Enhanced SIC and Initial Guess ML Receivers for Collaborative MIMO of the LTE Uplink

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1 Enhanced SIC and Initial Guess ML Receivers for Collaborative MIMO of the LTE Uplink Karim A. Banawan Electrical Engineering Department Faculty of Engineering, Alexandria University Alexandria, Egypt Essam A. Sourour Electrical Engineering Department Faculty of Engineering, Alexandria University Alexandria, Egypt Abstract In this paper, Collaborative MIMO is introduced to the Uplink of the Long Term Evolution (LTE) system. This technique uses two or more single carrier frequency division multiple access based user equipments (UEs) with single antenna each. These UEs transmit their data collaboratively over the same Resource block (RB). The Evolved Node B (enodeb) separates the users' data by means of multiuser frequency domain equalization. This increases the whole throughput of the LTE Uplink, while moving the complexity of implementing multiple antennas to the enodeb. In order to decode the data ZF, MMSE and successive interference cancellation (SIC) are traditionally employed although they don t exploit the full spatial diversity, whereas the standard ML is suffers from exponential complexity. In this paper, we propose a novel Initial Guess based ML (IGML) receiver whose complexity is in the same order of ML receiver of OFDM-MIMO system. Then we introduce a simplified QR-based version of the IGML receiver. We also propose two ordering techniques for the SIC receiver when used in shadowing environment. Various simulation parameters are examined to study the performance. Simulation results reveal that our IGML receiver is better by almost 4.5dB at target of compared to the traditional MMSE receiver. Keywords--- CSM; LTE; SIC; SC-FDMA; ML I. INTRODUCTION The Long Term Evolution (LTE) is developed in Releases 8 and 9 of the 3GPP specifications [1], [2]. LTE downlink (DL) uses Orthogonal Division Multiple Access (OFDMA). The uplink (UL) uses Single Carrier Division Multiple Access (SC-FDMA), which offers lower Peak to the Average Power Ratio (PAPR) property [3]. To support higher UL data rate and achieve space diversity gains the use of MIMO is proposed [4]. However, using multiple antennas in the User Equipment (UE) is challenging, so the idea of Collaborative Spatial Multiplexing (CSM) (also known as Virtual MIMO) is attractive [5]. In CSM two or more UEs equipped with single antenna each transmit independent data stream. Those users are collaboratively transmitting to the same resource blocks (RBs), i.e. same frequency/time grid resource. The Evolved Node B (enodeb), equipped by a number of antennas equal to or more than the number of collaborative users, separates the users' data using means of multiuser frequency domain equalization. The CSM technique increases the whole throughput of the UL as RBs are reused among different users, and constitute virtual MIMO without increasing the complexity of the UE. Traditional multiuser equalization techniques include Zero Forcing (ZF), Minimum Mean Squares Errors (MMSE) and Maximum likelihood (ML). ZF suffers from noise and interference enhancement. MMSE accounts for the SNR/SIR value and provides better performance. However, the optimal receiver is the ML which performs exhaustive search to find the symbols with minimum detection error. Unfortunately the full-fledge ML receiver is abandoned when employing SC- FDMA signals since its complexity increases exponentially with the -block size as well as the modulation index. To reduce complexity and maintain performance Successive Interference Cancellation (SIC) is a good choice. SIC is a decision feedback (DFE) that sequentially demodulates UE signals, one at a time, and cancels the contribution from the received signal [6]. In this paper, we first propose a novel initial guess based ML (IGML) receiver which dramatically enhances the performance of the collaborative LTE SC-FDMA system. Its complexity grows exponentially with the modulation index only. Moreover, we present two novel ordering techniques to enhance the performance of the SIC receiver, especially in the case of shadowing environments. A comprehensive study of various key parameters of the collaborative system, including the number of collaborative UEs, the number of receiving antennas, channel selectivity and mobility are studied. To obtain realistic results, Least Squares (LS) and MMSE channel estimations are included [7]. The paper is organized as follows. Section II introduces the collaborative system model, while sections III and IV present the conventional and proposed CSM equalization techniques. Section V provides the simulation results in various collaborative environments. Notations: bold face letters denote matrices,(.), (. ),. are Hermitian, transpose and Euclidean norm. II. SYSTEM MODEL The CSM system shown in Fig.1 has users each has a UE equipped with a single antenna. The data of user is encoded and symbol mapped. The modulation symbols y k are then transformed to the frequency domain using Discrete Fourier transform () of size to have () = 1 () exp 2 (1) ( 1)( 1) where m is the subcarrier index and n is the symbol index,, 1,2,,. The output of the is then mapped using localized subcarrier mapping [3], where the user's symbols are mapped into consecutive subcarriers. This is important to keep the single carrier property. For simplicity, in this work, we assume full RB utilization by the UE /11/$ IEEE

2 Data1 coding 1 mapping 1 (base band modulation) "M" 1 mapping and DRS 1 I "N" Demodulation Data K coding mapping (base band modulation) Figure 1. LTE user equipments transmitters Hence, the output of the subcarrier mapping is given by () = () Γ (2) 0 h where Γ is the M-elements subcarrier set of the user Γ,, and is the size. The output of the subcarrier mapping stage is fed to a conventional OFDM transmitter which consists of I to yield () = 1 () exp 2 ( 1)( 1) (3) "M" Finally, the cyclic prefix () is inserted with length larger than the maximum delay spread of the multipath channel, to mitigate the inter-symbol interference (ISI) and enable simple frequency domain equalization (FDE). The above steps result in SC-FDMA signal,, for the k th UE. Each user's data is transmitted through an L paths Rayleigh fading channel. The channel impulse response is h (, ) where is the time instant, is the path number of and is the receiving antenna index. We consider a uniform power delay profile where path gains are complex-gaussian with variance 1/L. We also employ the Jakes model to take the Doppler frequency into consideration. [8]. The faded signal of the user to receiving antenna channel can be written as () =h (, ) ( ) (4) At enodeb, which is equipped by antennas ( ), the collaborative users' signals are added together with contamination of AWGN, which is modeled by IID complex Gaussian noise samples () with zero mean and variance =1/., where is the SNR per subcarrier. Hence, the received signal at the antenna is written as () = () () mapping and DRS I "N" The enodeb takes the of each received stream to transform it back into frequency domain and prepare it for the FDE. The received signal in the frequency domain at any subcarrier can be written as () =()() () (6) where is the subcarrier index and () is the channel matrix of the subcarrier. (5) Figure 2. The channel matrix is given by enodeb receiver () = (7) Here, each subcarrier carries a combination of modulated symbols due to precoding in contrast to OFDMA [3]. III. CSM EQUALIZATION TECHNIQUES A. domain multiuser Zero forcing (ZF ) The ZF receiver is a suboptimal linear receiver [9]. It behaves like a linear filter and separates the data streams and thereafter independently decodes each stream while neglecting the effect of noise. Assuming that the channel matrix on the subcarrier () (simply ) is invertible then the equalized subcarrier will be () = () =( ) () (8) where =( ) is the Moore-Penrose pseudoinverse of a non square channel matrix.the ZF receiver suffers from noise enhancement of poorly conditioned subcarriers. Note that this noise enhancement will be averaged all over the received symbols ruining the entire data symbols frame, and hence leads to a poor performance. B. domain multiuser Minimum mean square error (MMSE ) Noise enhancement that occurs in the ZF receiver can be solved by regularizing the inverse of the ZF filter i.e. finding the regularized equalizing filter of the subcarrier which minimizes the mean square error i.e. minimize = () () () () = () () () () (9) This will lead to the LMMSE solution as [9] () = () =( 1/ ) () (10) Note that because of the regularizing factor1/, the MMSE minimizes the overall error caused by noise and mutual interference between the co-channel signals, thus outperforms the ZF. C. domain multiuser successive interference cancellation (SIC ) To benefit from the inherent spatial diversity of the CSM, SIC is a promising technique; it is a DFE which makes a decision on one of the user s data, re-generate its signal and subtract it as interference to other users. [5]. The SIC is shown in Fig.3, assuming user is the desired user: Demodulation

3 First, begin detection by user 1 using ZF or MMSE algorithms as of equations (8) or (10). This yields (). Second, perform to the SC-FDMA symbol followed by symbol detection to have (). Third, simulate the transmission procedure of user 1 i.e. repeat symbol mapping, spreading, subcarrier mapping to have (). Fourth, remove the interference obtained from the first user: () () = () () (11) where is the cancellation stage, () : is user channel vector on the subcarrier i.e. () =. Repeat the previous steps for the first ( 1) users till we have the () () = () () (12) () Now, spatial diversity exists which can be combined using Maximum Ratio Combiner (MRC) as 1 () = () () () (13) IV. PROPOSED CSM EQUALIZATION SCHEMES A. Proposed Ordered frequency domain Successive interference cancellation (OSIC) a) Optimal ordering based SIC The optimal SIC receiver relies on ordering the users powers in a descending order so that the user corresponds to the highest detection SNR is detected first, this decreases the effect of error propagation, also the user with highest power has the largest interference contribution to the received signal, which makes it useful to be cancelled first. Ordering must be done in a subcarrier by subcarrier basis i.e. users are sorted along all the loaded subcarriers and at each subcarrier the larger user is cancelled first. The algorithm works as follows: First, begin FDE as in equation (8) or (10), to yield the initial guess of all subcarriers. Then for the first subcarrier determine the highest power user to be detected first = argmax,,.., () (14) Then, the user will be cancelled first, so we will detect the user s data and simulate the transmission procedure of this user then remove its interference as equation (11). Repeat the previous steps along all subcarriers with fixing the result of cancellation of all previous subcarriers. Note that the optimal scheme is highly complex and is here for reference only. b) Suboptimal average norm ordering based SIC To decrease complexity of optimal ordering, we propose a suboptimal ordering scheme based on the sum of the channel power of all subcarriers and cancels the largest user first () = argmax,,.., (15) Figure 3. SIC receiver This makes the sorting process one time only instead of times along each subcarrier as the optimal case. B. Proposed Initial guess based Maximum likelihood Receiver (IGML receiver) In this section, we propose a novel ML receiver that performs exhaustive search along all time domain symbols to find symbols that minimize the Euclidean distance to the received symbol. For this, two issues are discussed: First, the exhaustive search domain is the time domain which differs from the equalization domain which is the frequency domain. Second, trying to directly apply exhaustive search in the frequency domain is not feasible because in this case the search will be applied along all possible permutations of the whole SC-FDMA signal, then the complexity of the ML receiver of users, points frame and constellation set of size of will be in the order of ( ). We jointly address the above issues by guessing all the values of time domain symbols using conventional FDE, and then find the error metric along all subcarriers. The algorithm works as follows as Fig.4: Perform FDE as of equations (8) or (10) to get (). Then, find the initial guess of all time domain symbols by process followed by slicing process as following () = () exp 2 ( 1)( 1) (16) - - where. is slicing to nearest constellation point operator. Then, perform a symbol-by-symbol exhaustive search: o Test all constellation values for the first symbol only while fixing other symbols to their initial guess, and the new -length precoded symbols. o Find the ML solution that corresponds to the minimum error metric along all subcarriers as follows: () = argmin () () (17) By this, the first symbol is optimally detected, so fix the value of first symbol to (). o Repeat the last two steps to all other symbols The IGML receiver exploits full diversity of the collaborative system on the complexity of only ( ). MRC user 2 h11 h12 Demod. Receiver user 2 (subcarrier,,demodulation Simulating transmitter user 1

4 extract extract Figure 4. Proposed IGML receiver C. Proposed simplified Initial guess based Maximum likelihood Receiver (simplified IGML receiver) The previous algorithm can be performed sequentially by means of Cholesky or -decomposition of channel matrix [10] which decomposes the channel matrix into an orthogonal matrix () and an upper triangular matrix (). This leads to a user by user separation of the received symbols on exhaustive search computation complexity of only (). The algorithm performs the first bullet of the previous scheme to get a conventional initial guess for all symbols. Then, the following steps are applied. The reader should take note of the difference between () of (18) and () of (6) Apply decomposition of the channel matrix along all subcarriers. () =()() (18) Filter the frequency domain components () with (). () = ()() (19) Begin with last user i.e. user exhaustive search to find the minimum error metric along all subcarriers with fixing all other symbols to their initial guess taking into account the upper triangular property of () as follows: () =argmin () () () (20) Proceed to ( 1) user after fixing the user symbol to () to find () = argmin () () () () ()() () (21) () Then, continue for the whole -users, this will lead to ML solution obtained using IGML with less number of exhaustive search combinations. Note that, this proposed scheme is similar to sphere detection [10] except for the absence of tree pruning step because the error is averaged along all subcarriers so it is unlikely to move away from the ML solution. V. SIMULATION RESULTS For link level simulations, Table.1 shows the simulation parameters of most of simulation cases, other simulation parameters are mentioned explicitly. TABLE I. COMMON SIMULATION PARAMETERS Simulation parameters values coding None (default) Modulation schemes QPSK Frame structure FDD, 10 ms duration size 256 Number of resource blocks 15, fully utilized Transmission bandwidth 2.7 MHz SC-FDMA symbols 6 Cyclic prefix choice extended Saving the guess of symbols and Exhaustive search for the h symbol while fixing previous ( 1) users Calculate ML error along all subcarriers () =1 () 2 And choose the minimum metric Demod. and decoding Demod. and decoding separation Carrier frequency Sampling frequency Collaborative system configuration Delay spread Delay- power profile / Users speed estimation 15KHz 2GHz 3.84MHz Variable (Default is 2x2 V-MIMO) 5s (default) Uniform/0 km/hr (default) Perfect (default) A. Comparison between different Detection techniques of the collaborative MIMO 2x2 system Fig.5 shows a comparison between all detection techniques presented above for the 2x2 CSM using simulation parameters in table.1. The figure shows that the ZF receiver is not suitable for CSM equalization (= at 25dB), and leads to severe degradation in performance as initial guesser. The figure also suggests using the other s like MMSE ( at 14.5dB), SIC-MMSE (12dB), or proposed suboptimal OSIC- MMSE in case of shadowing variance of 12dB (11.3dB). Note that in case of no shadowing no enhancement is achieved, and the proposed IGML-MMSE (10.1dB) is almost 0.4 db away from the full receive diversity 1x2 system. This confirms the claim of the optimality of IGML. On the other hand the simplified IGML is 0.2dB inferior to the IGML. Figure 5. Comparison between the proposed schemes B. Effect of increasing number of receiving antennas Fig.6 shows the enhancement of the MMSE equalized CSM system with more receiving antennas than the collaborative users. The diversity benefit decreases from almost of 10dB from 2 to 4 antennas, 3dB from to 4 to 6 antennas and 2dB from 6 to 8 antennas. These results advise us to use at least 4 antennas at the receiver side when using CSM. Fig.7 shows the effect of increasing the CSM order, the simulation results reveals that the SIC exploits the increase of CSM order more efficiently than the ordinary MMSE receiver, that is enhanced slightly ( ~ 1.5dB) when increasing order from 2x2 to 4x4 system, while SIC is clearly enhanced (~4.5dB). Figure 6. Comparison between detection techniques of 2x2 VMIMO systems proposed IGML-MMSE2x2 simplified ML 2x2 SIC- Suboptimal OSIC-MMSE ZF 2x2 proposed IGML-ZF2x2 SIC-ZF 2x2 full diversity 1x2(reference) Effect of increasing number of receiving antennas to V-MIMO system of 2 users MMSE 2x4 MMSE 2x6 MMSE 2x Effect of increasing number of receiving antennas

5 C. Effect of Diverse channel conditions Fig.8 shows that increasing the delay spread of the channel leads to more frequency selectivity and hence better output SNR because of the inherent frequency diversity property of the SC-FDMA. Therefore it is advised to use CSM in highly selective channels. Fig. 9 shows that CSM is optimized for low speeds up to 10km/hr. It has an error floor when the users velocity exceeds 15km/hr, and severely degrades when velocity exceeds 20km/hr. Imperfect channel estimation is examined. Figure 10 shows that in case of fixed users the MMSE channel estimation almost coincides with the perfect one ( 0.5dB penalty), while LS channel estimation is far by 5dB than the perfect one. Figure.11 shows that using MMSE channel estimation with spline interpolation along SC-FDMA symbols leads to decrease the susceptibility of CSM to Doppler shift, then CSM will operate efficiently to almost 60km/hr having an error floor at almost 100 km/hr. Figure 7. Figure Figure 9. effect of changing the V-MIMO order to MMSE and MMSased SIC s Effect of increasing the V-MIMO order using MMSE and SICreceivers Effect of changing the delay spread of the MUltipath channel flat fading channel delay spread=1us delay spread=3us delay spread=5us delay spread=15us Effect of changing the delay spread of frequency selective channel Effect of users mobility MMSE 4x4 MMSE 6x6 SIC- SIC-MMSE 4x4 SIC-MMSE 6x6 users' velocity = 0,10Km/hr users' velocity=15km/hr users' velocity=20km/hr users' velocity=30km/hr users' velocity=60km/hr Effect of users' mobility Figure 10. Effect of imperfect channel estimation for MMSE receivers and SIC-MMSE receivers perfect channel est.,mmse equaliz. LS channel est.,mmse equaliz. MMSE channel est.,mmse equaliz. LS channel est.,sic-mmse equaliz. MMSE channel est.,sic-mmse equaliz. perfect channel est.,sic-mmse equaliz. Effect of imperfect channel estimation, no Doppler for MMSE, SIC-MMSE Effect of MMSE channel estimation with spline time interpolation in presence of doppler shift effect perfect channel estimation, no doppler MMSE est.,velocity=20km/hr,spline interp. MMSE est.,velocity=40km/hr,spline interp. MMSE est.,velocity=60km/hr,spline interp. MMSE est.,velocity=80km/hr,spline interp. MMSE est.,velocity=100km/hr,spline interp. MMSE est.,velocity=120km/hr,spline interp. Figure 11. MMSE channel estimation with spline interpolation in presence of Doppler CONCLUSIONS CSM system is proposed to increase the capacity of the LTE UL. In this paper, we proposed a near-ml receiver (IGML) and a simplified version of it. We also proposed two ordering techniques to enhance the SIC receiver, the results suggests to using IGML receiver or its simplification is sense of reliable transmission.on the other hand, the paper results advise to use the collaborative system in low speed, MMSE channel estimated, highly selective channels with equipping the enodeb by number of receiving antennas exceeds the number of collaborative users. REFERENCES [1] E. Dahlman et al., 3G Evolution: HSPA and LTE for Mobile Broadband, 2nd ed., Academic Press, [2] TS V8.3.0, 3rd Generation Partnership Project Std., May [3] H. G. Myung, J. Lim, and D. J. Goodman, Single Carrier FDMA for Uplink Wireless Transmission, IEEE Vehicular Technology Mag., vol. 1, no. 3, pp , Sep [4] A.J. Paulraj, D.A. Gore, R.U. Nabar, and H. Bolcskei, An overview of MIMO communications A key to gigabit wire-less," Proc. IEEE, vol.92, no.2, pp , Feb [5] Ruder, M.A.; Dang, U.L.; Gerstacker, W.H.; User Pairing for SC-FDMA Transmission over Virtual MIMO ISI s, Global Telecommunications Conference, GLOBECOM IEEE. [6] WOLNIANSKY, P.W., et al.: V-BLAST: An architecture for realizing very high data rates over the rich-scattering wireless channel. Proc. IEEE ISSSE-98, Pisa, Italy, 30 September [7] J.-J. van de Beek, O. Edfors, M. Sandell, S. K. Wilson, and P. O. B orjesson, On channel estimation in OFDM systems, in Proc. 45 th IEEE Vehicular Technology Conf., Chicago, IL, July 1995, pp [8] W. Jakes and D. Cox, Microwave Mobile Communications. Wiley-IEEE Press, [9] M. Jankiraman, Space Time Codes and MIMO Systems. Boston, MA: Artech House, [10] E. Zimmerman, W. Rave, G. Fettweis, On the complexity of sphere decoding, Proc. Int. Symp. on Wireless and Pers. Multimedia Commun. (WPMC), in press, Sept. 2004