Improved channel estimation for massive MIMO systems using hybrid pilots with pilot anchoring

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1 Improved channel estimation for massive MIMO systems using hybrid pilots with pilot anchoring Karthik Upadhya, Sergiy A. Vorobyov, Mikko Vehkapera Department of Signal Processing and Acoustics Aalto University, School of Electrical Engineering Espoo, Finland Department of Electronic and Electrical Engineering The University of Sheffield Sheffield, UK WSA Mar 2017 Berlin

2 Outline Channel estimation and pilot contamination in massive MIMO Review of superimposed pilots for massive MIMO Improving superimposed pilots with pilot anchoring Simulation Results

3 Pilot Contamination Time-multiplexed Pilots Uplink time slot is partitioned for pilots and data τ C d Pilots Uplink Data Downlink Data C u Orthogonal pilots are used to estimate the channel of K users The same pilot sequences are shared between L neighboring cells

4 Pilot Contamination Time-multiplexed Pilots: Uplink Received signal during training at desired BS (l = 0) L 1 Y = H l Φ T + W C M τ l=0 H l : M K channel matrix between desired BS and users in cell l Φ : τ K orthogonal pilot sequences (Φ T Φ = τ I) The least squares estimate of the k th user at desired cell 0,k 1 L 1 τ Yφ k = h 0,k + h l,k + n 0,k ĥ TP l=1 h l,k : k th column of H l, h l,k CN (0, β l,k I) φ k : k th column of Φ

5 Overview of Superimposed Pilots Superimposed Pilots (1/2) Pilots of length C u are transmitted along the data Ideally C u KL orthogonal pilots used; no overhead in time-domain, but causes interference between data and pilots Received signal at BS j when employing superimposed pilots L 1 Y = K 1 l=0 k=0 h l,k (ρx l,k + λp l,k ) T + W C M Cu ρ 2 and λ 2 : fractions of the transmit power reserved for data and pilots, respectively, such that ρ 2 + λ 2 = 1 p l,k : C u 1 orthogonal pilot transmitted by user k of cell l x l,k : C u 1 data vector transmitted by user k of cell l

6 Overview of Superimposed Pilots Superimposed Pilots (2/2) The least squares estimate of the channel when C u KL ĥ 0,k = Yp 0,k λc u = h 0,k + ρ λc u L 1 K 1 l=0 m=0 h l,m x T l,mp 0,k + n 0,k Uplink data, estimated using a matched filter (MF) x T 0,k = 1 ( ) ρmβ ĥh 0,k Y λĥ0,kp T 0,k 0,k and the usual MF precoding with channel estimate in downlink

7 Overview of Superimposed Pilots Performance Overview of Superimposed Pilots Values of ρ and λ that maximize SINR lower bound in UL Data power: ρ 2 opt M+LK C u Pilot power: λ 2 opt = 1 ρ 2 opt Cu M+LK The resulting DL SINR reads SINR SP dl 0,k ρopt,λopt Cu (M + LK)β 2 0,k K 1 L 1 βl,m 2 m=0 l=0 Increases as M if the assumption LK C u holds

8 Overview of Superimposed Pilots Comments on Performance of Superimposed Pilots The UL performance of time-multiplexed pilots is limited by inter-cell interference. On the other hand, the UL performance of superimposed pilots is limited to a large extent by intra-cell interference. The UL performance of these pilot transmissions are complementary However, downlink performance of superimposed pilots is significantly better than time-multiplexed pilots Therefore, the objective of this work is to use superimposed pilots to improve the resilience of the channel estimate obtained from time-multiplexed pilots to pilot contamination

9 Proposed Method Proposed Pilot Structure C u τ Time Multiplexed Pilots Superimposed Pilots + Uplink Data Downlink Data τ C d The received signal in UL at BS j = 0 has two parts Y = [Y p, Y s ] where L 1 Y p = H l Φ T + W p Y s = l=0 L 1 K 1 l=0 k=0 h l,k (ρx l,k + λp l,k ) T + W s

10 Proposed Method Objective Reduce the inter-cell component of UL interference in superimposed pilots using time-multiplexed pilots This is accomplished by adding a shaping constraint on the LS objective function The pilot sequences are used as known data to implement this shaping constraint

11 Proposed Method Proposed Method (1/4) The optimization problem can be written as where ĥ 0,k = arg min Y s hλp T h 0,k 2 F subject to 1 M hh Y p = φ T 0,k L 1 Y s = Y p = K 1 l=0 k=0 L 1 l=0 h l,k (ρx l,k + λp l,k ) T + W s H l Φ T + W p

12 Proposed Method Proposed Method (2/4) This optimization problem has an equivalent form ĥ 0,k = arg min h ĥsp h 0,k 2 2 subject to 1 M hhĥtp 0 = e T k where e k is the k th column of the identity matrix. ĥ SP 0,k Y s = L 1 K 1 l=0 k=0 L 1 Ĥ TP 0 Y p = H l Φ T + W p l=0 h l,k (ρx l,k + λp l,k ) T + W s

13 Proposed Method Proposed Method (3/4) Setting x = h ĥsp 0,k, the optimization problem can be simplified as min x x 2 2 subject to (ĤTP 0,k ) H x = Mek (ĤTP ) H 0,k ĥsp 0,k This problem has the form of the generalized sidelobe canceller [ ] min x H Rx subject to C H x = d x ( ) which has the optimal solution x = R 1 C C H R 1 C d, where R is positive definite Sergiy A. Vorobyov, Principles of minimum variance robust adaptive beamforming design, Signal Processing, Volume 93, Issue 12, December 2013, Pages , ISSN

14 Proposed Method Proposed Method (4/4) Since x = h ĥsp 0,k, the output of the channel combiner is ĥ 0,k = ĤTP 0,k ( (ĤTP 0,k ) H ĤTP 0,k The UL data is then estimated as ) 1 ( Me m x 0,k T = MρĥH 1 0,kY s λp T 0,k (ĤTP ) ) H 0,k ĥsp 0,k + ĥsp 0,k

15 Simulation Simulation Setup Number of cells in system (L) : 7 Number of users per cell (K) : 5 Uplink duration (C u ) : 40 > 7 5 symbols Cell Radius : 1km Path-loss exponent : 3 No shadowing Constellation : QPSK Two channel scenarios are considered Scenario 1 : Users are uniformly distributed across the cell. Scenario 2 : Users in all cells are equally spaced on a circle.

16 Simulation Uplink BER Performance - Scenario 1 (Uniform) 10 1 Time-multiplexed - ZF Pilot anchoring Superimposed pilot 10 2 UL BER ,000 1,500 2,000 2,500 3,000 3,500 4,000 Figure: Uplink BER of users in reference cell vs M M

17 Simulation Uplink SINR - Scenario 2 (Circle) Time-multiplexed - ZF Pilot anchoring Superimposed Pilot UL SINR Radius Figure: Uplink SINR of an arbitrary user vs user radius. M = 300.

18 Simulation Downlink BER - Scenario 1 (Uniform) DL BER Time-multiplexed Pilot anchoring Superimposed pilot M Figure: Downlink BER vs M

19 Simulation Downlink SINR - Scenario 2 (Circle) Time-multiplexed Pilot anchoring Superimposed pilot DL SINR Radius Figure: Downlink SINR of an arbitrary user vs user radius. M = 300.

20 Simulation Summary Superimposed pilots can augment a system with time-multiplexed pilots to improve receiver performance Instead of anchoring with known data/pilots, the proposed method can be easily modified to anchor with estimated data, and the equality constraint can be replaced with a norm-constraint The above can be implemented via an iterative method that tries to cancel both intra- and inter-cell interference

21 Simulation Thank You. Any Questions?

22 Simulation Backup Slides

23 Simulation Alternative Norm Constraint for Estimated Data The optimization problem with the norm constraint can be written as ĥ 0,k = arg min Y s λhp T h 0,k 2 F subject to 1 M hh Y d ĉ T 2 0,k < ɛ where ɛ is a design parameter, ĉ 0,k are the N decoded symbols of user m in cell j, and Y d is the corresponding matrix of received symbols. The above optimization problem is a quadratically constrained quadratic program (QCQP)

24 Simulation Performance Overview of Superimposed Pilots The asymptotic uplink SINR after MF SINR SP ul 0,k = β0,k 2 L 1 1 K 1 λ 2 C u βl,k 2 l=0 k=0 The downlink SINR for large M when using MF precoding SINR SP dl 0,k = β 2 0,k ρ 2 L 1 λ 2 C u l=0 K 1 βl,k 2 k=0

25 Simulation Uplink BER Performance - Scenario Time-multiplexed - ZF Pilot anchoring Superimposed pilot UL BER Radius Figure: Uplink BER of users in reference cell vs user radius with M = 300

26 Simulation Downlink BER - Scenario Time-mulitplexed Pilot anchoring Superimposed pilot 10 2 UL BER Radius Figure: Downlink BER vs user radius

Random Access Protocols for Massive MIMO

Random Access Protocols for Massive MIMO Elisabeth de Carvalho Jesper H. Sørensen Petar Popovski Aalborg University Denmark Emil Björnson Erik G. Larsson Linköping University Sweden 2016 Tyrrhenian International