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W1 Introduction
ith the rapid development of 5G wireless networks， heterogeneous links， which support the co?existence of multilayer cells， multiple standards， and multiple applications， are playing an important role in increasing capacity and coverage and satisfying huge traffic demand [1]. This paper discusses technical issues， in particular， interference cancellation， in a heterogeneous network with macro and pico cell. In the topology of a network with macro and pico cells， the high?power 1～40 W macro cell provides basic coverage and the low power 250 mW pico cell is the complementary cell. The pico cell extends network coverage and offloads data traffic of the macro?cell. This reduces cost and increases frequency efficiency. However， the user equipment （UE） served by the pico cell also receives RF signals from neighboring high?power macro cells. This interference is even more severe when users in the pico cell stay within the coverage area of macro cells with range?extension enabled [2].
Enhanced inter?cell interference coordination （eICIC） addresses this issue [2]. eICIC involves two techniques. First， the signal strength is biased to the pico cell， which reduces the interference power. Second， the macro cell remains silent for a certain period， called Almost?Blank Subframe （ABS） [2]. In the ABS， the physical downlink shared channel （PDSCH） is emptied. Therefore， UE does not receive PDSCH during the ABS， and interference can be alleviated. However， users may still receive the cell?specific reference signal （CRS）， paging channel （PCH）， physical broadcast channel （PBCH）， and synchronization channels （PSS/SSS）， all of which degrade performance. Further eICIC （FeICIC） has been proposed to eliminate CRS interference.
Some research has been done on CRS interference cancellation （IC）. The authors of [3] and [4] investigate direct IC and log?likelihood ratio （LLR） puncturing methods. The simulation results show that direct IC results in better performance. The authors of [5] propose a receiver algorithm that combines IC with a direct?decision channel estimation （CE） algorithm for colliding CRS. The authors of [6] propose a space?alternating generalized expectation?maximization （SAGE） with a maximum a?posteriori （MAP） method for estimating the interfering channel. This method involves reduced computation complexity compared with the linear minimum mean square error （LMMSE） method. However， timing error and frequency offsets can severely degrade performance. In this paper， we theoretically analyze and run simulations on the CRS interference?cancellation algorithm in a non?colliding scenario where channel statistics are taken into consideration. First， we analyze and model the interference signal and then discuss the interference?cancellation algorithm based on this model. The algorithm makes use of the primary synchronization signal （PSS） and secondary synchronization signal （SSS） to obtain the timing offset （TO） and carrier frequency offset （CFO）. Then， the channel response is estimated using channel statistics. Then， the interference signal is reconstructed taking into account the channel effect， TO and CFO. Interference is alleviated by subtracting the interference signal from the received signal.
The rest of this paper is organized as follows. In section 2， the interference is analyzed and modeled. In section 3， we discuss IC algorithms. In section 4， results of the computer simulation are presented. In section 5， we sum up.
2 Interference Analysis and Model
Fig. 1 shows typical non?colliding inter?cell interference between macro and pico cells. The wireless data service is delivered to the subscriber via pico cell， and the downlink signal from the macro cell interferes with the subscriber at the edge of the pico cell. To alleviate the inter?cell interference， the ABS is transmitted by the macro cell. During the ABS， only certain control signals， such as CRS ， are transmitted.
However， the CRS still causes interference for the subscriber. Fig. 2 shows the received signal of one resource block （RB） with one interference cell. The CRS from a neighboring macro cell overlaps the resource elements （REs） from a serving cell （SC）. The SC RE can be divided into data RE and CRS RE. Because of the TO and CFO between the interfering cell and subscriber， the received interfering signal suffers TO and CFO （Fig. 2）.
Four modulation schemes are being considered for 5G： generalized frequency?division multiplexing （GFDM）， filter bank multicarrier （FBMC）， universal filtered multicarrier （UFMC）， and biorthogonal frequency?division multiplexing （BFDM）. However， these four schemes are all generalizations of OFDM， so we address the original OFDM modulation in the following way （for simplicity’s sake）.
In the downlink side of OFDM modulation， the frequency?domain signal of the [ith] symbol is transferred to time domain signal [xi（n）] via N?point Inverse Fast Fourier Transform （IFFT）： [xi（n）=1Nk=0N-1Xi，kej2πnk/N=1Nk=0N-1di，k+pi，kej2πnk/N] （1）
where [di，k] and [pi，k] are the data and pilot， respectively.
Then the signal is transmitted over a multipath propagation channel that takes into account additive white Gaussian noise （AWGN）. At the receiver side， the received signal is given by
[yi（n）=l=0L-1hlxin-τl+ω（n）] （2）
where [hl] and [τl] are the gain and delay of the lth path， respectively； and ω（n） is the AWGN. Because of the TO and CFO， the corrupted receiver signal in the case of inter?cell interference is
[yi（n）=y（0）i（n）+y（1）i（n）+ω（n）=1Nk=0N-1H（0）i，kX（0）i，kej2πnk/N+ 1Nk=0N-1H（1）i，kX（1）i，kej2π（n-d）（k+fΔ）/N+ω（n）]
where [y（0）i] and [y（1）i] are the desired signal and interference signal， respectively； [H（0）i，k] and [H（1）i，k] are the frequency response of the serving channel and interfering channel， respectively； and [d] and [fΔ] are the relative timing and frequency offset， respectively， between the macro and pico cell. After applying the N?point Fast Fourier Transform （FFT）， the OFDM symbol is [7]：
[Yi，k=Y（0）i，k+Y（1）i，k=H（0）i，kX（0）i，k+n=-N/1N2ej2πndNH（1）i，nX（1）i，nΦn+Wi，k] （4）
where [H（0）i，k] and [H（1）i，k] are the channel coefficients of the serving and interfering cell at kth subcarrier， respectively； and [Φn] is the inter?carrier interference （ICI）. During the ABS， only certain control signals are transmitted， and the CRS from the macro cell overlaps the data REs （Fig. 2）. At the data REs， the signal model of the serving cell with interference is
[Yi，k=H（0）i，kd（0）i，k+n=-N/2N2ej2πndNH（1）i，nd（1）i，nΦn+Wi，k] （5）
According to （5）， the relative timing offset [d] between interfering and serving cells causes phase shift [ej2πndN] on the kth subcarrier. The terms [Φn] in （5） arises from the CFO term[fΔ]， which results in intercarrier interference （ICI）. Therefore， the CFO and TO need to be compensated. In addition， this model shows the case of single?input single?output （SISO） antenna only. The case of multiple?input multiple?output （MIMO） antenna can be easily derived from （5）. However， the number of REs increases because the number of interference CRSs increases with number of antenna ports， which results in more severe interference [8]. These problems will be addressed in section 3.
3 IC Algorithm
The proposed inter?cell IC algorithm is shown in Fig. 3. This algorithm includes estimation of CFO and TO， estimation of the interfering channel， modeling of the interfering cell， and reconstruction and reduction of the interfering signal. With CFO and TO estimation， the relative frequency offset and timing offset between the interfering cell and serving cell is estimated using the PSS or SSS generated by modeling the interfering cell. Next， the interfering channel is estimated according to the compensated signal. The interfering signal is then reconstructed according to the previous estimation and subtracted from the received signal. 3.1 CFO and TO Estimation
The objective of this module is to retrieve OFDM symbol timing and estimate the CFO of the interfering cell. Many timing? and frequency?synchronization algorithms have been developed. Most of these exploit the periodic nature of the time?domain signal by using cyclic prefix （CP） [9]-[11] or pilot data [12]-[13]. However， there are no data REs in an ABS， which severely reduces the power of the CP. The low SNR of the CP makes both timing and frequency synchronization difficult. Apart from the CP and pilot， there are still the PSS and SSS， which are dedicated to timing and frequency synchronization in the downlink. The PSS and SSS are located at the last and second?last symbol in the time slot 0 and 10. The PSS [pss（n）] and SSS [sss（n）] are given by
[pss（n）=ejπμn（n+1）63 n=0，1，...，30ejπμ（n+1）（n+2）63 n=31，32，...，61]
and
[sss（2n）=s（m0）0（n）c0（n） time slot 0s（m1）1（n）c0（n） time slot 10]
[sss（2n+1）=s（m1）1（n）c1（n）z1（m0）（n） time slot 0s（m0）0（n）c1（n）z1（m1）（n） time slot 10]
where [μ]is 25， 29 or 34 and corresponds to the physical layer identity [N（2）ID]； and [m0] and [m1] are derived from the physical layer cell identity group [N（1）ID]； [s（m1）0]， [s（m0）1]， [c0（n）] ， [c1（n）]， [z1（m0）] and [z1（m1）] are defined in [8]. The timing and frequency offset can be estimated using the cross?correlation of PSS/SSS [14]：
[d，fΔ=arg maxd，fΔC（d，fΔ）] （6）
where
[Cd，fΔ=m=1N2s?i（n）r（n+m）e-2πfΔnN] （7）
The generation of PSS/SSS is based on the assumption of an ideal cell search. The cell?search algorithm in the case of inter?cell interference is beyond the scope of this paper. After the timing and frequency synchronization of the interfering signal， the interfering?channel response can be estimated.
3.2 InterferingChannel Estimation
Before interference cancellation， it is essential to estimate the interfering?channel response. The channel estimation can be based on least squares （LS） or minimum mean?square error （MMSE） [15]， [16]. The MMSE algorithm gives 10-15 dB gain in signal?to?noise ratio （SNR） for the same mean?square error of CE over LS estimation [15]. However， the MMSE is more complex than the LS algorithm. After timing and frequency offset compensation， （5） can be rewritten as
[Yi，k=H（0）i，kd（0）i，k+H（1）i，kd（1）i，k+Wi，k] （9）
From （10）， the interfering CRS sequence [p（1）] can be expressed as
[p（1）=12（1-2c（2n））+j12（1-2c（2n+1））] （10）
where [c（n）] is generated by Gold Sequence with a length of 31， the state of which is initialized according to the cell ID， slot number， and antenna port. Assuming that the user conducts ideal cell research， the interfering CRS [p（1）i，k] can be generated locally. Applying LS CE， the interfering channel can be estimated with [H（1）i，k=Yi，k/p（1）i，k=H（1）i，k+H（0）i，kd（0）i，k/p（1）i，k+Wi，k/p（1）i，k] （11）
According to （11）， the data RE of serving cell [H（0）i，kd（0）i，k/p（1）i，k] becomes interference with relatively high power. Thus， the estimation in （11） is inaccurate. Numerical studies in [17] show that the distribution of the interference signal is close to Gaussian for a larger RB and non?Gaussian for a smaller. However， the mean of the distribution converges to 0. Therefore， the expectation of （11） can be derived：
[E{H（1）i，k}=EYi，kp（1）i，k=EH（1）i，k+H（0）i，kd（0）i，k/p（1）i，k+Wi，k/p（1）i，k =EH（1）i，k+EH（0）i，kd（0）i，k/p（1）i，k+EWi，kp（1）i，k ≈EH（1）i，k]
Equation （12） provides a good estimation of mean value of the interfering channel. This value can be estimated by using a moving?average window in the time dimension （Fig. 4）. If the moving?average window of length M is within the coherence time of the channel， [H（1）i，k] could be approximated by[E{H（1）i，k}]. The procedure of the interfering?channel estimation is show in Fig. 4.
The IC algorithm should set the correct antenna number and bandwidth of the interfering cell for interfering?cell CE and interference modelling block. Usually this information is not available at the UE unless the UE decides to hand over to that cell. Therefore， the antenna number and bandwidth of the interfering cell need to be estimated at the UE.
A straightforward method for interfering?cell CE is to enable the IC control block to always set the maximum possible bandwidth and number of antennas， i.e.， 20 MHz and 4 antennas， so that the interfering?cell CE and interference modelling block estimates the channel accordingly. If the actual bandwidth is less than 20 MHz， the power of the pilots outside the signal band will be zero. In the mathematical form， the estimation of the channel that is out of the signal bandwidth is
[EH（1）i，k，out=EH（1）i，kout+EH（0）i，kd（0）i，k/p（1）i，kout+EWi，kp（1）i，kout≈0+0+0]
Equation （13） indicates that the estimation of the neighbouring cell channel could filter out the interference and noise by moving average. Therefore， the power derived from the channel estimation is reliable way of detecting the signal bandwidth. A similar approach could be taken for detecting the number of antennas as well.
3.3 InterferingSignal Reconstruction and Reduction
After estimating CFO， TO， and the channel response， the estimated interference signal can be reconstructed on the basis of the local time?domain CRS. The relative timing offset [d] is potentially larger than the duration of CP， which causes ISI within the OFDM window of a desired signal. Thus， reconstructing a frequency?domain interference signal symbol by symbol could result in inaccurate IC. This algorithm reconstructs the interference signal in the time domain and subtracts it from the received signal in time domain： [y（0）（n）=y（n）-y（1）（n+d）e-2πfΔnN?hl] （14）
where [hl=FFTH（1）i].
4 Simulation Results
In this section， we evaluate the performance of the IC algorithm using Monte Carlo simulation. We simulate a typical two?cell interference scenario （Fig. 1）. The serving cell is set to work in MBSFN mode with 10 MHz bandwidth and different modulation and coding schemes to deliver the service. The interfering cell transmits a normal ABS with a bandwidth of 5 MHz. During the ABS， the CRS overlaps the data RE of desired signal， which causes inter?cell interference. The desired and interfering signal both pass through the time?varying channel with a delay spread smaller than the duration of CP. In the simulation， the WINNER II C2 （EVA） [18] channel model is used with different Doppler frequency determine the effectiveness of IC under different channel conditions. The arrival time of desired and interfering signal is adjusted to determine the effect of relative timing offset. In addition， different CFOs are applied to the interfering signal to evaluate the effect of CFO. To generate the correct PSS， SSS， and CRS for IC， the user is assumed to conduct an ideal cell search.
Figs. 5a to d show BLER versus SNR for different IC scenarios. MCS 8 and MCS 16 are used. The signal is transmitted via EVA channel with 5 Hz Doppler frequency and with different SNRs. The antenna multiplex mode is set to SIMO and MIMO. The block error rate （BLER） is a performance criteria and is calculated on the basis of 10，000 block transmissions. The BLER of transmission without interference is used as the reference. Fig. 5 also shows the performance with and without IC （red and grey curves， respectively）. The inter?cell interference degrades performance during the SNR range of interest. When the IC algorithm is used， BLER approaches that of transmission without interference.
Fig. 6 shows the BLER in different Doppler frequency scenarios. SIMO MCS 18 modulation is used in this simulation， and the Doppler frequency varies from 5 Hz to 200 Hz. The BLER in the case of no interference is the reference （blue curve）. The BLER in the case of interference and IC are shown by the grey and red curves， respectively. In Figs. 6a?d， IC significantly improves the BLER for different SNR and Doppler frequencies. This proves the robustness of the IC algorithm.
Fig. 7 shows the effect of CFO on BLER when the proposed IC algorithm and combined IC （comIC） algorithm in [5] are used. The performance of the algorithm in [5] gradually degrades as CFO increases. On the contrary， there is no significant degradation in performance using the proposed algorithm. This proves the effectiveness of frequency synchronization when the CFO is large. Fig. 8 shows the effect of TO on BLER， when MCS 22 modulation is used. The channel is set at EVA 5Hz， and SNR is set at 16 dB. The performance of proposed IC algorithm is shown by the red curve， and the performance of the comIC algorithm in [5] is shown by the grey curve. The red curve shows that proposed IC algorithm greatly improves BLER when there is a short delay or a very long delay （the inference pilot almost overlaps the following symbol）. When the delay is larger than half an OFDM symbol， the BLER for comIC increases， which means that timing synchronization is required. The red curve shows that IC with timing synchronization achieves results in robust performance within the TO range of interest.
5 Conclusions
This paper discusses cancellation of inter?cell interference caused by the CRS at the edge of a cell in a multilayer cellular network. This paper describes a signal model that takes into account the interfering signal from a neighboring cell， channel effect， and timing and frequency offset. Using this model， we estimate the TO， CFO， and interfering channel. The interfering signal is then reconstructed locally. Finally， the interference is alleviated by subtracting the reconstructed interference signal. The computer simulation shows this IC algorithm significantly improves performance in different channel conditions. In future work， we will generalize the proposed scheme to non?OFDM cells， such as sparse codebook multiple?access （SCMA） cells and non?orthogonal multiple?access （NOMA） cells， which will also be used in 5G networks.
References
[1] H. Baligh， M. Hong， W.?C. Liao， et al.， “Cross layer provision of future cellular networks，” IEEE Signal Processing Magazine， vol.31， no.6， pp. 56-68， Nov. 2014.
[2] S. Deb， P. Monogioudis， J. Miernik， and J. P. Seymour， “Algorithms for enhanced inter?cell interference coordination （eICIC） in LTE HetNets，” IEEE/ACM Transaction on Networking， vol. 22， no. 1， pp. 137-150， Feb. 2014. doi： 10.1109/TNET.2013.2246820.
[3] Qualcomm Inc， “Enabling communication in harsh interference scenarios，” R4?102350， 3GPP?RAN WG4 AH#10?03， Bratislava， Jul. 2010.
[4] Qualcomm Inc， “Link level simulations for FeICIC with 9dB cell range expansion，” R4?123313， 3GPP?RAN WG4 #63， Prague， May 2012.
[5] M. Huang and W. Xu， “Macro?femto inter?cell interference mitigation for 3GPP LTE?A downlink，” in IEEE Wireless Communications and Networking Conference Workshops， Paris， France， Apr. 2012， pp. 75-80. doi： 10.1109/WCNCW.2012.6215544. [6] B. E. Priyanto， S. Kant， F. Rusek， et al.， “Robust UE receiver with interference cancellation in LTE advanced heterogeneous network，” in IEEE 78th Vehicular Technology Conference， Las Vegas， USA， Sept. 2013， pp. 1-7. doi： 10.1109/VTCFall.2013.6692396.
[7] H. Nguyen?Le， T. Le?Ngoc， and C. C. Ko， “RLS?basedjoint estimation and tracking of channel response， sampling， and carrier frequency offsets for OFDM，” IEEE Transaction on Broadcasting， vol. 55， no. 1， pp.84-94， Mar. 2009. doi： 10.1109/TBC.2008.2012361.
[8] Evolved Universal Terrestrial Radio Access （E?UTRA）； Physical Channels and Modulation， 3GPP TS 36.211， Feb. 2013.
[9] J.?J. van de Beek， M. Sandell， and P. O. B?rjesson， “ML estimation of time and frequency offset in OFDM systems，” IEEE Transactions on Signal Processing， vol. 45， no. 7， pp. 1800-1805， Jul. 1997. doi： 10.1109/78.599949.
[10] M. Speth， D. Daecke， and H. Meyr， “Minimum overhead burst synchronization for OFDM based broadband transmission，” in IEEE Global Telecommunications Conference， Sydney， Australia， Nov. 1998， pp. 2777-2782. doi： 10.1109/GLOCOM.1998.776494.
[11] C. C. Ko， R. Mo， and M. Shi， “A new data rotation based CP synchronization scheme for OFDM systems，” IEEE Transaction on Broadcasting， vol. 51， no. 3， pp. 315-321， Sept. 2005. doi： 10.1109/TBC.2005.851135.
[12] J.?S. Baek and J.?S. Seo， “Effective symbol timing recovery based on pilot?aided channel estimation for MISO transmission mode of DVB?T2 system，” IEEE Transaction on Broadcasting， vol. 56， no. 2， pp. 193-200， Jun. 2010. doi： 10.1109/TBC.2010.2049054.
[13] X. Wang， T. T. Tjhung， Y. Wu， and B. Caron， “SER performance evaluation and optimization of OFDM system with residual frequency and timing offsets from imperfect synchronization，” IEEE Transaction on Broadcasting， vol. 49， no. 2， pp. 170-177， Jun. 2003. doi： 10.1109/TGRS.2003.810271.
[14] Y.?H. Tsai and T.?H. Sang， “A new timing synchronization and cell search procedure resistant to carrier frequency offsets for 3GPP?LTE downlink，” in First IEEE International Conference on Communications in China， Beijing， China， Aug. 2012， pp. 334-338. doi： 10.1109/ICCChina.2012.6356903.
[15] J.?J. van de Beek， O. Edfors， M. Sandell， et al.， “On channel estimation in OFDM systems，” in IEEE 45th Vehicular Technology Conference， Chicago， USA， Jul. 1995， pp. 815-819. doi： 10.1109/VETEC.1995.504981.
[16] V. Srivastava， C. Ho， P. Fung， and Sumei Sun， “Robust MMSE channel estimation in OFDM systems with practical timing synchronization，” in IEEE Wireless Communications and Networking Conference， Atlanta， USA， Mar. 2004， pp. 711-716.? doi： 10.1109/WCNC.2004.1311273.
[17] C. Feng， H. Cui， M. Ma， and B. Jiao， “On statistical properties of co?channel interference in OFDM systems，” IEEE Communication Letters， vol. 17， no. 12， pp. 2328-2331， Oct. 2013. doi： 10.1109/LCOMM.2013.101813.131297.
[18] Evolved Universal Terrestrial Radio Access （E?UTRA）， User Equipment （UE） Radio Transmission and Reception， 3GPP TS 36.101， Jul. 2013.
Manuscript received： 2014?09?18
ith the rapid development of 5G wireless networks， heterogeneous links， which support the co?existence of multilayer cells， multiple standards， and multiple applications， are playing an important role in increasing capacity and coverage and satisfying huge traffic demand [1]. This paper discusses technical issues， in particular， interference cancellation， in a heterogeneous network with macro and pico cell. In the topology of a network with macro and pico cells， the high?power 1～40 W macro cell provides basic coverage and the low power 250 mW pico cell is the complementary cell. The pico cell extends network coverage and offloads data traffic of the macro?cell. This reduces cost and increases frequency efficiency. However， the user equipment （UE） served by the pico cell also receives RF signals from neighboring high?power macro cells. This interference is even more severe when users in the pico cell stay within the coverage area of macro cells with range?extension enabled [2].
Enhanced inter?cell interference coordination （eICIC） addresses this issue [2]. eICIC involves two techniques. First， the signal strength is biased to the pico cell， which reduces the interference power. Second， the macro cell remains silent for a certain period， called Almost?Blank Subframe （ABS） [2]. In the ABS， the physical downlink shared channel （PDSCH） is emptied. Therefore， UE does not receive PDSCH during the ABS， and interference can be alleviated. However， users may still receive the cell?specific reference signal （CRS）， paging channel （PCH）， physical broadcast channel （PBCH）， and synchronization channels （PSS/SSS）， all of which degrade performance. Further eICIC （FeICIC） has been proposed to eliminate CRS interference.
Some research has been done on CRS interference cancellation （IC）. The authors of [3] and [4] investigate direct IC and log?likelihood ratio （LLR） puncturing methods. The simulation results show that direct IC results in better performance. The authors of [5] propose a receiver algorithm that combines IC with a direct?decision channel estimation （CE） algorithm for colliding CRS. The authors of [6] propose a space?alternating generalized expectation?maximization （SAGE） with a maximum a?posteriori （MAP） method for estimating the interfering channel. This method involves reduced computation complexity compared with the linear minimum mean square error （LMMSE） method. However， timing error and frequency offsets can severely degrade performance. In this paper， we theoretically analyze and run simulations on the CRS interference?cancellation algorithm in a non?colliding scenario where channel statistics are taken into consideration. First， we analyze and model the interference signal and then discuss the interference?cancellation algorithm based on this model. The algorithm makes use of the primary synchronization signal （PSS） and secondary synchronization signal （SSS） to obtain the timing offset （TO） and carrier frequency offset （CFO）. Then， the channel response is estimated using channel statistics. Then， the interference signal is reconstructed taking into account the channel effect， TO and CFO. Interference is alleviated by subtracting the interference signal from the received signal.
The rest of this paper is organized as follows. In section 2， the interference is analyzed and modeled. In section 3， we discuss IC algorithms. In section 4， results of the computer simulation are presented. In section 5， we sum up.
2 Interference Analysis and Model
Fig. 1 shows typical non?colliding inter?cell interference between macro and pico cells. The wireless data service is delivered to the subscriber via pico cell， and the downlink signal from the macro cell interferes with the subscriber at the edge of the pico cell. To alleviate the inter?cell interference， the ABS is transmitted by the macro cell. During the ABS， only certain control signals， such as CRS ， are transmitted.
However， the CRS still causes interference for the subscriber. Fig. 2 shows the received signal of one resource block （RB） with one interference cell. The CRS from a neighboring macro cell overlaps the resource elements （REs） from a serving cell （SC）. The SC RE can be divided into data RE and CRS RE. Because of the TO and CFO between the interfering cell and subscriber， the received interfering signal suffers TO and CFO （Fig. 2）.
Four modulation schemes are being considered for 5G： generalized frequency?division multiplexing （GFDM）， filter bank multicarrier （FBMC）， universal filtered multicarrier （UFMC）， and biorthogonal frequency?division multiplexing （BFDM）. However， these four schemes are all generalizations of OFDM， so we address the original OFDM modulation in the following way （for simplicity’s sake）.
In the downlink side of OFDM modulation， the frequency?domain signal of the [ith] symbol is transferred to time domain signal [xi（n）] via N?point Inverse Fast Fourier Transform （IFFT）： [xi（n）=1Nk=0N-1Xi，kej2πnk/N=1Nk=0N-1di，k+pi，kej2πnk/N] （1）
where [di，k] and [pi，k] are the data and pilot， respectively.
Then the signal is transmitted over a multipath propagation channel that takes into account additive white Gaussian noise （AWGN）. At the receiver side， the received signal is given by
[yi（n）=l=0L-1hlxin-τl+ω（n）] （2）
where [hl] and [τl] are the gain and delay of the lth path， respectively； and ω（n） is the AWGN. Because of the TO and CFO， the corrupted receiver signal in the case of inter?cell interference is
[yi（n）=y（0）i（n）+y（1）i（n）+ω（n）=1Nk=0N-1H（0）i，kX（0）i，kej2πnk/N+ 1Nk=0N-1H（1）i，kX（1）i，kej2π（n-d）（k+fΔ）/N+ω（n）]
where [y（0）i] and [y（1）i] are the desired signal and interference signal， respectively； [H（0）i，k] and [H（1）i，k] are the frequency response of the serving channel and interfering channel， respectively； and [d] and [fΔ] are the relative timing and frequency offset， respectively， between the macro and pico cell. After applying the N?point Fast Fourier Transform （FFT）， the OFDM symbol is [7]：
[Yi，k=Y（0）i，k+Y（1）i，k=H（0）i，kX（0）i，k+n=-N/1N2ej2πndNH（1）i，nX（1）i，nΦn+Wi，k] （4）
where [H（0）i，k] and [H（1）i，k] are the channel coefficients of the serving and interfering cell at kth subcarrier， respectively； and [Φn] is the inter?carrier interference （ICI）. During the ABS， only certain control signals are transmitted， and the CRS from the macro cell overlaps the data REs （Fig. 2）. At the data REs， the signal model of the serving cell with interference is
[Yi，k=H（0）i，kd（0）i，k+n=-N/2N2ej2πndNH（1）i，nd（1）i，nΦn+Wi，k] （5）
According to （5）， the relative timing offset [d] between interfering and serving cells causes phase shift [ej2πndN] on the kth subcarrier. The terms [Φn] in （5） arises from the CFO term[fΔ]， which results in intercarrier interference （ICI）. Therefore， the CFO and TO need to be compensated. In addition， this model shows the case of single?input single?output （SISO） antenna only. The case of multiple?input multiple?output （MIMO） antenna can be easily derived from （5）. However， the number of REs increases because the number of interference CRSs increases with number of antenna ports， which results in more severe interference [8]. These problems will be addressed in section 3.
3 IC Algorithm
The proposed inter?cell IC algorithm is shown in Fig. 3. This algorithm includes estimation of CFO and TO， estimation of the interfering channel， modeling of the interfering cell， and reconstruction and reduction of the interfering signal. With CFO and TO estimation， the relative frequency offset and timing offset between the interfering cell and serving cell is estimated using the PSS or SSS generated by modeling the interfering cell. Next， the interfering channel is estimated according to the compensated signal. The interfering signal is then reconstructed according to the previous estimation and subtracted from the received signal. 3.1 CFO and TO Estimation
The objective of this module is to retrieve OFDM symbol timing and estimate the CFO of the interfering cell. Many timing? and frequency?synchronization algorithms have been developed. Most of these exploit the periodic nature of the time?domain signal by using cyclic prefix （CP） [9]-[11] or pilot data [12]-[13]. However， there are no data REs in an ABS， which severely reduces the power of the CP. The low SNR of the CP makes both timing and frequency synchronization difficult. Apart from the CP and pilot， there are still the PSS and SSS， which are dedicated to timing and frequency synchronization in the downlink. The PSS and SSS are located at the last and second?last symbol in the time slot 0 and 10. The PSS [pss（n）] and SSS [sss（n）] are given by
[pss（n）=ejπμn（n+1）63 n=0，1，...，30ejπμ（n+1）（n+2）63 n=31，32，...，61]
and
[sss（2n）=s（m0）0（n）c0（n） time slot 0s（m1）1（n）c0（n） time slot 10]
[sss（2n+1）=s（m1）1（n）c1（n）z1（m0）（n） time slot 0s（m0）0（n）c1（n）z1（m1）（n） time slot 10]
where [μ]is 25， 29 or 34 and corresponds to the physical layer identity [N（2）ID]； and [m0] and [m1] are derived from the physical layer cell identity group [N（1）ID]； [s（m1）0]， [s（m0）1]， [c0（n）] ， [c1（n）]， [z1（m0）] and [z1（m1）] are defined in [8]. The timing and frequency offset can be estimated using the cross?correlation of PSS/SSS [14]：
[d，fΔ=arg maxd，fΔC（d，fΔ）] （6）
where
[Cd，fΔ=m=1N2s?i（n）r（n+m）e-2πfΔnN] （7）
The generation of PSS/SSS is based on the assumption of an ideal cell search. The cell?search algorithm in the case of inter?cell interference is beyond the scope of this paper. After the timing and frequency synchronization of the interfering signal， the interfering?channel response can be estimated.
3.2 InterferingChannel Estimation
Before interference cancellation， it is essential to estimate the interfering?channel response. The channel estimation can be based on least squares （LS） or minimum mean?square error （MMSE） [15]， [16]. The MMSE algorithm gives 10-15 dB gain in signal?to?noise ratio （SNR） for the same mean?square error of CE over LS estimation [15]. However， the MMSE is more complex than the LS algorithm. After timing and frequency offset compensation， （5） can be rewritten as
[Yi，k=H（0）i，kd（0）i，k+H（1）i，kd（1）i，k+Wi，k] （9）
From （10）， the interfering CRS sequence [p（1）] can be expressed as
[p（1）=12（1-2c（2n））+j12（1-2c（2n+1））] （10）
where [c（n）] is generated by Gold Sequence with a length of 31， the state of which is initialized according to the cell ID， slot number， and antenna port. Assuming that the user conducts ideal cell research， the interfering CRS [p（1）i，k] can be generated locally. Applying LS CE， the interfering channel can be estimated with [H（1）i，k=Yi，k/p（1）i，k=H（1）i，k+H（0）i，kd（0）i，k/p（1）i，k+Wi，k/p（1）i，k] （11）
According to （11）， the data RE of serving cell [H（0）i，kd（0）i，k/p（1）i，k] becomes interference with relatively high power. Thus， the estimation in （11） is inaccurate. Numerical studies in [17] show that the distribution of the interference signal is close to Gaussian for a larger RB and non?Gaussian for a smaller. However， the mean of the distribution converges to 0. Therefore， the expectation of （11） can be derived：
[E{H（1）i，k}=EYi，kp（1）i，k=EH（1）i，k+H（0）i，kd（0）i，k/p（1）i，k+Wi，k/p（1）i，k =EH（1）i，k+EH（0）i，kd（0）i，k/p（1）i，k+EWi，kp（1）i，k ≈EH（1）i，k]
Equation （12） provides a good estimation of mean value of the interfering channel. This value can be estimated by using a moving?average window in the time dimension （Fig. 4）. If the moving?average window of length M is within the coherence time of the channel， [H（1）i，k] could be approximated by[E{H（1）i，k}]. The procedure of the interfering?channel estimation is show in Fig. 4.
The IC algorithm should set the correct antenna number and bandwidth of the interfering cell for interfering?cell CE and interference modelling block. Usually this information is not available at the UE unless the UE decides to hand over to that cell. Therefore， the antenna number and bandwidth of the interfering cell need to be estimated at the UE.
A straightforward method for interfering?cell CE is to enable the IC control block to always set the maximum possible bandwidth and number of antennas， i.e.， 20 MHz and 4 antennas， so that the interfering?cell CE and interference modelling block estimates the channel accordingly. If the actual bandwidth is less than 20 MHz， the power of the pilots outside the signal band will be zero. In the mathematical form， the estimation of the channel that is out of the signal bandwidth is
[EH（1）i，k，out=EH（1）i，kout+EH（0）i，kd（0）i，k/p（1）i，kout+EWi，kp（1）i，kout≈0+0+0]
Equation （13） indicates that the estimation of the neighbouring cell channel could filter out the interference and noise by moving average. Therefore， the power derived from the channel estimation is reliable way of detecting the signal bandwidth. A similar approach could be taken for detecting the number of antennas as well.
3.3 InterferingSignal Reconstruction and Reduction
After estimating CFO， TO， and the channel response， the estimated interference signal can be reconstructed on the basis of the local time?domain CRS. The relative timing offset [d] is potentially larger than the duration of CP， which causes ISI within the OFDM window of a desired signal. Thus， reconstructing a frequency?domain interference signal symbol by symbol could result in inaccurate IC. This algorithm reconstructs the interference signal in the time domain and subtracts it from the received signal in time domain： [y（0）（n）=y（n）-y（1）（n+d）e-2πfΔnN?hl] （14）
where [hl=FFTH（1）i].
4 Simulation Results
In this section， we evaluate the performance of the IC algorithm using Monte Carlo simulation. We simulate a typical two?cell interference scenario （Fig. 1）. The serving cell is set to work in MBSFN mode with 10 MHz bandwidth and different modulation and coding schemes to deliver the service. The interfering cell transmits a normal ABS with a bandwidth of 5 MHz. During the ABS， the CRS overlaps the data RE of desired signal， which causes inter?cell interference. The desired and interfering signal both pass through the time?varying channel with a delay spread smaller than the duration of CP. In the simulation， the WINNER II C2 （EVA） [18] channel model is used with different Doppler frequency determine the effectiveness of IC under different channel conditions. The arrival time of desired and interfering signal is adjusted to determine the effect of relative timing offset. In addition， different CFOs are applied to the interfering signal to evaluate the effect of CFO. To generate the correct PSS， SSS， and CRS for IC， the user is assumed to conduct an ideal cell search.
Figs. 5a to d show BLER versus SNR for different IC scenarios. MCS 8 and MCS 16 are used. The signal is transmitted via EVA channel with 5 Hz Doppler frequency and with different SNRs. The antenna multiplex mode is set to SIMO and MIMO. The block error rate （BLER） is a performance criteria and is calculated on the basis of 10，000 block transmissions. The BLER of transmission without interference is used as the reference. Fig. 5 also shows the performance with and without IC （red and grey curves， respectively）. The inter?cell interference degrades performance during the SNR range of interest. When the IC algorithm is used， BLER approaches that of transmission without interference.
Fig. 6 shows the BLER in different Doppler frequency scenarios. SIMO MCS 18 modulation is used in this simulation， and the Doppler frequency varies from 5 Hz to 200 Hz. The BLER in the case of no interference is the reference （blue curve）. The BLER in the case of interference and IC are shown by the grey and red curves， respectively. In Figs. 6a?d， IC significantly improves the BLER for different SNR and Doppler frequencies. This proves the robustness of the IC algorithm.
Fig. 7 shows the effect of CFO on BLER when the proposed IC algorithm and combined IC （comIC） algorithm in [5] are used. The performance of the algorithm in [5] gradually degrades as CFO increases. On the contrary， there is no significant degradation in performance using the proposed algorithm. This proves the effectiveness of frequency synchronization when the CFO is large. Fig. 8 shows the effect of TO on BLER， when MCS 22 modulation is used. The channel is set at EVA 5Hz， and SNR is set at 16 dB. The performance of proposed IC algorithm is shown by the red curve， and the performance of the comIC algorithm in [5] is shown by the grey curve. The red curve shows that proposed IC algorithm greatly improves BLER when there is a short delay or a very long delay （the inference pilot almost overlaps the following symbol）. When the delay is larger than half an OFDM symbol， the BLER for comIC increases， which means that timing synchronization is required. The red curve shows that IC with timing synchronization achieves results in robust performance within the TO range of interest.
5 Conclusions
This paper discusses cancellation of inter?cell interference caused by the CRS at the edge of a cell in a multilayer cellular network. This paper describes a signal model that takes into account the interfering signal from a neighboring cell， channel effect， and timing and frequency offset. Using this model， we estimate the TO， CFO， and interfering channel. The interfering signal is then reconstructed locally. Finally， the interference is alleviated by subtracting the reconstructed interference signal. The computer simulation shows this IC algorithm significantly improves performance in different channel conditions. In future work， we will generalize the proposed scheme to non?OFDM cells， such as sparse codebook multiple?access （SCMA） cells and non?orthogonal multiple?access （NOMA） cells， which will also be used in 5G networks.
References
[1] H. Baligh， M. Hong， W.?C. Liao， et al.， “Cross layer provision of future cellular networks，” IEEE Signal Processing Magazine， vol.31， no.6， pp. 56-68， Nov. 2014.
[2] S. Deb， P. Monogioudis， J. Miernik， and J. P. Seymour， “Algorithms for enhanced inter?cell interference coordination （eICIC） in LTE HetNets，” IEEE/ACM Transaction on Networking， vol. 22， no. 1， pp. 137-150， Feb. 2014. doi： 10.1109/TNET.2013.2246820.
[3] Qualcomm Inc， “Enabling communication in harsh interference scenarios，” R4?102350， 3GPP?RAN WG4 AH#10?03， Bratislava， Jul. 2010.
[4] Qualcomm Inc， “Link level simulations for FeICIC with 9dB cell range expansion，” R4?123313， 3GPP?RAN WG4 #63， Prague， May 2012.
[5] M. Huang and W. Xu， “Macro?femto inter?cell interference mitigation for 3GPP LTE?A downlink，” in IEEE Wireless Communications and Networking Conference Workshops， Paris， France， Apr. 2012， pp. 75-80. doi： 10.1109/WCNCW.2012.6215544. [6] B. E. Priyanto， S. Kant， F. Rusek， et al.， “Robust UE receiver with interference cancellation in LTE advanced heterogeneous network，” in IEEE 78th Vehicular Technology Conference， Las Vegas， USA， Sept. 2013， pp. 1-7. doi： 10.1109/VTCFall.2013.6692396.
[7] H. Nguyen?Le， T. Le?Ngoc， and C. C. Ko， “RLS?basedjoint estimation and tracking of channel response， sampling， and carrier frequency offsets for OFDM，” IEEE Transaction on Broadcasting， vol. 55， no. 1， pp.84-94， Mar. 2009. doi： 10.1109/TBC.2008.2012361.
[8] Evolved Universal Terrestrial Radio Access （E?UTRA）； Physical Channels and Modulation， 3GPP TS 36.211， Feb. 2013.
[9] J.?J. van de Beek， M. Sandell， and P. O. B?rjesson， “ML estimation of time and frequency offset in OFDM systems，” IEEE Transactions on Signal Processing， vol. 45， no. 7， pp. 1800-1805， Jul. 1997. doi： 10.1109/78.599949.
[10] M. Speth， D. Daecke， and H. Meyr， “Minimum overhead burst synchronization for OFDM based broadband transmission，” in IEEE Global Telecommunications Conference， Sydney， Australia， Nov. 1998， pp. 2777-2782. doi： 10.1109/GLOCOM.1998.776494.
[11] C. C. Ko， R. Mo， and M. Shi， “A new data rotation based CP synchronization scheme for OFDM systems，” IEEE Transaction on Broadcasting， vol. 51， no. 3， pp. 315-321， Sept. 2005. doi： 10.1109/TBC.2005.851135.
[12] J.?S. Baek and J.?S. Seo， “Effective symbol timing recovery based on pilot?aided channel estimation for MISO transmission mode of DVB?T2 system，” IEEE Transaction on Broadcasting， vol. 56， no. 2， pp. 193-200， Jun. 2010. doi： 10.1109/TBC.2010.2049054.
[13] X. Wang， T. T. Tjhung， Y. Wu， and B. Caron， “SER performance evaluation and optimization of OFDM system with residual frequency and timing offsets from imperfect synchronization，” IEEE Transaction on Broadcasting， vol. 49， no. 2， pp. 170-177， Jun. 2003. doi： 10.1109/TGRS.2003.810271.
[14] Y.?H. Tsai and T.?H. Sang， “A new timing synchronization and cell search procedure resistant to carrier frequency offsets for 3GPP?LTE downlink，” in First IEEE International Conference on Communications in China， Beijing， China， Aug. 2012， pp. 334-338. doi： 10.1109/ICCChina.2012.6356903.
[15] J.?J. van de Beek， O. Edfors， M. Sandell， et al.， “On channel estimation in OFDM systems，” in IEEE 45th Vehicular Technology Conference， Chicago， USA， Jul. 1995， pp. 815-819. doi： 10.1109/VETEC.1995.504981.
[16] V. Srivastava， C. Ho， P. Fung， and Sumei Sun， “Robust MMSE channel estimation in OFDM systems with practical timing synchronization，” in IEEE Wireless Communications and Networking Conference， Atlanta， USA， Mar. 2004， pp. 711-716.? doi： 10.1109/WCNC.2004.1311273.
[17] C. Feng， H. Cui， M. Ma， and B. Jiao， “On statistical properties of co?channel interference in OFDM systems，” IEEE Communication Letters， vol. 17， no. 12， pp. 2328-2331， Oct. 2013. doi： 10.1109/LCOMM.2013.101813.131297.
[18] Evolved Universal Terrestrial Radio Access （E?UTRA）， User Equipment （UE） Radio Transmission and Reception， 3GPP TS 36.101， Jul. 2013.
Manuscript received： 2014?09?18