of the estimated channel and interference covariance. Normally, the time-frequency resource allocated to the user will be divided into several sub units, which we call physical resource unit (PRU) and each PRU may be precoded using a different precoding matrix. Hence, the channel estimation and interference covariance estimation are usually performed over the PRU. The 2D-MMSE algorithm [5] is one of the most commonly used algorithm for localized channel estimation in 4G systems. A single averaged interference covariance matrix is used in a PRU. The estimation of the interference covariance matrix is explained in the next section. The post-processing SNR values over a set of PRUs can be mapped to an optimum MCS using techniques like EESM, RBIR, MMIB [4] or averaging the SNRs over the PRUs. III. P ILOT D ESIGN S TRATEGIES A. Pilot-on-Pilot OFDMA based cellular systems transmit pilots in the same set of physical resource elements, in all the cells and sectors. A ’cell’ is defined as the coverage area of a Base station(BS), and a cell is usually divided in to 3 sectors. The interference in the received pilots is from the pilot tones of the adjacent sectors and cells. An example of this in a 18x6 PRU is depicted in Fig 1. All the cells and sectors transmit pilot tones in these locations (marked as ’P ’) with different modulation sequences. Channel estimation algorithms use the information from the pilots to interpolate the channel coefficients in a PRU. As the channel selectivity is low within a PRU, the set of coefficients used in the channel estimator to combine the information from the pilots to form the estimate at a resource element remain very close. So, if an interfering signal uses a pilot modulation sequence which has very low cross-correlation with that of the desired signal, the effect of that interfering signal is removed in the channel estimation. The interference covariance matrix for a PRU is estimated as follows: X ˆ j xj )(yj − h ˆ j xj )H ˆ in = 1 (yj − h (6) R B|P | jP

where P is the set of all pilot tones in a PRU as illustrated ˆ is the channel estimate. B is the pilot power in Fig 1 and h

Fig. 1.

Pilot Pattern of a sector in PoP and DoP

boosting relative to data and |P | is the cardinality of the set P . The estimation algorithm assumes that the pilot sequences are constant amplitude and this amplitude is known to all receivers, which is quite common. It is important to note that since only a single interference covariance value is estimated for the entire PRU, the performance will be upper bounded by the covariance truncation error when compared with per tone interference covariance. However, a single interference covariance estimate is sufficient to compare different pilot design techniques of interest as the relative performances will be similar to using a per tone covariance estimator. The quality of interference covariance estimates are also dependent on the cross-correlation between these pilot modulation sequences. The low cross correlation property will reduce the effect of cross-terms in the interference covariance estimate. However, highly frequency and time selective channels will destroy the pilot modulation sequence (code domain) orthogonality. Moreover, the number of sequences with lowcross correlation is limited by the number of dedicated pilot tones, and this is not very high. B. Data-on-Pilot 4G wireless systems such as IEEE 802.16m and 3GPP LTE transmit pilots in different sets of physical resource elements in different sectors in a cell. This is also called ’interlaced pilots’. This causes the received pilot symbols collide with the data symbols transmitted by the interferers. Moreover, the received data symbols are corrupted by the pilot symbols transmitted by the interferers. The pilot pattern of a particular sector could be derived from Fig 1 using time domain cyclic shifts of pilot and data positions. Here, the channel estimation is noisy because the cross correlation between the pilot sequence and random interfering data is unpredictable. Boosting the power of pilots relative to data is a method used to improve channel estimation. But the data decoding is severely affected by the boosted pilot interference especially at high code rates. In DoP, the interference covariance is estimated as: X ˆ j xj )(yj − h ˆ j xj )H ˆ in = 1 (yj − h (7) R |P | jP

This approach assumes that the interference samples contain only data tones and hence there is no division by B. The poor channel estimation quality will adversely affect the

Fig. 2.

NoP patterns for the three sectors in a cell

interference covariance estimates. Even though, pilot boosting improves the channel estimation, it degrades the covariance estimation. This is because the actual interference samples contains not only data tones of neighbouring sectors but also pilot tones of second tier interferers. For any boost factor other than 0dB, each one of the second tier pilot interferers introduces a scaling mismatch of B in its covairance contribution. The higher the boosting, the higher the number of significant second tier pilot interference and the higher the mismatch in each of their individual contributions. These effects are clearly illustrated in Section IV.

IV. RESULTS The different pilot design strategies are compared using the performance metrics such as normalized mean square error (NMSE) of channel estimates and interference covariance estimates, block error rate (BLER) and system throughput. The NMSE of the channel estimates is defined as ˆ =E N M SE(h)

C. Null-on-Pilot In this strategy, the pilot patterns are planned among the 3 different sectors of a cell, such that, in the pilot tone locations of a given sector, all other sectors in that cell do not transmit pilot or data. This is equivalent to a reuse factor R = 3 in the pilots. An example pilot pattern as defined in the IEEE 802.16m standard [1] is shown in Fig 2. The same set of the 3 patterns are reused in every cells so that there is no CCI in the received pilots from the same cell, and hence boosts the signal to interference ratio (SIR) at pilot locations significantly. This approach can be extended for higher reuse factor also. The low cross correlation between the set of sequences used to modulate the pilots across the different transmitters and the distribution of pilots (and nulls) in the time-frequency domain are of importance to obtain good estimates of the channel parameters. For the same ’pilot+null’ density (overhead) , the higher SIR comes at the expense of reduced channel tracking capability due to the necessity of null tones in a PRU. In NoP, the interference covariance is estimated as: X ˆ j xj )(yj − h ˆ j xj )H ˆ in = 1 (yj − h R B|P | jP

+

leads to a highly accurate interference covariance estimate. So, this approach is highly suitable for MMSE interference suppression receivers. Both PoP and NoP rely on orthogonality to reject interference from the first tier. PoP uses the orthogonality in code domain whereas NoP uses orthogonality in time/frequency domain. To reject interference from the second tier, both PoP and NoP uses code domain orthogonality. When these three pilot schemes with same ’pilot+null’ density are compared, the receiver complexity in NoP is the minimum because the number of pilots is 1/3 times that of PoP and DoP. Moreover, NoP could also enable to estimate the interference of the two dominant interfering channels, which will be useful in certain advanced receivers, and also during handoff when the interfering channel may become the desired channel.

1 B

R−1 X k=1

1 X yj yj H |Qk |

(8)

jQk

where Qk is the set of null tones in the k th null tone set as illustrated in Fig 2. Another important advantage of this approach is that the interference samples of the dominant CCIs in the data can be obtained from the pilots and null tone locations. This

# "N r ˆ 2 X |h(i) − h(i)| i=1

(9)

|h(i)|2

The NMSE of covariance estimates is defined as   Nr X Nr 2 X ˆ |R (i, j) − R (i, j)| in in ˆ in ) = E   N M SE(R 2 |R (i, j)| in i=1 j=1 (10) For the purpose of simulations, a interference profile vector Cp is defined with the ith element being the SIR with respect to the ith interferer. Cp (i) = S/Ii (dB); i = 1, 2, ..., N

(11)

Cp models the strong interferers in the system. For system simulations, N equals 8 as required by 802.16m evaluation methodology [3]. The rest of the interference and thermal noise is modelled as AWGN with variance N0 . All the simulations uses BPSK modulated pilots. The re-use factor used in NoP is 3 and pilots are boosted 4.7dB (10log(3)) higher than that of PoP so that both have same transmit power per PRU. The system level performance metric is the normalized spectral efficiency CDF, sector and cell-edge spectral efficency[3]. Sections A and B discuss the behavior of the various pilot designs with respect to channel estimation and covariance estimation, respectively. Section C discusses the performance of the pilot designs in a cellular system with scheduling, HARQ and link adaptation. All simulations uses modified PED-B for small scale fading.

Fig. 3.

Fig. 4.

Channel estimation performance for Cp = [0 3]

Channel estimation performance for Cp = [0 3 6]

A. Channel Estimation The NMSE of channel estimates at two different interference profiles Cp = [0 3] and Cp = [0 3 6] are provided in Figs 3 and 4. The pilot power boosting is denoted as B, and the variables r1 , r2 , and r3 denote the cross-correlation between the pilot sequences of desired signal and 1st , 2nd and 3rd interferers, respectively. The channel estimation performance is comparable for NoP and PoP with low cross correlation sequences since most of the interference power on pilots is rejected by the orthogonality either in time-frequency or code domain. For all the other pilot designs considered, the estimation performance is inferior, and ˆ of NoP the NMSE curve exhibits flooring. The NMSE(h) is unaffected by the number of interferers, which is evident from Fig 3. The pilot-pilot collisions from the second tier interferers in NoP should be protected by the low crosscorrelation properties of the colliding pilot sequences, as can

Fig. 5.

Fig. 6.

Interference Covariance estimation performance for Cp = [0 3]

Interference Covariance estimation performance for Cp = [0 3 6]

be inferred from Fig 4. In NoP, the reduction in the number of non-zero pilots deteriorates the channel tracking capability. Still, for a PED-B channel, which is quite frequency selective, NoP’s performance is very close to that of PoP with nearly orthogonal sequences. In DoP, since we cannot control the cross correlations, the performance is worse and more closer to PoP with high pilot sequence correlation. Though pilot boosting helps to improve the performance, it only results in a shift in the curve but not the slope. B. Interference Covariance Estimation The interference covariance estimation performance is studied under the same three interference profiles, and the results are provided in Fig 5 and 6. NoP and PoP with low cross correlation sequences give superior interference covariance estimation too, partly because of the better channel estimation. The effect of cross-terms in the covariance estimate is reduced by the low cross-correlation sequence in PoP. The NoP design

avoids cross-terms between strong interferers and hence gives good covariance estimates. Fig 6 shows the mismatch in covariance estimate in DoP, which is worsened by the power boosting of the pilots, as described in section III B. All the ˆ in ) curves floor at high SNRs, because there is only NMSE(R ˆ one Rin per PRU. It can be seen in PoP that lower the cross-correlation between the pilot modulation sequences, better is the performance. In PoP and DoP each received pilot get collisions from all N interferers, whereas in a re-use R NoP, the collisions on pilots are from N/R interferers only. For example in a cellular system modelled using 8 strong interferers, with re-use 3 NoP, the first null tone set Q1 contains collisions from the 1st, 4th and 7th strongest interferers, the second null tone set Q2 contains collisions from the 2nd, 5th and 8th strongest interferers and the pilot tone set P gets collisions from the 3rd and 6th strongest interferers. This means that for Q1 , covariance estimation error is dependent on the cross-correlation between pilots of 1st, 4th and 7th strongest interferers. In most practical scenarios, 1st strongest interferer will be much stronger than the 4th and 7th. Due to these reasons, NoP gives a better covariance estimate than PoP with low cross-correlation in the interference limited regime, which is clear from Figs 5 and 6 and as most cellular systems are interference limited, NoP is well suited for them. C. System Level Simulations The pilot designs are evaluated in a cellular system using system simulations. The simulation parameters are listed in Table I. TABLE I S YSTEM SIMULATION PARAMETERS Simulation setup Frame structure Bandwidth, DL:UL HARQ type Channel model Number of MCS levels Codec Receiver type Channel Estimation CQI feedback, delay Scheduler 1st transmission Error rate Pilot Boosting ’Pilot + Null’ , control overheads

57 sectors, 10 users per sector IEEE 802.16m 10 MHz, 5:3 Chase combining (CC-HARQ) 1Tx-2Rx, Urban micro 16 CTC MMSE 2D-MMSE Post processing SNR based, 1 ms Proportionally Fair, Tc=50ms 10% 3 dB (PoP,DoP),7.7 dB (NoP) 16.6 %, 13 %

The normalized spectral efficiency CDF of a 1Tx-2Rx antenna system is given in Fig 7. The ’ideal’ simulation uses ideal channel and interference covariance knowledge at the receiver. The error in the channel and interference covariance estimates affects the receiver performance as well as the CQI estimation (post-processing SNR based). So, an adaptable/tunable offset has to be subtracted from the estimated CQI in order to keep the first transmission error rate equal to 10% as mentioned in Table I. This means, the poorer the estimates, the lower the MCS which is selected, and thus a lower throughput. The performance of PoP and NoP are almost identical. DoP is the least performing, as expected. The key performance metrics are summarized in Table II. 802.16m uses a DoP design with 6.6% pilot overhead. Since a DoP with 16.6% overhead itself is inferior to PoP and NoP,

Fig. 7.

The Spectral Efficiency comparison

TABLE II N ORMALIZED S PECTRAL E FFICIENCY Type Ideal PoP NoP DoP

Average Sector spectral efficiency in bps/Hz/sector 2.25 1.83 1.85 1.42

Cell-Edge spectral efficiency in bps/Hz 0.066 0.058 0.052 0.032

the performance of 6.6% pilot overhead design of 802.16m will be much worse. One implementation friendly way to improve the performance of this 6.6% overhead DoP design is to convert it to a NoP with 16.6% design via data nulling. V. CONCLUSION In an interference limited OFDM based cellular network, when the demodulation pilots are dedicated to a user, the DoP scheme which is widely used, is not a good strategy. The NoP and PoP schemes in which the effect of interference on the pilots can be reduced based on time-frequency or code domain orthogonality give superior performance. The NoP scheme has an added advantage of reduced receiver complexity because the number of pilots are reduced, while giving the same performance as PoP. Also, NoP avoids the need to define new pilot sequences, and therefore is an easier way to upgrade existing standards with minimum impact on the implementations. R EFERENCES [1] IEEE, “DRAFT Amendment to IEEE Standard for Local and metropolitan area networks - Part 16: Air Interface for Broadband Wireless Access Systems Advance Air Interface,” Available at http://ieee802.org/16/published.html. [2] 3GPP, “3GPP TS 36.211 V9.1.0, LTE standard document,” Available at http://www.3gpp.org/ftp/Specs/html-info/ 36213.htm. [3] IEEE, “IEEE 802.16m Evaluation Methodology Document (EMD),” Available at http://ieee802.org/16/tgm, January 2009. [4] Krishna Sayana, Jeff Zhuang, Ken Stewart, “Link Performance Abstraction based on Mean Mutual Information per Bit (MMIB) of the LLR Channel,” IEEE C802.16m-07/097, May 2007. [5] P.Hoeher, S.Kaiser, and P.Robertson, “Two-Dimensional Pilot- symbolaided channel estimation by Wiener filtering,” Acoustics, Speech and Signal processing, ICASSP-97, 1997.