Algorithmic aspects of Massive MIMO

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Algorithmic Aspects of Massive MIMO

And Application to the 5G PHY Layer

Maxime Guillaud

Mathematical and Alorithmic Sciences Lab, Huawei Technologies France

IRACON (COST Action 15104) Technical Meeting

Lille, France, May 30, 2016

HUAWEI TECHNOLOGIES CO., LTD. Huawei Proprietary - Restricted Distribution Page 2

Covered Topics

Use cases in 5G (IoT / eMBB…) / KPIs

Introduction to Massive MIMO

CSI acquisition

Multi-User precoding / Resource allocation

Multiple access issues

Hardware impairments

Array geometries and channel models

Full duplex / relays


5G Standardization Objectives (3GPP TR38.913)

Usage scenarios, requirements and deployment scenarios

Enhanced mobile broadband (eMBB)

Massive-to-machine (M2M) communications

Ultra reliable and low latency communications (V2V, traffic safety…)

(Some) key performance indicators targets

Peak data rate (20Gbps DL/10 Gbps UL for 1 user)

Peak spectral efficiency (30bps/Hz DL / 15bps/Hz UL)

Control plane latency (<10ms energy saving mode -> active transmission)

User plane latency (1ms over the radio link)

Reliability (99.999% packet delivery within 1ms)

UE battery life (10 years for 200 bytes/day UL + 20 bytes/day DL with 5Wh stored energy)

Area traffic capacity (in Mbit/s/m2)

User experienced data rate (5%-percentile of the user throughput)

Connection density (1 000 000 device/km2)

New!


What is Massive MIMO?

In theory, like standard MIMO with some key differences

More BTS antennas (M) than users (K): 𝑀

𝐾≫ 1

Simplified multi-user processing, link adaptation, scheduling

Revisited CSI acquisition

M antennas

Consider the downlink of a multi-user channel. BTS has M antennas. Each user has 1 antenna.

Channel of user i: 𝒉𝑖 is a M-dimensional vector

Consider jointly the (downlink) channels to all users: 𝐇 = 𝒉𝟏 , … , 𝒉𝐾𝑇.

Downlink transmission:

𝑦1⋮𝑦𝐾

= 𝐇 𝐱 (+ noise). 𝐱 is the M-dimensional transmitted signal


Intuition: DL linear precoding consisting in superposition coding with simple matched precoder

𝐱 =𝟏

𝑴 𝒊=𝟏…𝑲𝒉𝒊𝑠𝑖 where 𝑠𝑖 is the data symbols for user i

At user j: 𝑦𝑗= 𝒉𝒋𝑻 𝟏

𝑴 𝒊=𝟏…𝑲𝒉𝒊𝑠𝑖 =

𝟏

𝑴𝒉𝒋

𝑻𝒉𝒋𝑠𝑗 +

𝟏

𝑴 𝒊≠𝒋𝒉𝒋

𝑻𝒉𝒊𝑠𝑖 (+ noise)

With iid unit-variance fading: lim𝑀→∞

𝟏

𝑴 𝒊≠𝒋𝒉𝒋

𝑻𝒉𝒊 = 0 while lim𝑀→∞

𝟏

𝑴𝒉𝒋

𝑻𝒉𝒋 = 1

Massive MIMO:

How did it all start?

Signal of interest Interference

SINR 𝑀→∞

∞

(without Tx power increase)

No fadingon the effective channel:

channel hardening


Certain “truths” about MIMO (single-user) need to be revisited:

In multi-user Massive MIMO, spatial separability of the users (from the BTS point of

view) is the key:

LoS is acceptable (as long as two users are not perfectly aligned)

Fading is not needed (exploit multi-user diversity rather than single-user MIMO diversity)

Array aperture ultimately governs the multiplexing gain (# of users served simultaneously)

What is a good Massive MIMO Channel?

LoS is detrimental to capacityi.i.d. fading channels are

preferable

𝜆

2antenna spacing

is necessary


Downlink transmission:

𝑦1⋮𝑦𝐾

= 𝐇 𝐱 (+ noise). 𝐱 is the M-dimensional transmitted signal

MRC Precoding: matched precoder: 𝐱 =𝟏

𝑴𝐇𝑻 𝐬 where 𝐬 =

𝑠1⋮𝑠𝐾

are user symbols

CSI in Massive MIMO Downlink Transmission

lim𝑀→∞

𝟏

𝑴𝐇𝐇𝑻 = 𝑰𝑲

𝑦1⋮𝑦𝐾

=

𝑠1⋮𝑠𝐾

Downlink Channel

Precoder:must be estimated


CSI Acquisition Strategies

Time Division Duplex (TDD) Frequency Division Duplex (FDD)

UL

DL

time

freq

uen

cy

Same time and different frequency

time

freq

uen

cy

Different time and same frequency

UL DL

UL channel estimation at the BTS

based on pilot sequences

DL channel obtained by reciprocity

(same as UL channel)

DL channel estimation at the UE based

on pilot sequences

Feedback (UE -> BTS) of estimated CSI


Why FDD Matters

Depending on the region, 65 to 94% of 4G spectrum is FDD


Uplink Multi-User Channel Estimation

Uplink Channel estimation: users transmit pilot sequences simultaneously:

𝑝𝑖(𝑡) is the (known) pilot symbol for user i at time t,

𝐲(t) = 𝒊=𝟏…𝑲 𝒉𝒊𝑝𝑖 𝑡 = 𝐇(𝒖𝒍) 𝐩 𝑡

Length-T training phase in matrix form: 𝐘 = 𝐲 1 ,… , 𝐲 𝐿 , 𝐇(𝒖𝒍) = 𝒉𝟏 , … , 𝒉𝐾 ,

𝐏 = 𝐩 1 ,… , 𝐩 𝐿

CSI acquisition for all K users:

𝐘 = 𝐇 𝐏 (+noise)

Intuition: linear estimation problem (observed 𝐘 is a linear combination of the etimee 𝐇).

Trivial solution if P is invertible: 𝐇 = 𝐘𝐏−𝟏


Uplink Multi-User Channel Estimation

CSI acquisition for all K users treated jointly:

𝐘 = 𝐇 𝐏 (+noise…)

Pilot design:

𝐏 = 𝐈𝑲 : round-robin CSI estimation across the users

𝐏𝐏𝐻 = 𝐈𝑲 : orthogonal pilots across the users (requires 𝐿 ≥ 𝐾)

Non-orthogonal pilots: not a problem as long as rank(P)=K

rank(𝐏) <K: 𝐇 can not be identified (under-determined linear system)

Pilot reuse across cells: 𝐏 =𝐏1𝐏1

(pilot contamination)

The properties of the pilot matrix Pgovern CSI estimation

M×L M×K K×L


Channel Covariance Information in Massive MIMO

θ

d

Tx correlation model: hi= Ri

1/2 .wi for user i

• Ri : the BTS-side channel covariance, assumed known (for now)• wi dimension d ≤ 𝑀, captures the fast fading

Motivation:• The contribution from a single scatterer (seen at angle 𝜃) to the channel is a fast-fading coefficient

times the rank-1 array response 𝐯𝜃 =

1

𝑒𝑗2𝜋𝑑

𝜆cos 𝜃

⋮

𝑒𝑗2𝜋(𝑀−1)𝑑

𝜆cos 𝜃

.

• In Massive MIMO, M ≫ #significant scatterers:

we expect low-rank Ri


Exploiting Channel Covariance Information:

Uplink Multi-User CSI Estimation

𝐘 = 𝐇 𝐏 ⇔ vec(𝐘) = 𝐏𝑇⨂𝐈𝑀 .

𝐑1 1 2

⋱

𝐑𝐾 1 2

.

𝒘𝟏

⋮𝒘𝑲

• Linear estimation of the the fast fading coefficients with known 𝐑𝑘

• Extreme case: users with 𝐑𝐾 1 2 spanning orthogonal linear subspaces

→ Users fully separated in spatial domain, do not require orthogonal pilots

• Pilots sequence length L can be reduced!

• This model captures pilot contamination



Uplink Multi-User CSI Estimation

vec(𝐘) = 𝐏𝑇⨂𝐈𝑀 .

𝐑1

1 2

⋱

𝐑𝐾

1 2

.

𝒘𝟏

⋮𝒘𝑲

How to choose the pilots (𝐏) as a function of 𝐑1…𝐑𝐾?

• Classical approach: reuse of orthogonal pilots across cells

• Reuse across groups of user (clustering based on 𝐑𝑘)

• “Unconstrained” optimization of 𝐏 based on covariance knowledge:

Reuse 𝑓 = 4“Universal” Reuse 𝑓 = 1

Reuse 𝑓 = 3

B. Tomasi, M. Guillaud , Pilot Length Optimization for Spatially Correlated Multi-User MIMO Channel Estimation, Asilomar 2015. http://arxiv.org/abs/1602.05480

http://arxiv.org/abs/1602.05480



Downlink Multi-User CSI Estimation

• Prior knowledge of covariance can similarly be leveraged to improve DL

channel estimation:

• Normally, pilots of length at least M should be required to be able to

discriminate the BTS antennas

• With prior knowledge of 𝐑𝑖(𝐷𝐿)

, DL pilot sequence length and the rate of

UE → BTS feedback can be reduced (JSDM - Joint Spatial Division and

Multiplexing, Adhikary, Nam, Ahn, Caire 2012)

• Unconstrained pilot design based on DL covariance

Hot topic: Estimating and tracking uplink 𝐑𝑖

and downlink 𝐑𝑖(𝐷𝐿) covariance matrices


The Massive number of antennas enables averaging over space:

Resource allocation, scheduling, link adaptation… can be done based on channel

statistics (channel hardening effect)

Multi-user Resource Allocation

lim𝑀→∞

𝟏

𝑴𝐇𝐇𝑻 = 𝑰𝑲

DL Channel Precoder


Large Arrays with many RF chains: need to consider using

cheap hardware

Typical impairments:

Imperfect Tx/Rx Reciprocity

Over-the-Air calibration being proposed (ARGOS…)

Clocks Phase noise

Classically mitigated and ignored – now

signal processing-based compensation approaches

Low-accuracy ADCs

Partly analog (hybrid) beamforming, other digital approaches

Hardware Impairments in Massive MIMO


Summary

Massive MIMO is like standard MIMO with some key differences:

More BTS antennas (M) than users (K): 𝑀

𝐾≫ 1

Simplified many aspects of the signal processing:

multi-user precoding

Scheduling and link adaptation (due to channel hardening)

CSI acquisition becomes the performance bottleneck

Revisited CSI estimation and feedback strategies

Pilot design (to minimize contamination)

TDD operation is preferred, FDD needed for legacy frequency allocation

M antennas

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Algorithmic aspects of Massive MIMO

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