Channel Prediction for Multiuser DownlinkLTE-TDD SystemsSubmit to IEEE GLOBECOM 2014

Qinxin LiuDepartment of Electrical and Electronic Engineering

Imperial College London, United KingdomEmail: qinxin.liu08@imperial.ac.uk

Mustafa K. GurcanMKGSYS Ltd., London, United Kingdom

Email: mkgurc56@gmail.com

Abstract—Base station side precoding takes the advantageof channel reciprocal properties in Long-Term Evolution TimeDivision Duplex (LTE-TDD) systems to achieve high data ratesfor multiple users. However, for proper precoder design, the basestation needs accurate up-to-date channel information. In thispaper, the forward-backward autoregressive (AR) process is em-ployed to predict the downlink channel of LTE-TDD systems. Theproposed integrated block diagonalization (BD) precoding andchannel predicting method can improve the sum system capacityin a time-variant Rayleigh fading channel environment that isbased on a Jakes model. The performance is compared with theconventional BD precoding method where channel prediction isnot present. The proposed approach is supported by computersimulation results which indicate that there are significant systemcapacity improvements under certain conditions.

Index Terms—Channel prediction, Block diagonalization (BD)precoding, OFDM, LTE-TDD, AR process, Multiuser MIMO

I. INTRODUCTION

Over recent years, the even increasing demand of high datarate transmission has led to a strong interest in multiple-inputmultiple-output (MIMO) systems. Compared to single-inputsingle-output systems, [1]–[3] showed that the channel capac-ity of a MIMO system with NTX transmit antennas and NRXreceive antennas, in principle, grows by the factor of number ofantennas without increasing transmission power or bandwidth.In practice, the performance of MIMO systems is influencedby the received signal-to-interference-and-noise-radio (SINR)and correlation properties of the MIMO channel. To improvethe system performance, signal processing techniques at thetransmitter, known as precoding techniques, are often used.Several precoding techniques have been successfully adoptedby the orthogonal frequency-division multiplexing (OFDM)based 3GPP Long Term Evolution (LTE) specifications [4].The main difficulty of spatial multiplexed MIMO systemsis the separation of the independent parallel data streamswith limited channel state information (CSI) available at thetransmitter side [5]. Also, it is shown in [6], that the entirechannel capacity of the MIMO channel can be achieved byusing nonlinear precoding.In frequency division duplexed (FDD) LTE systems, where

uplink and downlink channels are in the separated frequen-cies, feedbacks from the receivers are used to obtain the

CSI at the transmitter. However, the feedback informationsize grows exponentially as the number of antennas of thesystem increases. As in LTE time division duplexed (TDD)systems, where uplink and downlink channels share the sametransmission frequency, the CSI can be obtained using thereciprocal property of the channel. The problem with such asystem is that the transmitter may have the outdated CSI dueto the time varying property of the channel. [7] and [8] alsoshow how AR-based algorithms for channel estimation andprediction could be used in MIMO OFDM systems. On theother hands,various channel modelling approaches are studiedin [9] showing that the least-squares (or forward-backward)AR-modelling has better performance than that of Yule-Walkeralgorithm as used in [7] and [8] in low AR orders.This paper is focused on improving the total system capacity

of a MU-MIMO LTE-TDD system using forward-backwardAR modelling approach when there is delay in CSI estimation.The rest of the paper is organized as follows: In Section II,a MU-MIMO OFDM system model is proposed. Section IIIdescribes channel prediction and block diagonalization pre-coding algorithm in details. In Section IV, simulation resultsare presented while the last section concludes the paper.

II. SYSTEM MODEL

List of NotationsA,Λ Blackboard Bold and Greek capitals denote matrices.a Underlined letters denote column vectors.A, a Normal letters (capital or small) denote scalars.AH The Hermitian transpose of A.AT The transpose of A.A−1 The inverse of A.A F The Frobenius-norm of A.IN N ×N identity matrix.ON×M N ×M matrix of zeros.

Consider a simplified downlink M -user MIMO system (orbroadcast system) with a single base station (BS). Supposethe BS is equipped with NTX antennas and each user isequipped with NRX antennas. In this paper, the point-to-pointsystem is visualized as a (M ×NRX , NTX) MIMO systemwithM×NRX = NTX . With reference to Fig 1, the system is

partitioned into three main blocks, the base station, the channelthat associate to the ith user and the ith user’s receiver. Themain blocks of the system will be introduced and modelledin following sections. For simplicity, IFFT and Cyclic Prefix(CP) appending blocks at the base station, and FFT and CPremoval blocks at the ith user’s receiver are removed in thesystem model.

Fig. 1: Simplified multiuser OFDM downlink system.

A. Base Station TransmitterAssume the number of independent transmission spatial

streams (or spatial layers) per user NS equals to NRX , forsimplicity. Let Ts denote the OFDM sampling period, and

a subcarrier k = 1, . . . , NC , where NC is total number ofsubcarriers, is assigned with frequency given by Fk = k F ,where F = 1/Tcis the subcarrier spacing. For each subcar-rier, k, of the nth OFDM symbol of duration Tcs = NCTs,the precoded signals for the transmission can be expressed as

z [k, n] = F [k, n]x [k, n] . (1)

Dropping the subcarrier index, in our system model, theabove expression is then simplified to

z [n] = F [n]x [n] (2)

where

x [n] = xT1 [n] , · · · , xTM [n]T ∈ C(MNS)×1 (3)

contains transmission symbols for all users.

F [n] = F1 [n] , . . . , FM [n] ∈ CNTX×(MNRX) (4)

is the overall precoding matrix for all users and

F1 [n] , . . . , FM [n] ∈ CNTX×NRX

are complex precoding matrices for each user which will bediscussed in details in Section III. Note that Equation (2) canbe written as (at point D in Fig 1)

z [n] =M

i=1

Fi [n]xi [n] . (5)

B. User i Downlink ChannelAssuming the cyclic prefix (CP) is long enough to cope

with the maximum delay spread, the channel that associatedto ith user is defined as:

Hi [n] =

⎡⎢⎢⎣h(1,1)i [n] · · · h

(1,NTX)i [n]

.... . .

...h(NRX ,1)i [n] · · · h

(NRX ,NTX)i [n]

⎤⎥⎥⎦ (6)

where h(nRX ,nTX)i [n] donates the complex channel transferfunction gain from the BS transmitter antenna nTX to the ithuser equipment receiver antenna nRX . Hence the ith user’sreceived signal vector (at point E in Fig 1) can be writtenas follows:

ri [n] = Hi [n] z [n] + ni [n] (7)

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where is the ith user’s downlink channel transfer functionmatrix that is obtained using the reciprocal property of theuplink channel, and ni [n] represents the complex valuedadditive white Gaussian noise (AWGN) vector with noisepower equals to 2σ2n.

C. User i ReceiverReferring to Equation (7), the received signal ri for the ith

user is recovered with a minimum-mean-square-error (MMSE)detector which compensates the amplitude and phase distortionand inter-antenna interference that introduced by the channeland the process of precoding. We assume complete channelstate information (CSI) is available at the receiver, the nor-malized MMSE weight matrix for the ith user is given as:

Wi [n] = FHi [n]HHi [n]Hi [n]Fi [n] + 2σ2nINRX

−1

FHi [n]HHi [n] . (8)

The output of the MMSE detector for the ith user can be thenwritten as (at point F in Fig 1)

yi[n] = Wi [n] ri [n]

= Wi [n] (Hi [n] z [n] + ni [n])= Wi [n]Hi [n] zi [n] +Wi [n]ni [n] . (9)

III. ZERO DELAY FEEDBACK AND PRECODER DESIGN

Zero-delay feedback can be achieved by mean of channelprediction using well-known autoregressive modelling, whichis a widely used prediction method that could be found inmany applications including tracking of a radio channel ina time-varying environment [9]. Unlike deterministic curvefitting techniques, such as interpolation and extrapolation, ARmodelling takes the advantage of the statistics of the data.Assuming the CSI controller at the base station (See Fig1) has P complete past CSI measurements, the current CSIcan be estimated or predicted with certain amount of error.Let h[n] denote the the complex channel h(nRX ,nTX)i [n] forsimplicity. It is shown in [7], that a state-space model can beconstructed. Fig 2 shows a P order tapped delay line (TDL)channel predictor, that uses the past P channel measurementsand multiplies them with the corresponding AR weights topredict the current state of the channel.

The process can be summarized by the following expres-sion:

h[n] =

P

u=1

auh[n− u]

= aTh[n] (10)

Fig. 2: State-Space model diagram.

where h[n] is the estimated channel transfer function. And

h[n] = h[n− 1], · · · , h[n− P ] T (11)

holds the past P samples of h[n]. The AR parameters

a = [a1, a2, . . . , aP ]T

can be estimated according to the environment. With increasedestimation error, multiple-step prediction can be achieved byfeeding back the current estimated channel state to the-tap-delay line recursively .

A. AR Parameter EstimationThe well-known optimum prediction model for a fixed order

time series is usually referring to the forward-backward linearprediction model or the modified covariance method [10]. Leth[1], h[2], . . . , h[L] denote L noise-free channel measurementsfrom a training sequence that are collected at point H in Fig1. To estimate the AR parameters, a, in Equation (10), anoverdetermined system model is firstly constructed:

Aa=b. (12)

The least squares AR parameters a can be found by solving

a= AHA −1 AHb. (13)

In the forward-backward method, the total squared sum of boththe forward and the backward prediction errors are minimized.We can construct A and b as below:

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A =

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎣

h[P ] · · · h[1]...

. . ....

h[L− 1] · · · h[L− P ]h∗[2] · · · h∗[P + 1]...

. . ....

h∗[L− P + 1] · · · h∗[L]

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎦, (14)

b =

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎣

h[P + 1]...

h[L]h∗[1]...

h∗[L− P ]

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎦(15)

where (·)∗ denotes complex conjugate.

B. PrecoderThe main consideration for downlink broadcast channel in

MU-MIMO transmission is the interference cancellation at theBS (the transmitter side). In this paper, block diagonalization(BD) [11], [12] is considered. The idea of BD is based onbeam steering so that interference is nulled at the undesiredusers. As oppose other popular precoding schemes such asdirty paper coding (DPC) [13]–[15] and Tomlinson-Harashimaprecoding (THP) [16]–[18], BD only cancels the interferencefrom other users respect to the target user. Signal detection,such as MMSE detection, is required to mitigate the inter-antenna interference in each user.In BD, an effective channel matrix is constructed between

BS and each user. The aim of BD method is to find a set ofprecoding matrices that are null-space of the effective channelmatrix except for the target user. In other words, interference-free transmission can be realized if the effective channel matrixcan be block-diagonalized. To design precoders, BD assumestotal number of antennas of all users equal to the number ofantennas of BS and also assumes all users have equal numberof antennas on each mobile device. We then take the right-singular vectors that correspond to vanishing (zeros) singularvalues of the channel matrix to produce the precoding matrixfor the each user since these vectors span the null space ofthe interference channel matrix.Let Hi Hi[n] and Fi Fi[n], referring to Equations (1),

and (7), it can be seen that, the interference-free transmissionis possible if the channel can be block-diagonalized, that is,

HiFu = ONM×NM,∀u = i. (16)

To obtain the precoder weight matrix, let us first constructa interference channel matrix Hi ∈ C(M−1)NRX×NTX thatcontains only the channel estimated gains from all other usersexcept for the target ith user,

Hi = HT1 , · · · ,HTi−1,HTi+1 · · · ,HTMT

(17)

where Hi is constructed from the estimated channel coeffi-cients, h(nRX ,nTX)i , from the previous section using Equation(6) that is (at point I in Fig 1)

Hi =

⎡⎢⎢⎣h(1,1)i · · · h

(1,NTX)i

.... . .

...h(NRX ,1)i · · · h

(NRX ,NTX)i

⎤⎥⎥⎦ . (18)

Equation (16) can then be rewritten as:

HiFi = O(M−1)NRX×NRX. (19)

This implies that the precoding matrix Fi ∈ CNTX×NRX

must be designed to sit in the null space of Hi so that theinterference-free transmission is warranted for the ith user. Toobtain such a precoding matrix, we take the singular valuedecomposition (SVD) of Hi, that is

Hi[n] = UiΛiVHi

= Ui[Λnon−zeroi Λzeroi ]

[Vnon−zeroi Vzeroi ]H (20)

where

Vnon−zeroi ∈ CNTX×(M−1)NRX

and

Vzeroi ∈ CNTX×NRX

are composed of right singular vectors that correspond to non-zero singular values

Λnon−zeroi ∈ R(M−1)NM×(NTX−NRX)

and vanishing singular values

Λzeroi = O(M−1)NRX×NRX

respectively. Since the right-singular vectors corresponding tothe vanishing singular values of Hi span the null space of Hi,we have the following relationship,

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HiVzeroi = O(M−1)NRX×NRX. (21)

From the equation above, we can see that if the signal istransmitted with weight matrix Vzeroi , all users other thanthe target user i receives no signal. Thus we can use thenormalized Vzeroi as the precoding matrix for the ith user,that is (at point J in Fig 1)

Fi =1

Vzeroi F

Vzeroi . (22)

IV. SIMULATION RESULTS

In this section the total system capacity is presented, whichillustrates the performance of a multiuser LTE-TDD systemwith AR based prediction. A MU-MIMO system with 8transmit antennas at the BS and 4 UEs that each equips with2 receive antennas is implemented. Results are collected byaveraging 2048 simulations using Monte-Carlo method. Foreach simulation we consider a OFDM system with parameterscomplying LTE-TDD 5MHz transmission showing in TableI.

TABLE I: Simulation configurations

Modulation scheme QPSKCarrier frequency 2.4GHzNo. of subcarriers 300Cyclic prefix LongBandwidth 5MHzSubcarrier spacing 15kHzSample rate 7.68MS/sNo. of users 2Symbol Duration 83.3μsTraining length 100 OFDM symbols over 100msAR order 6Prediction step size 1ms (every 12 OFDM symbols)

For each simulation, 12 OFDM symbols (1 pilot symbol and11 payload symbols) are generated for each user. Assumingeach user has one receiver antenna and noise free channelestimation is available at the transmitter for AR parameterestimation at 1ms step size. Multipath fading coefficients aregenerated using Jake’s model [19] using Extended VehicularA model from [4] with Doppler spread 5 and 70Hz simulatingthe user travel speed of 2 and 32Km/h respectively. Typicalchannel state information (CSI) latencies, 1, 5, 10 and 20ms,at the base station of a LTE-TDD system are considered. Theaverage signal-to-noise ratio (SNR) of all NC subcarriers isgiven by

SNR =1

NC

NC

k=1

β2 [k]ETX [k]

2σ2nNRX(23)

where

ETX [k] = E zH [k, n] z [k, n] (24)

is the average total transmission energy and E {·} denotesexpected value. Note, subcarrier index, k, and symbol index,n, are re-included. β2 [k] is the average channel power gainthat is defined by

β2 [k] =1

NTXE H [k, n] 2F . (25)

The average system capacity is measured as the sum of allusers’ MMSE receiver outputs, that is

C =1

NC

NC

k=1

log2 1 +E xH [k, n]x [k, n]

E {eH [k, n] e [k, n]} in bps/Hz.

(26)

where

e [k, n] = y [k, n]− x [k, n] (27)

is the post-detection error and

y [k, n] = yT1[k, n] , yT

2[k, n] , · · · , yT

M[k, n]

T

(28)

contains recovered symbols for all users.

Fig. 3: Average system capacity [bps/Hz] against receivedSNR [dB] for various CSI delays w/i and w/o prediction onEVA 5Hz channel.

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Fig. 4: Average system capacity [bps/Hz] against receivedSNR [dB] for various CSI delays w/i and w/o prediction onEVA 70Hz channel.

As shown in Fig 3, for the EVA 5Hz channel, the proposedapproach is able to recover the full system capacity for allthe entire SNR region that are under simulation. Comparingto the case with no channel prediction, the system capacitiesdrop to 50% and 25% for 5ms and 10ms delays respectivelyat SNR = 30dB. As shown in Fig 4, the EVA 70Hz channel,which is a much more vigorous, fast varying channel, completedestroys the MU-MIMO capacity when CSI delays are present.Without channel prediction, the system capacity drop to 15%for 1ms delay and becomes unusable for 5ms at SNR = 30dB.The proposed method recovers full system capacity for 1msCSI delay at entire SNR region and recovers over 60% ofcapacity at SNR = 30dB for 5ms CSI delay.

V. CONCLUSION

In this paper, an AR-based solution for the LTE-TDDmultiuser downlink system is proposed for a time-varyingfrequency-selective environment. By estimating and predictingOFDM channels in the impulse response domain, the solutionmanages to reduce the computational burden by only consid-ering the significant taps of the impulse response. Simulationresults also proved that the proposed method is able to increasethe system capacity dramatically under the described testcondition. The performance of the algorithm can be furtherimproved by assimilating the antenna geometry [20] into thesystem model.

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