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Blind Pilot Decontamination Ralf R. Mller Professor for Digital Communications Friedrich-Alexander University Erlangen-Nuremberg Adjunct Professor for Wireless Networks Norwegian University of Science and Technology joint work with Laura

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Blind Pilot Decontamination

Ralf R. Müller

Professor for Digital Communications Friedrich-Alexander University Erlangen-Nuremberg Adjunct Professor for Wireless Networks Norwegian University of Science and Technology joint work with Laura Cottatellucci Mikko Vehkaperä

Institute Eurecom, France Aalto University, Finland

25-Jun-2013

This work was supported in part by the FP7 project

Ralf Müller (FAU & NTNU) 25-Jun-2013 1 / 20

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Introduction

Massive MIMO

Massive MIMO mimics the idea of spread spectrum. Spread spectrum:

◮ Massive use of bandwidth Ralf Müller (FAU & NTNU) 25-Jun-2013 2 / 20

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Introduction

Massive MIMO

Massive MIMO mimics the idea of spread spectrum. Spread spectrum:

◮ Massive use of bandwidth ◮ Large processing gain Ralf Müller (FAU & NTNU) 25-Jun-2013 2 / 20

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SLIDE 4

Introduction

Massive MIMO

Massive MIMO mimics the idea of spread spectrum. Spread spectrum:

◮ Massive use of bandwidth ◮ Large processing gain

Massive MIMO:

◮ Massive use of antenna elements Ralf Müller (FAU & NTNU) 25-Jun-2013 2 / 20

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SLIDE 5

Introduction

Massive MIMO

Massive MIMO mimics the idea of spread spectrum. Spread spectrum:

◮ Massive use of bandwidth ◮ Large processing gain

Massive MIMO:

◮ Massive use of antenna elements ◮ Large array gain Ralf Müller (FAU & NTNU) 25-Jun-2013 2 / 20

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Introduction

Massive MIMO

Massive MIMO mimics the idea of spread spectrum. Spread spectrum:

◮ Massive use of bandwidth ◮ Large processing gain

Massive MIMO:

◮ Massive use of antenna elements ◮ Large array gain

Both systems can operate in arbitrarily strong noise and interference.

Ralf Müller (FAU & NTNU) 25-Jun-2013 2 / 20

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Introduction

Uplink (Reverse Link) System Model

R L T R ≫ T L ∼ T Y = HX + Z

Ralf Müller (FAU & NTNU) 25-Jun-2013 3 / 20

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Introduction

Pilot Contamination

For T transmit antennas and R receive antennas, even for a static channel, RT channel coefficients must be estimated. Linear channel estimation:

◮ The array gain, can be utilized for data detection, but not for channel

estimation.

Ralf Müller (FAU & NTNU) 25-Jun-2013 4 / 20

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Introduction

Pilot Contamination

For T transmit antennas and R receive antennas, even for a static channel, RT channel coefficients must be estimated. Linear channel estimation:

◮ The array gain, can be utilized for data detection, but not for channel

estimation.

◮ Channel estimation ultimately limits performance. Ralf Müller (FAU & NTNU) 25-Jun-2013 4 / 20

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SLIDE 10

Introduction

Pilot Contamination

For T transmit antennas and R receive antennas, even for a static channel, RT channel coefficients must be estimated. Linear channel estimation:

◮ The array gain, can be utilized for data detection, but not for channel

estimation.

◮ Channel estimation ultimately limits performance.

General channel estimation:

◮ Can the array gain can be utilized for both channel estimation and data

detection?

Ralf Müller (FAU & NTNU) 25-Jun-2013 4 / 20

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Introduction

Pilot Contamination

For T transmit antennas and R receive antennas, even for a static channel, RT channel coefficients must be estimated. Linear channel estimation:

◮ The array gain, can be utilized for data detection, but not for channel

estimation.

◮ Channel estimation ultimately limits performance.

General channel estimation:

◮ Can the array gain can be utilized for both channel estimation and data

detection?

◮ Is the performance limited by channel estimation? Ralf Müller (FAU & NTNU) 25-Jun-2013 4 / 20

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SLIDE 12

Introduction

Pilot Contamination

For T transmit antennas and R receive antennas, even for a static channel, RT channel coefficients must be estimated. Linear channel estimation:

◮ The array gain, can be utilized for data detection, but not for channel

estimation.

◮ Channel estimation ultimately limits performance.

General channel estimation:

◮ Can the array gain can be utilized for both channel estimation and data

detection?

◮ Is the performance limited by channel estimation?

How to estimate a massive MIMO channel appropriately?

Ralf Müller (FAU & NTNU) 25-Jun-2013 4 / 20

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Algorithm

Blind Interference Rejection

This topic was well studied in the ’90s in context of spread-spectrum, see e.g.

  • U. Madhow: ”Blind adaptive interference suppression for direct sequence CDMA,“

Proceedings of the IEEE, Oct. 1998.

Ralf Müller (FAU & NTNU) 25-Jun-2013 5 / 20

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Algorithm

Blind Interference Rejection

This topic was well studied in the ’90s in context of spread-spectrum, see e.g.

  • U. Madhow: ”Blind adaptive interference suppression for direct sequence CDMA,“

Proceedings of the IEEE, Oct. 1998.

Idea:

◮ The signal of interest and the interference are almost orthogonal. Ralf Müller (FAU & NTNU) 25-Jun-2013 5 / 20

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Algorithm

Blind Interference Rejection

This topic was well studied in the ’90s in context of spread-spectrum, see e.g.

  • U. Madhow: ”Blind adaptive interference suppression for direct sequence CDMA,“

Proceedings of the IEEE, Oct. 1998.

Idea:

◮ The signal of interest and the interference are almost orthogonal. ◮ We need not know the channel coefficients of the interference, but only the

subspace the interference occupies.

Ralf Müller (FAU & NTNU) 25-Jun-2013 5 / 20

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Algorithm

Blind Interference Rejection

This topic was well studied in the ’90s in context of spread-spectrum, see e.g.

  • U. Madhow: ”Blind adaptive interference suppression for direct sequence CDMA,“

Proceedings of the IEEE, Oct. 1998.

Idea:

◮ The signal of interest and the interference are almost orthogonal. ◮ We need not know the channel coefficients of the interference, but only the

subspace the interference occupies.

Implementation:

◮ Project onto the orthogonal complement of the interference subspace. Ralf Müller (FAU & NTNU) 25-Jun-2013 5 / 20

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Algorithm

Blind Interference Rejection

This topic was well studied in the ’90s in context of spread-spectrum, see e.g.

  • U. Madhow: ”Blind adaptive interference suppression for direct sequence CDMA,“

Proceedings of the IEEE, Oct. 1998.

Idea:

◮ The signal of interest and the interference are almost orthogonal. ◮ We need not know the channel coefficients of the interference, but only the

subspace the interference occupies.

Implementation:

◮ Project onto the orthogonal complement of the interference subspace.

How to find the interference subspace or its orthogonal complement?

Ralf Müller (FAU & NTNU) 25-Jun-2013 5 / 20

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Algorithm

Matched Filter Projection

Let us start the considerations with a SIMO system and white noise only.

Ralf Müller (FAU & NTNU) 25-Jun-2013 6 / 20

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Algorithm

Matched Filter Projection

Let us start the considerations with a SIMO system and white noise only. Let yc be the column vector received at the receive array at time c and Y = [y1, . . . , yC] with C denoting the coherence time.

Ralf Müller (FAU & NTNU) 25-Jun-2013 6 / 20

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Algorithm

Matched Filter Projection

Let us start the considerations with a SIMO system and white noise only. Let yc be the column vector received at the receive array at time c and Y = [y1, . . . , yC] with C denoting the coherence time. We would like to find a linear filter m, such that m†Y has high SNR.

Ralf Müller (FAU & NTNU) 25-Jun-2013 6 / 20

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Algorithm

Matched Filter Projection

Let us start the considerations with a SIMO system and white noise only. Let yc be the column vector received at the receive array at time c and Y = [y1, . . . , yC] with C denoting the coherence time. We would like to find a linear filter m, such that m†Y has high SNR. We get m = argmax

m0

||m†

0Y||2

||m0||2 = argmax

m0

m†

0YY†m0

m†

0m0

is that eigenvector of YY† that corresponds to the largest eigenvalue.

Ralf Müller (FAU & NTNU) 25-Jun-2013 6 / 20

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Algorithm

Matched Filter Projection II

Next, consider a MIMO system with T > 1 transmit antennas and white noise.

Ralf Müller (FAU & NTNU) 25-Jun-2013 7 / 20

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Algorithm

Matched Filter Projection II

Next, consider a MIMO system with T > 1 transmit antennas and white noise. Now, we look for a basis M of the T-dimensional subspace containing the signal of interest.

Ralf Müller (FAU & NTNU) 25-Jun-2013 7 / 20

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Algorithm

Matched Filter Projection II

Next, consider a MIMO system with T > 1 transmit antennas and white noise. Now, we look for a basis M of the T-dimensional subspace containing the signal of interest. We find it by an eigenvalue decomposition of YY† picking those eigenvectors which correspond to the T largest eigenvalues.

Ralf Müller (FAU & NTNU) 25-Jun-2013 7 / 20

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Algorithm

Matched Filter Projection II

Next, consider a MIMO system with T > 1 transmit antennas and white noise. Now, we look for a basis M of the T-dimensional subspace containing the signal of interest. We find it by an eigenvalue decomposition of YY† picking those eigenvectors which correspond to the T largest eigenvalues. We now project the received signal onto that subspace Y′ = M†Y and dismiss all noise components outside that subspace.

Ralf Müller (FAU & NTNU) 25-Jun-2013 7 / 20

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Algorithm

Matched Filter Projection II

Next, consider a MIMO system with T > 1 transmit antennas and white noise. Now, we look for a basis M of the T-dimensional subspace containing the signal of interest. We find it by an eigenvalue decomposition of YY† picking those eigenvectors which correspond to the T largest eigenvalues. We now project the received signal onto that subspace Y′ = M†Y and dismiss all noise components outside that subspace. By the massive MIMO philosophy, i.e. T ≪ R, this subspace is much smaller than the full space.

Ralf Müller (FAU & NTNU) 25-Jun-2013 7 / 20

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Algorithm

Matched Filter Projection II

Next, consider a MIMO system with T > 1 transmit antennas and white noise. Now, we look for a basis M of the T-dimensional subspace containing the signal of interest. We find it by an eigenvalue decomposition of YY† picking those eigenvectors which correspond to the T largest eigenvalues. We now project the received signal onto that subspace Y′ = M†Y and dismiss all noise components outside that subspace. By the massive MIMO philosophy, i.e. T ≪ R, this subspace is much smaller than the full space. We have utilized the array gain without estimating the channel.

Ralf Müller (FAU & NTNU) 25-Jun-2013 7 / 20

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Algorithm

Matched Filter Projection III

Consider now the general case (noise, interference and a MIMO system with T > 1 transmit antennas and R ≫ T receive antennas).

Ralf Müller (FAU & NTNU) 25-Jun-2013 8 / 20

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Algorithm

Matched Filter Projection III

Consider now the general case (noise, interference and a MIMO system with T > 1 transmit antennas and R ≫ T receive antennas). While white noise is small in all components if SNR ≫ T R the interference typically concentrates in few signal dimensions where it is strong.

Ralf Müller (FAU & NTNU) 25-Jun-2013 8 / 20

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Algorithm

Matched Filter Projection III

Consider now the general case (noise, interference and a MIMO system with T > 1 transmit antennas and R ≫ T receive antennas). While white noise is small in all components if SNR ≫ T R ≪ 1, the interference typically concentrates in few signal dimensions where it is strong.

Ralf Müller (FAU & NTNU) 25-Jun-2013 8 / 20

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Algorithm

Matched Filter Projection III

Consider now the general case (noise, interference and a MIMO system with T > 1 transmit antennas and R ≫ T receive antennas). While white noise is small in all components if SNR ≫ T R ≪ 1, the interference typically concentrates in few signal dimensions where it is strong. How to distinguish the signal of interest from interference?

Ralf Müller (FAU & NTNU) 25-Jun-2013 8 / 20

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Algorithm

Power Controlled Hand-Off

Consider power-controlled hand-off and perfect received power control.

I P I

Ralf Müller (FAU & NTNU) 25-Jun-2013 9 / 20

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Algorithm

Power Controlled Hand-Off

Consider power-controlled hand-off and perfect received power control.

I P I

Interfering signals cannot be stronger than signals of interest, i.e. P ≥ I.

Ralf Müller (FAU & NTNU) 25-Jun-2013 9 / 20

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Algorithm

Power Controlled Hand-Off

Consider power-controlled hand-off and perfect received power control.

I P I

Interfering signals cannot be stronger than signals of interest, i.e. P ≥ I. Most interfering signals are noticeably weaker than the signals of interest.

Ralf Müller (FAU & NTNU) 25-Jun-2013 9 / 20

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Algorithm

Power Controlled Hand-Off

Consider power-controlled hand-off and perfect received power control.

I P I

Interfering signals cannot be stronger than signals of interest, i.e. P ≥ I. Most interfering signals are noticeably weaker than the signals of interest. For vanishing load α = T/R → 0, the signals of interest can be separated from the interference.

Ralf Müller (FAU & NTNU) 25-Jun-2013 9 / 20

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Algorithm

Power Controlled Hand-Off

Consider power-controlled hand-off and perfect received power control.

I P I

Interfering signals cannot be stronger than signals of interest, i.e. P ≥ I. Most interfering signals are noticeably weaker than the signals of interest. For vanishing load α = T/R → 0, the signals of interest can be separated from the interference. What if the load is small, but not vanishing?

Ralf Müller (FAU & NTNU) 25-Jun-2013 9 / 20

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Algorithm

Asymptotic Eigenvalue Distribution

The exact asymptotic eigenvalue distribution can be given implicitly in terms of its Stieltjes transform G(s) = dP(x) x − s . For an iid. channel, we find sG(s) + 1 = − PTCα

  • sG(s) + 1 − κ
  • G(s)

ακ − PTC

  • sG(s) + 1 − κ
  • G(s)

−

  • xLTCα
  • sG(s) + 1 − κ
  • G(s) dPI(x)

ακ pI(x) − xTC

  • sG(s) + 1 − κ
  • G(s)

− WCα

  • sG(s) + 1 − κ
  • G(s)

κ with W denoting the noise power, κ = C

R , and PI(x) denoting the power

distribution of the interference.

Ralf Müller (FAU & NTNU) 25-Jun-2013 10 / 20

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Algorithm

Asymptotic Eigenvalue Distribution

Assuming that all LT interferers have power I, i.e. pI(x) = δ(x − I), the fixed-point equation for the Stieltjes transform simplifies to sG(s) + 1 = − PTCα

  • sG(s) + 1 − κ
  • G(s)

ακ − PTC

  • sG(s) + 1 − κ
  • G(s)

− ILTCα

  • sG(s) + 1 − κ
  • G(s)

ακ − ITC

  • sG(s) + 1 − κ
  • G(s)

− WCα

  • sG(s) + 1 − κ
  • G(s)

κ with W denoting the noise power and κ = C

R .

Ralf Müller (FAU & NTNU) 25-Jun-2013 11 / 20

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Algorithm

Empirical Eigenvalue Distribution

50 100 150 200 0.001 0.002 0.003 0.004 λ pλ(λ)

signal of interest interference white noise

R = 300 T = 10 C = 1000 L = 2 W = 1000 P = 100 I = 25

Ralf Müller (FAU & NTNU) 25-Jun-2013 12 / 20

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Algorithm

Uplink vs. Downlink

We have detected the uplink data without estimating the full channel. For energy concentration on the downlink (forward link), we need a good estimate

  • f the full channel matrix H.

Ralf Müller (FAU & NTNU) 25-Jun-2013 13 / 20

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Algorithm

Uplink vs. Downlink

We have detected the uplink data without estimating the full channel. For energy concentration on the downlink (forward link), we need a good estimate

  • f the full channel matrix H.

1

We use time-division duplex.

Ralf Müller (FAU & NTNU) 25-Jun-2013 13 / 20

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Algorithm

Uplink vs. Downlink

We have detected the uplink data without estimating the full channel. For energy concentration on the downlink (forward link), we need a good estimate

  • f the full channel matrix H.

1

We use time-division duplex.

2

We project the received signal Y onto the orthogonal complement of the interference.

Ralf Müller (FAU & NTNU) 25-Jun-2013 13 / 20

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Algorithm

Uplink vs. Downlink

We have detected the uplink data without estimating the full channel. For energy concentration on the downlink (forward link), we need a good estimate

  • f the full channel matrix H.

1

We use time-division duplex.

2

We project the received signal Y onto the orthogonal complement of the interference.

3

We use all uplink data to estimate the downlink (forward link) channel to high accuracy.

Ralf Müller (FAU & NTNU) 25-Jun-2013 13 / 20

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Analysis

Eigenvalue Spread

Assume an i.i.d. channel matrix and R ≫ T → ∞. The eigenvalues of the signal of interest are confined in an interval centered at the received power P with width 4P

  • T

R + T C .

Ralf Müller (FAU & NTNU) 25-Jun-2013 14 / 20

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Analysis

Eigenvalue Spread

Assume an i.i.d. channel matrix and R ≫ T → ∞. The eigenvalues of the signal of interest are confined in an interval centered at the received power P with width 4P

  • T

R + T C . The eigenvalues of the interference are confined in an interval centered at the interference power I with width 4I

  • LT

R + LT C where L denotes the number of interfering cells. For massive MIMO, the two widths are quite small.

Ralf Müller (FAU & NTNU) 25-Jun-2013 14 / 20

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Analysis

Eigenvalue Separation

The two intervals do not overlap if P I > 1 + 2

  • LT

R + LT C

1 − 2

  • T

R + T C

.

Ralf Müller (FAU & NTNU) 25-Jun-2013 15 / 20

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Analysis

Eigenvalue Separation

The two intervals do not overlap if P I > 1 + 2

  • LT

R + LT C

1 − 2

  • T

R + T C

. If the two intervals do not overlap, we can totally reject the interference by means

  • f eigenvalue decomposition.

Ralf Müller (FAU & NTNU) 25-Jun-2013 15 / 20

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Analysis

Eigenvalue Separation

The two intervals do not overlap if P I > 1 + 2

  • LT

R + LT C

1 − 2

  • T

R + T C

. If the two intervals do not overlap, we can totally reject the interference by means

  • f eigenvalue decomposition.

For finite number of receive antennas, the interval boundaries are not sharp, but have exponentially decaying tails.

Ralf Müller (FAU & NTNU) 25-Jun-2013 15 / 20

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Simulation Results

BER vs. Array Size

50 100 150 200 250 300 350 400 450 10

−3

10

−2

10

−1

10 BER R

subspace conventional

P / I = 2 P/ I = 4

T = 3 C = 1000 L = 2 SNR = −10dB 1 pilot symbol per transmit antenna and cell

Ralf Müller (FAU & NTNU) 25-Jun-2013 16 / 20

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Simulation Results

BER vs. Power Margin

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10

−5

10

−4

10

−3

10

−2

10

−1

10 I/P uncoded BER threshold for no overlap

  • conv. method of Marzetta

proposed subspace method

R = 200 T = 2 C = 400 L = 2 W = 1 P = 0.1 1 (–) or 10 (- -) pilot symbols per transmit antenna and cell

Ralf Müller (FAU & NTNU) 25-Jun-2013 17 / 20

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Power Margin

How to guarantee a sufficient power margin between the signal of interest and the interference?

Ralf Müller (FAU & NTNU) 25-Jun-2013 18 / 20

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Power Margin

How to guarantee a sufficient power margin between the signal of interest and the interference? Two antennas per user.

Ralf Müller (FAU & NTNU) 25-Jun-2013 18 / 20

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Power Margin

How to guarantee a sufficient power margin between the signal of interest and the interference? Two antennas per user. If a user experiences equally good channel conditions to several base stations/access points, the user forms a beam that favors one of the base stations/access points over the others.

Ralf Müller (FAU & NTNU) 25-Jun-2013 18 / 20

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Power Margin

How to guarantee a sufficient power margin between the signal of interest and the interference? Two antennas per user. If a user experiences equally good channel conditions to several base stations/access points, the user forms a beam that favors one of the base stations/access points over the others. If the power margin is sufficient without beam forming, the user can use the two antennas for spatial multiplexing.

Ralf Müller (FAU & NTNU) 25-Jun-2013 18 / 20

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Power Margin

How to guarantee a sufficient power margin between the signal of interest and the interference? Two antennas per user. If a user experiences equally good channel conditions to several base stations/access points, the user forms a beam that favors one of the base stations/access points over the others. If the power margin is sufficient without beam forming, the user can use the two antennas for spatial multiplexing. Pro: A sufficient power margin can be established (with high probability). Con: Users at cell boundaries may suffer from reduced data rate.

Ralf Müller (FAU & NTNU) 25-Jun-2013 18 / 20

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Conclusions

Pilot contamination is not a fundamental effect, but an artefact of linear channel estimation.

Ralf Müller (FAU & NTNU) 25-Jun-2013 19 / 20

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Conclusions

Pilot contamination is not a fundamental effect, but an artefact of linear channel estimation. Pilot decontamination based on power control works well under the simulated conditions.

Ralf Müller (FAU & NTNU) 25-Jun-2013 19 / 20

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Conclusions

Pilot contamination is not a fundamental effect, but an artefact of linear channel estimation. Pilot decontamination based on power control works well under the simulated conditions. The algorithm requires real-time eigenvalue or singular value decompositions.

Ralf Müller (FAU & NTNU) 25-Jun-2013 19 / 20

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Literature

  • U. Madhow,”Blind adaptive interference suppression for direct sequence

CDMA,“ Proc. of the IEEE, vol. 86, no. 10, pp. 2049–2069, Oct. 1998.

  • H. Q. Ngo and E. G. Larsson,”EVD-based channel estimation in multicell

multiuser MIMO system with very large antenna arrays,“ Proc. of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Kyoto, Japan, Mar. 2012.

  • H. Yin, D. Gesbert, M. Filippou, and Y. Liu, ”A coordinated approach to

channel estimation in large-scale multiple-antenna systems,“ IEEE Journal on Selected Areas in Communications, vol. 31, no. 2, pp. 264–273, Feb. 2013.

  • R. R. Müller, M. Vehkaperä, and L. Cottatellucci,”Blind pilot

decontamination,“Proc. of 17th International ITG Workshop on Smart Antennas (WSA 2013), Stuttgart, Germany, Mar. 2013.

  • L. Cottatellucci, R. R. Müller, M. Vehaperä, ”Analysis of pilot

decontamination based on power control“, Proc. of IEEE Vehicular Technology Conference (VTC), Dresden, Germany, Jun. 2013.

Ralf Müller (FAU & NTNU) 25-Jun-2013 20 / 20