High Performance Interference Suppression in Multi-User Massive MIMO Detector
Andrey Ivanov, Alexander Osinsky, Dmitry Lakontsev, Dmitry Yarotsky
HHigh Performance Interference Suppressionin Multi-User Massive MIMO Detector
Andrey Ivanov, Alexander Osinsky, Dmitry Lakontsev, Dmitry Yarotsky
Skolkovo Institute of Science and TechnologyMoscow, [email protected], [email protected], [email protected], [email protected]
Abstract —In this paper, we propose a new nonlinear detectorwith improved interference suppression in Multi-User Multiple In-put, Multiple Output (MU-MIMO) system. The proposed detectoris a combination of the following parts: QR decomposition (QRD),low complexity users sorting before QRD, sorting-reduced (SR)K-best method and minimum mean square error (MMSE) pre-processing. Our method outperforms a linear interference rejec-tion combining (IRC, i.e. MMSE naturally) method significantlyin both strong interference and additive white noise scenarioswith both ideal and real channel estimations. This result has wideapplication importance for scenarios with strong interference, i.e.when co-located users utilize the internet in stadium, highway,shopping center, etc. Simulation results are presented for the non-line of sight 3D-UMa model of 5G QuaDRiGa 2.0 channel for 16highly correlated single-antenna users with QAM16 modulationin 64 antennas of Massive MIMO system. The performance wascompared with MMSE and other detection approaches.
Index Terms —Massive MIMO; MIMO Detection; InterferenceCancellation; Multi-User MIMO
I. I
NTRODUCTION
The fifth generation (5G) of wireless systems will demandmore users with a much higher overall capacity [1]. In recentyears, multi-user Massive Multiple Input, Multiple Output(MU-MIMO) and massive MIMO have been adopted as thekey technologies to address the capacity requirements of en-hanced Mobile Broadband (eMBB) in G [1], [2]. MIMOdetection [3] is a method of antennas digital signal processingto extract user signals in an uplink channel of a base station.Compared to conventional MIMO systems, which have alreadyreached their throughput limits, massive MIMO has becomethe most promising candidates to increase transmission datarate over wireless networks. In massive MIMO systems, eachbase station is equipped with tens or hundreds of antennasdedicated to serving tens of users. It has been proved [2] thata massive MIMO system can increase the spectrum efficiencyof a wireless channel by several times. Spatially multiplexedMIMO systems can support several independent data streams,resulting in a significant increase of the system throughput [1],[2] due to multiple spectrum reuse. In this context, a greatdeal of effort has been made in the development of multi-userMassive MIMO detection method, which is robust to unknowninterference from users of other (neighbour) cells [4].
The research was carried out at Skoltech and supported by the RussianScience Foundation (project no. 18-19-00673).
A. ML detector
The maximum likelihood (ML) detector performs an exhaus-tive search by calculating the Euclidean distance for everypossible symbol vector candidate. The number of candidatesymbol vectors grows exponentially with the number of usersand the number of bits per constellation point [5], [6], [7].Thus, with high order constellations (QAM or higher) in MU-MIMO mode, ML detection becomes computationally heavy.The ML estimation is given in the frequency domain by [3]: y = Hx + n + i , (1) x ML = arg x min (cid:107) y − Hx (cid:107) , where y is the frequency domain received signal vector of size N ; N is the number of RX antennas; H is the channel matrixof size [ N × M ] , x is the TX vector of size M ; M is thenumber of single-antenna users in the uplink channel; n is thewhite noise; i is the interference (unknown); x ML is the MLestimation of vector x . B. Single user MMSE detector
Linear detection methods [3], [8] consider the input-outputrelation of a MIMO system as an unconstrained linear estima-tion problem, which can be solved by using minimum meansquare error (MMSE) method. The resulting unconstrainedestimate ignores the fact that the transmitted symbols are froma limited set of constellation points. Let us describe the baselineMMSE detector for one single antenna user and N = 3 receiving antennas of the base station. Define h as a vectorof frequency domain channel estimations for one subcarrier: h = (cid:2) ˆ h ˆ h ˆ h (cid:3) T Define (interference + noise) signal as follows: u k = n k + i k , where k is the antenna index. Define (interference + noise)covariance matrix as: R uu = E u u u (cid:2) u ∗ u ∗ u ∗ (cid:3) (2) R uu = R R R R R R R R R (3) a r X i v : . [ c s . OH ] M a r ssume interference + noise matrix R uu has the same valueinside each resource block. This assumption is quite valid sincethe interference power from other cells is also approximatelythe same inside each resource block in frequency domainand the same inside time transmission interval in the timedomain. Therefore, in case of smooth channel response insidethe mentioned time and frequency unit, element of R uu matrixin equation (2) can be estimated as: (cid:98) R uu ( j, k ) = E ( u j u ∗ k ) , where j, k are antenna indexes; u ∗ is the complex conjugate of u . In practice, u k can be estimated with reference signals as: (cid:98) u k = y k − ˆ h k x The MMSE detection algorithm is intended to minimize e = | x − (cid:98) x | and can be obtained as a frequency domain Wienerfilter [9], as expressed by the classical equations: (cid:98) x = wyw = R − yy h H , (4)where w is the weight vector, h is the channel estimation vectoras described in [10] and [11], y = (cid:2) y y y (cid:3) T , covari-ance matrix R yy of the received signal is defined similarly to(2). The matrix R yy can also be calculated as: R yy = R uu + hh H (5)From equations (4) and (5) using the Sherman–Morrison for-mula we can derive the MMSE estimation as: w = h H R − uu h H R − uu h (6)In equation (5) the matrix R uu is an interference plus noisematrix, which is responsible for interference suppression, i.e.interference rejection combining (IRC). It focuses null of the w pattern to the interference sources to suppress it, while h focuses the main beam to the user, i.e. Maximum RatioCombining (MRC). C. Multi-user MMSE detector
Assume we have M single antenna users per subcarrier. Inthis case the MMSE detector is given by: (cid:98) x = W y , W = ( σ n I + H H R − uu H ) − H H R − uu , (7)where (cid:98) x is the linear estimation of the frequency domain vector x ; W is the weight matrix of size [ N × M ] ; σ n is the RXantennas noise power; I is the identity matrix of size [ M × M ] .In case of i = , equation (7) represents the MRC detector: W = ( σ n I + H H H ) − H H (8)Linear detection schemes are simple, but unfortunately, theydo not consider the lattice structure of the transmitted complexamplitudes x , and, therefore, do not provide good enough per-formance, especially when the channel matrix is near singular. D. MMSE OSIC detector
MMSE with ordered successive interference cancellation(MMSE-OSIC) detection is performed with QR decomposition(QRD) of the permuted channel matrix H perm , which isdefined as in [9], [12] and [13]: y ext = H perm x perm + n + i , x perm = P x , H perm = P H ext , (9) H ext = (cid:2) H T (cid:112) σ n + σ i I (cid:3) T , y ext = (cid:2) y T (cid:3) T , where σ i is the RX antennas interference power, P is thepermutation matrix, x perm is the permuted version of x , and H ext matrix is utilized instead of H for the regularization rea-son. MMSE with ordered successive interference cancellation(OSIC) detector is based on QR factorization of the channelmatrix as shown in [12]: H perm = QR , Q H y ext = (cid:16) Q H Q (cid:17) Rx perm + Q H ( n + i ) , Q H y ext = Rx perm + Q H ( n + i ) , (10)where R is the [( N + M ) × M ] upper triangular matrix; P is the permutation matrix. Detection starts with x perm ( M ) amplitude detection and stops after x perm (1) calculation ac-cording to the upper triangle matrix R structure. Therefore, theinitial vector x can be derived as x = P T x perm . The MMSE-OSIC method demonstrates better performance in comparisonwith the MMSE detection, but the gain is limited due to errorpropagation, caused by non-ideal user sorting before QRD, highcorrelation among layers and imperfect channel estimation. Theusers sorting is intended to reorder diagonal elements of theupper triangular matrix R in ascending order to prevent errorpropagation in MU-MIMO scenario.Using only MMSE-OSIC doesn’t achieve the best perfor-mance in multi-user scenarios of × MIMO system.Therefore, a post-processing K-best algorithm should be used toenhance performance in acceptable complexity, as described in[5], [6], [7]. Sorting reduced K-best (SR-K-best in [5]) is a ver-sion of the K-best with low sorting complexity. Sorting the best K survivors from KM candidates, where M = 4 , is reduced tosorting the best S from much less number of candidates, whilethe residual K − S survivors are defined as ”most expected”and taken from the full candidates set of size KM beforethe sorting according to a special selection algorithm. Thepaper [5] proposes SR-K-best with parameters ( K, S, p ) . Thevector p means the positions of the ”most expected” candidates.Unfortunately, the SR-K-best with ( K, S, p ) parameters alsoresults in performance losses in high correlated scenarios.Therefore, we utilize a new flexible structure ( K, S, p , v , q ) of SR-K-best algorithm [6], [7]. The vector v defines a set oforting child nodes (i.e. a set for S sorted candidates search);while the vector q defines the location of S sorted candidates inthe final composed list of K candidates for the next detectioniteration.Finally, MMSE-OSIC with the optimized user sorting andthe SR-K-best demonstrates performance close to the maximumlikelihood algorithm in the additive white noise channel, i.e. incase of i = in (10). However, the mentioned MMSE-OSICis quite sensitive to external interference from unknown users(when i (cid:54) = ), while the basic MMSE algorithm is robust tothe correlated noise due to the IRC algorithm with the matrix R uu . To overcome the interference suppression problem, wepropose a new pre-processing algorithm.II. S IMULATION TOOL
QuaDRiGa, short for ”QUAsi Deterministic RadIo channelGenerAtor” [14], is mainly used to generate realistic radiochannel responses for use in system-level simulations of 5Gmobile networks. We test our algorithms in high correlated 3D-UMa, BERLIN-UMa and DRESDEN-UMa non-line of sight(NLOS) models of MIMO × scenario for users with aspeed of km/h. The number of users = is chosen as themax number of active users per subcarrier in a cross-polarized RX antennas system according to G standard [2]. Theantenna array is mounted on meters high and consists of co-located rectangle subarrays with antennas each. Thecarrier frequency is . GHz, a maximum distance to the useris meters. The interference is given by unknown userswith QAM16 modulation and approximately the same poweras target users. A short D fragment of the channel magnitudespectrum is shown in Fig. 1.Fig. 1: Magnitude spectrum of QuaDRiGa channelIII. SR-K- BEST DETECTOR
A functional scheme of the QRD-based detection approachis shown in Fig. 2. It consists of pre-processing and post-processing parts [5], [6]. Pre-processing is required to calculatesorted QRD in two steps.
Step : QRD interpolation, as described in [15].For QRD calculation in the MIMO system, we have to per-form the QRD for each subcarrier. In practice, the interpolation-based QRD only computes the Q and R matrixes for the pilotsubcarriers to reduce computational complexity. Then, the Q and R of the data subcarriers are interpolated from those ofthe pilot subcarriers. Step : users sorting (strings permutation in H ext ) isrequired to achieve the permutation matrix P in equation (9).Users sorting problem is well-known, for example, a post-sorting algorithm and pre-sorting solution are analyzed in [12].We take P matrix from QRD of the pilot symbols as the firststep of P matrix calculation for the data symbol to realizesorting track as proposed in [6]. The P matrix changes veryslowly from one symbol to another, and a low sorting complex-ity is required to update it. Loss function L = L { diag ( R ) } ofdiagonal entries of interpolated R matrix is used to guaranteethe least number of matrix P updates.Fig. 2: Detector schemePost-Processing part is represented by SR-K-best detec-tion. The ( K, S, p , v , q ) parameters were optimized in [6] forQuaDRiGa channel of × MIMO system and given by: ( K, S ) = (16 , , p = [2 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0] , v = [2 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2] , q = [2 4 6 8] . (11)Simulation results for Lattice Reduction Aided (LRA) OSICdetector [5], MMSE, ML and some other state-of-the-art detec-ton algorithms are presented in additive white noise (AWGN)channel in Fig. 3 for target users, bit error rate (BER) isgiven for uncoded case [6]. The SR-K-best detector of type ( K, S, p , v , q ) with ( K, S ) = (16 , parameters demonstratesperformance, close to ML. In Fig. 4 and Fig. 5 simulation re-sults are presented for the same coded users in scenario withlow-density parity-check (LDPC) decoder with (144 , codein the MIMO receiver for ideal and real channel estimations(DFT-based channel estimation from [10] was implemented).The min-sum decoding algorithm was utilized as described in[16]. The SR-K-best detector outperforms the MMSE detectorin the AWGN channel for both ideal and real channel estima-tion. Therefore, the SR-K-best detector with ( K, S ) = (16 , parameters is a good choice for the 5G receiver.IV. R OBUST
SR-K-
BEST DETECTOR
Simulation results of SR-K-best detector with parameters(11) are shown in Fig. 6 and Fig. 7 for target users withboth ideal and realistic channel estimation in an interferenceig. 3: Uncoded BER in AWGN channel with ideal CEFig. 4: Coded BER in AWGN channel with ideal CEenvironment with unknown users. It is clear that a commonSR-K-best detector demonstrates the gain in AWGN channelonly and does not detect users at the presence of interference,while the MMSE detector (7) is quite stable. It happens becausethe SR-K-best detector does not consider matrix R uu . Toovercome this problem, let us modify the SR-K-best pre- andpost-processing algorithms. Equation (1) is given by: y = Hx + u , (12)where u = i + n is the interference + noise signal. To avoidcorrelation between antennas in signal u we multiply (12) by (cid:113) R − uu as follows: (cid:113) R − uu y = (cid:113) R − uu Hx + (cid:113) R − uu u , (13) y = H x + u , (14) Fig. 5: Coded BER in AWGN channel with real CEwhere y = (cid:113) R − uu y , H = (cid:113) R − uu H and u = (cid:113) R − uu u .Autocorrelation matrix of vector u can be calculated as: E ( u u H ) = E (cid:18)(cid:113) R − uu uu H (cid:113) R − uu (cid:19) = (cid:113) R − uu E (cid:0) uu H (cid:1) (cid:113) R − uu = (cid:113) R − uu R uu (cid:113) R − uu = I, therefore, signal u represents uncorrelated noise. After apply-ing QR decomposition to matrix H we achieve the equation: y = Q R x + u (15)The result of multiplying (15) by Q H is given by: Q H y = Q H Q R x + Q H u y = R x + u (16)where y = Q H y is the modified input vector and u = Q H u is the new white noise signal. In fact, the users sortingcan be used with matrix H in (14) and further applying SR-K-best algorithm on (16) to achieve a fine detection performance.However, performance will be improved if we apply the MMSEdetection to get (cid:98) x from (16). Remember, that u is a whitenoise with the variance of σ = 1 , therefore, linear MRCdetector (8) can be utilized to (16) to calculate (cid:98) x as follows: (cid:98) x = ( I + R H R ) − R H y . (17) R H y = ( I + R H R ) (cid:98) x + u , y = (( R H ) − + R ) (cid:98) x + ( R H ) − u , where u is the leftover noise after MMSE. Finally, we achievethe equation: y = H (cid:98) x + u , (18)here H = (( R H ) − + R ) and noise u = ( R H ) − u .Then we again apply QR decomposition to matrix H toachieve the following equation: y = Q R (cid:98) x + u (19)The result of multiplying (19) by Q H is given by: Q H y = Q H Q R (cid:98) x + Q H u y = R (cid:98) x + u , (20)where y = Q H y and white noise is defined as u = Q H u .Finally, equations (18) and (20) are the best choice for SR-K-best detection according to out simulations and definesas Robust SR-K-best detector. Users sorting and permutationmatrix P calculation should be used with matrix H , whilepost-processing is implemented on the upper triangular matrix R . Simulation results are presented in Fig. 6 and Fig. 7for the Robust SR-K-best with parameters of (11) in theinterference scenario. It should be noticed, that the developednonlinear algorithm is robust to both interference and channelestimation errors (DFT-based channel estimation from [10] wasimplemented) and outperforms the linear MMSE.Fig. 6: Performance in interference channel with ideal CEV. C ONCLUSION
We proposed a new pre-processing for the nonlinear detectorstructure, which demonstrates significant performance gaincompared to the MMSE detector in scenarios with unknowninterference. Moreover, the achieved detector is robust to chan-nel estimation errors. Simulation results show that the proposedalgorithm is quite stable with non-ideal channel estimationin both AWGN and interference channels, while the MMSEdetector demonstrates BER saturation after the LDPC decoder.Traditionally, the linear detector is known to be the best solutionfor unknown interference scenarios or non-ideal channel esti-mation, but our results say that even in these cases performancecan be enhanced due to nonlinear detector nature. Simulationresults with modulation QAM16 and LDPC(144,288) decoderare provided for the co-located scenario with antennas of Fig. 7: Performance in interference channel with real CEMassive MIMO: single antenna target users and interferersin the D -UMa model of 5G QuaDRiGa 2.0 channel.R EFERENCES[1] M. Shafi et al., 5G: A Tutorial Overview of Standards, Trials, Chal-lenges, Deployment, and Practice,
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