Novel Detection Scheme for LSAS Multi User Scenario with LTE-A MMB Channels Saransh Malik, Sangmi Moon, Hun Choi, Cheolhong Kim. Daeijin Kim, Intae Hwang, Non-Member, IEEE Abstract In this paper, we analyze the ergodic spectral efficiency upper bound of large-scale MIMO, key technologies including channel uplink detection. We also present new approaches for detection power allocation. Assuming arbitrary antenna correlation user distributions, we derive approximations of achievable rates with linear detection techniques, namely Zero Forcing (ZF), Maximum Ratio Combining (MRC), Minimum Mean Squared Error (MMSE) Eigen-Value Decomposition Power Allocation (EVD-PA).The approximations are tight in the large system limit with an infinitely large number of antennas user terminals (UTs), but match our simulations for realistic system dimensions. We further show that a simple EVD-PA detection scheme can achieve the same performance as MMSE with one order of magnitude fewer antennas in both uncorrelated correlated fading channels. Our simulation results show that our proposal is a better detection scheme than the conventional scheme for LSAS. Also, we consider the use of two channel environment channels for further analysis of our algorithm given as Long Term Evolution Advanced (LTE-A) Millimeter wave Mobile Broadb (MMB) channel.. Index Terms EVD-PA, LSAS, LTE-A, MMB, MMSE, MRC, Power Allocation, ZF. U I. INTRODUCTION SE of multiple antennas at the base stations (BSs) is an integral part of future wireless cellular systems [1-3] as it allows serving multiple User Terminals (UTs) simultaneously on the same resource block to counter inter intracell interference [4]. However, these advantages come at the cost of overhead for the acquisition of channel state information (CSI) at the BTSs. In Frequency-Division Duplexing (FDD) systems, this overhead scales linearly with the number of antennas renders the use of very large antenna arrays essentially impossible [5]. In Time-Division Duplexing (TDD) systems where channel reciprocity can be exploited, the training overhead scales linearly with the number of UTs. Hence, additional antenna elements can be added at no overhead cost to significantly improve the system "This research was supported by the MSIP (Ministry of Science, ICT Future Planning), Korea, under the ITRC (Information Technology Research Center) support program (NIPA-2014-H0301-14-1014) supervised by the NIPA(National IT Industry Promotion Agency)". "This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2013R1A1A2007779)". Authors are with Chonnam National University, Republic of Korea (phone: +82-062-530-0654; fax: +82-062-530-0659; e-mail: saranshmk@ gmail.com, msm0804@naver.com, chnss8812@naver.com, chkim22@chonnam.ac.kr, djinkim@jnu.ac.kr hit@jnu.ac.kr). performance [6]. Due to the low power consumption high spectrum efficiency, LSAS can offer excellent green technology Quality of Service (QOS) benefits. Fig. 1. Singe Cell Multiuser LSAS system. In Fig. 1, we show the exemplary LSAS system proposed in recent researches [7]. It has been proved from previous work that the system performance is limited by pilot contamination, the simplest detector, i.e. MRC ZF, are optimal, the transmission power can be made arbitrarily small when the number of antennas approaches infinite [7,8]. Numerous papers have researched on transmission mechanisms of MU-MIMO. Simple Zero-Forcing (ZF) based linear algorithms were proposed in [9] [10] for MU-MIMO where the transmitters receivers are equipped with multiple antennas. In a single-cell system, it is always advantageous to have an unlimited number of antennas at the transmitter [1] also at the receiver. In [11], the author proposed massive MIMO systems using a simple linear algorithm MRC in uplink. In [12], the downlink performance of MRT ZF beamforming for massive MIMO systems were investigated. In this paper, we design the massive MIMO downlink, considering explicitly for path loss, Multi-User (MU). The similar model was analyzed in [11] for the uplink. We consider a large system limit where the number of BTS antennas N the number of UTs grow infinitely large at the same speed derive approximations of achievable rates for different detection strategies, i.e., ZF, MRC, MMSE our proposal Eigen EVD-PA. These approximations are easy to compute shown by simulations to be accurate for realistic system dimensions. We further demonstrate that even a simple detection scheme, such as EVD-PA, outperforms MMSE achieves a similar performance with one order of magnitude fewer antennas per UT. Our simulation results clearly explain
proposed detection scheme EVD-PA is well suited for large scale MIMO in LTE-A MMB. Proposed system can outperform basic detection schemes in massive MIMO by using SINR of user allocating the power at each UE. The paper is organized as follows: In Section II, we describe the system model derive achievable Uplink rates of detection schemes with the conventional techniques proposed EVD-PA scheme. Section III contains power allocation scheme explaining the concepts with SINR various achievable rate. In Section IV, we present some numerical results with LTE-A MMB channel scenarios, in Section V we give the final conclusion based on our analysis of experimental results of detection scheme in different channel environments. Additional mathematical algorithms are given in Appendix. II. SYSTEM MODEL AND PROBLEM FORMULATION A. Detection Schemes In this section, we discuss the conventional detection schemes for large scale antenna system. We analyze ZF, MRC MMSE with our proposed EVD-PA scheme, whose performance is mainly based on the performance of power allocation scheme proposed in next section. The channel matrix from the BTS to K multiple UTs can be written as (3) where,, the component, consists of path loss fading, is a constant related to carrier frequency antennas gain, is the distance between BTS UT k, is the path loss exponent, represents shadowing with the distribution of, where, is the shadowing variance component in fast fading channel matrix is. For a single user based detection scheme the estimated symbol x of UT in its cell by calculating the product of received signal vector linear vector detector value G. Which are thoroughly calculated in following subsections for each detector case of MRC, ZF, MMSE EVD-PA. Overall SINR for this case is given as (4) Fig. 2. System Model of Detection schemes Consider a cellular system consisting of BTS l equipped with N antennas K (where, K<<N) UTs, each UT equipped with single antenna, as schematically shown in Fig. 2. Detection of an antenna array is often said to direct the signal from the antenna array towards BTS. The assumption that users have single antennas can be considered as a special case of users having multiple antennas when we treat the extra antennas as if they were additional autonomous users. We consider the addition of noise interference of signal from neighboring cells. The composite received K 1 vector y at the users can be described as (1) where, H is a composite N K channel matrix, given by H=, is the transmission power z is the transmitted vector across the N antennas, n is a noise vector with unit variance. The M 1 transmit vector z contains a pre-coded version of the K 1data symbol vector x. Through detection at the receiver side we have (2) where, G is a N K detection matrix including power allocation to the data symbols. The vector x comprises data symbols from an alphabet, each entry has unit average power,. Taken together, the energy constraints on x z yield power constraint on, where Tr ( ) is the trace-operator ( ) H denotes the Hermitian transpose. is the SNR gap between Shannon channel capacity a practical scheme achieving the BER [12]. Now, since we have the expression for power allocation SINR for the overall UE in the massive MIMO cell. Now, we just need to calculate the G matrix for each detection schemes as ZF, MRC, MMSE EVD-PA. MRC Detection The design of MRC based on CSI using the combination of all CSI combined at BTS. Where, H is the channel c is the constant of power normalization. (5) ZF Detection ZF pre-coding eliminates the interference of transmitting the signals from the users which is nullified in the direction of other users. The ZF detector is given as. (6) where, channel matrix H. is the pseudo inverse of the MMSE Detection Here, the transmit weights are taken as, scalar power constraint, H is channel, I is channel coefficient [13]. (7) This p u has the interpretation of normalized transmit power per UT. We use the result of [12] which minimized the sum of squared errors at all the users receivers, obtained the simple, closed-form solution, as (8) EVD-PA Detection Here, we made an assumption that the element of channel matrix H is Rayleigh distributed the covariance matrix. We now diagonalise using Eigen Value Decomposition (EVD), (9)
where,, (.)H is the complex conjugate transpose operator. is unitary denotes eigen value of. It has been demonstrated that the beam direction satisfies. It uses channel with power normalization as (10) Finally, ξ is normalization scalar power constraint III. NOVEL POWER ALLOCATION ALGORITHM FOR LSAS In this section, detailed analysis is given firstly, then the approximately optimal power allocation is given the power allocation algorithm is developed. According to the description in previous section, rom channel vectors are independent of rom vector. Denote, then are i.i.d. Gaussian Rom Variable (GRV) with parameters (1,1) according to [14]. Denote, then is also GRV with parameters (N,1). Since the expectation of is E[ ]=1, then, (11) (12) As shown in (5), the SINR at BTS l is complicated, the optimal power allocation is impossible to be got by it. In order to develop the power allocation algorithm, we have to consider the maximum approximation case as [8], by this we consider the simplified SINR values as (13) Parameter TABLE I SIMULATION PARAMETERS Value Bwidth 20 MHz Sample frequency 30.72 MHz Subframe duration 1 ms Subcarrier spacing 15 khz FFT size 2048 Occupied subcarriers 1200 No. of subcarriers/prb 12 No. of available PRBs 100 CP size (samples) 512 (Extended CP) No. of OFDM symbols/slot 6 (Extended CP) Modulation scheme QPSK, 16QAM Noise AWGN Antenna Configuration 100~Unlimited No. of User 100 Channel models Detection Scheme Flat, EPA, EVA, ETU MRC, ZF, MMSE, EVD-PA TABLE II POWER DELAY PROFILE FOR LTE-A CHANNEL Channel τmax [ns] Bc [MHz] EPA 410 2.5 EVA 2510 0.4 ETU 5000 0.2 power delay profile (PDP) of various channel scenarios in 3GPP LTE-A. In this case, we have performed the simulation for ETU case which has the maximum delay spread simple case with Flat channel. (14) (15) (16) The rate of uplink for the whole l BTS cell is given by (17) IV. SIMULATION RESULTS The simulation results are based on the link level Monte Carlo simulations. We have used two scenarios for our proposal simulation performance given LTE-A another is MMB. In the section-a, simulation parameters are based on 3GPP LTE-A 20 MHz bwidth are given as A. Simulations on LTE-A Environment Table I shows the general simulation parameters gives a definition of the environment simulated. Table II, shows the Fig. 3. Spectrum Efficiency performances of Detection technique in Flat channel. Fig. 3 simulations results show the performance of Spectrum Efficiency of detection schemes in LTE-A Flat Channel. Since, in Flat channel the impulse response is stationary. Here, we observe spectral efficiency with 400+ antenna system case of LSAS in Perfect CSI. Performance Rate is shown best with the MRC as the worst case of SE as 70 bps/s/hz compare to ZF whose maximum achieved SE is at least 75 bps/s/hz with a minimum 22 bps/s/hz. On the other h, MMSE achieves 78bps/s/Hz our proposed EBF-PA gains 4 bps/s/hz more at 82 bps/s/hz with the minimum performance of similar to MMSE. The system clearly shows better stability better
approach for required power normalization with our proposal EVD-PA. Fig. 4. Spectrum Efficiency performances of Detection technique in ETU channel. Fig. 4 simulations results show the performance of detection schemes in ETU Channel. ETU channel performance is considered to be the worst channel performance. But, the performance is similar to that of the flat channel so we can say that the performance is of the schemes are unaffected by variation of channel impulse response high Doppler spread. We can say that the EVD-PA can outperform the conventional algorithms in any scenario can easily combat Inter User Interference (IUI) also Inter Symbol Interference (ISI). B. Simulations on MMB-A/B/C Channel Environment Table III shows the general simulation parameters gives a definition of the environment simulated. Table IV, shows the power delay profile (PDP) of various channel scenarios in MMB A/B/C channels. We can see the best channel case is MMB-A worst case channel is MMB-C based on PDP. But, we discuss all the cases in MMB channel. Fig. 6. Spectrum Efficiency performances of Detection technique in MMB-B channel. Fig. 6 shows the spectrum efficiency performance of similar algorithms in MMB-B channel environment. Here, as well EVD-PA outperforms the conventional algorithms, but, similar to previous case the performance improves in the case of MMB-B channel. So, if we implement EVD-PA algorithm with MMB channel it can outperform the basic algorithms. Parameter TABLE III SIMULATION PARAMETERS Value Carrier Frequency 28 GHz Bwidth 500 MHz Sample frequency 552.96 MHz Subframe duration 1 ms Subcarrier spacing 270 khz FFT size 2048 Occupied subcarriers 1728 No. of subcarriers/prb 18 No. of available PRBs 96 CP size (samples) 512 (Extended CP) No. of OFDM symbols/slot 27 (Extended CP) Modulation scheme QPSK, 16QAM Noise AWGN Antenna Configuration 100~unlimited No. of Users 100 Channel models MMB channel models: MMB-A/MMB-B/MMB-C Fig. 5. Spectrum Efficiency performances of Detection technique in MMB-A channel. Fig. 5 shows the spectrum efficiency performance of similar algorithms in MMB-A channel environment. Clearly, EVD-PA outperforms the conventional algorithms. But, if we compare the performance with LTE-A channel case the performance improves in this case. TABLE IV POWER DELAY PROFILE FOR MMB-A/B/C CHANNEL Channel τmax [ns] Bc [MHz] MMB-A 75 13.3 MMB-B 753.5 1.3 MMB-C 1388.4 0.7
, the rank of the matrix is K., So, is invertible the power allocation expressed as Fig. 7. Spectrum Efficiency performance of Detection techniques in MMB-C channel. Fig. 7 the spectrum efficiency performance of similar algorithms in MMB-C channel environment. Compare to MMB-A/B channel the performance is severely degraded in this case due to high Delay spread. The case MMB-C is observed to be very unstable compared to MMB-A/B, as the involvement of ISI, which reduced the overall system performance. The spectral efficiency is considerably reduced in MMB-C case. V. CONCLUSION We show that the proposed Detection scheme EVD-PA is well suited for large scale MIMO in Multiuser environment. Lower bounds are considered for power normalization fading environments. We observed the detection schemes in LTE A MMB channel environments. LTE-A performance proved better for Massive MIMO case for present simulation results compared to MMB system. Generally, ZF outperforms MRC showing ability to cancel intracell interference. But, in multicell case with strong pilot contamination, this advantage will probably diminish. For the future prospect, we can implement discussed algorithm for channel estimation through pilots also in imperfect CSI. Moreover, they can be implemented for pilot contamination scenario. We can also be implemented with the time variant/ invariant channel cases. REFERENCES [1] T. L. Marzetta, Noncooperative Cellular Wireless with Unlimited Numbers of Base Station Antennas, IEEE Trans. Wireless Communications, vol. 9, no. 11, pp. 3590-3600, Nov. 2010. [2] A. Pitarokoilis, S. K. Mohammed, E. G. Larsson, "On the Optimality of Single-Carrier Transmission in Large-Scale Antenna Systems", IEEE Wireless Commun. Lett., vol. 1, no. 4, pp. 276-279, Aug. 2012. [3] M. Hong, R-Y. Sun, H. Baligh, Z-Q. Luo, "Joint Base Station Clustering Beamformer Design for Partial Coordinated Transmission in Heterogenous Networks", IEEE J. Sel. Areas Commun, vol. 31, no. 2, pp. 226-240, Feb. 2013. [4] T. L. Marzetta, How much training is required for multiuser MIMO? in Proc. Asilomar Conf. on Signals, Systems Computers, Urbana Champaign, Illinois, US, Sep. 2006, pp. 359?363. [5] F. Rusek et al., Scaling Up MIMO: Opportuities Challenges with Very Large Arrays, IEEE Signal Processing Magazine, vol. 30, no. 1, pp. 40-60, Jan. 2013. [6] J. Hoydis, S. ten Brink, M. Debbah, Massive MIMO in the UL/DL of Cellular Networks: How Many Antennas Do We Need? IEEE J. Sel.Area Commun., vol. 31, no. 2, pp.160-170, Feb. 2013 [7] Q. Spencer, A. L. Swindlehurst, M. Haardt, Zero-forcing methods for downlink spatial multiplexing in multiuser MIMO channels, IEEE Trans. Signal Process., vol. 52, pp. 462 471, Feb. 2004. [8] C.B. Chae, D. Mazzarese, N. Jindal, R. W. Heath, Jr., Coordinated beamforming with limited feedback in the MIMO broadcast channel, IEEE J. Sel. Areas Commun., vol. 26, no. 8, pp. 1505 1515, Oct. 2008. [9] B. K. Lau, E. G. Larsson, T. L. Marzetta, O. Edfors, F. Rusek, D. Persson, F. Tufvesson, Scaling up MIMO: Opportunities challenges with large arrays, IEEE Signal Process. Mag., vol. 30, no. 1, pp. 40?60, Jan. 2013 [10] Rusek, F.; Persson, D.; Buon Kiong Lau; Larsson, E.G.; Marzetta, T.L.; Edfors, O.; Tufvesson, F., "Scaling Up MIMO: Opportunities Challenges with Very Large Arrays," Signal Processing Magazine, IEEE, vol.30, no.1, pp.40,60, Jan. 2013 [11] C. He et al., Energy Efficiency Spectral Efficiency Tradeoff in Downlink Distributed Antenna Systems, IEEE wireless commun., Let.,vol. 1, no. 3, pp. 153-156, June, 2012. [12] Y. Yang et al., Transmitter Beamforming Artificial Noise with Delayed Feedback: Secrecy Rate Power Allocation, Journal of Communications Networks, vol. 14, no. 4, pp. 374-384, Aug. 2012. APPENDIX When the massive MIMO system adopts detection, the approximately power allocation vector achieving the optimal PA where,, where,, unique globally optimal power allocation. As the independence of