David versus Goliath:Small Cells versus Massive...
Transcript of David versus Goliath:Small Cells versus Massive...
David versus Goliath:SmallCells versus Massive MIMO
Jakob Hoydis and Mérouane Debbah
1948: Cybernetics and Theory of Communications
• ”A Mathematical Theory of Communication”, Bell System Technical Journal, 1948, C. E. Shannon
• ”Cybernetics, or Control and Communication in the Animal and the Machine”, Herman et Cie/The Technology Press, 1948, N. Wiener
60 years later... MIMO Flexible Networks
We must learn and control the black box
• within a fraction of time• with finite energy.
In many cases, the number of inputs/outputs (the dimensionality of the system) is of the same order as the time scale changes of the box.
“David vs Goliath“ or ”Small Cells vs Massive MIMO“
How to densify: “More antennas or more BSs?”
Questions:
I Should we install more base stations or simply more antennas per base?
I How can massively many antennas be efficiently used?
I Can massive MIMO simplify the signal processing?
4 / 25
Vision
Bell Labs lightradio antenna module – the next generation small cell (picture from www.washingtonpost.com)
A thought experiment
Consider an infinite large network of randomly uniformly distributed basestations and user terminals.
What would be better?
A 2 × more base stations
B 2 × more antennas per base station
Stochastic geometry can provide an answer.
5 / 25
A thought experiment
Consider an infinite large network of randomly uniformly distributed basestations and user terminals.
What would be better?
A 2 × more base stations
B 2 × more antennas per base station
Stochastic geometry can provide an answer.
5 / 25
System model: Downlink
Received signal at a tagged UT at the origin:
y =1
rα/20
hH0 x0︸ ︷︷ ︸
desired signal
+∞∑i=1
1
rα/2i
hHi xi︸ ︷︷ ︸
interference
+ n
I hi ∼ CN (0, IN ): fast fading channel vectors
I ri : distance to ith closest BS
I P = E[xH
i xi
]: average transmit power constraint per BS
Assumptions:
I infinitely large network of uniformly randomly distributed BSs and UTswith densities λBS and λUT, respectively
I single-antenna UTs, N antennas per BS
I each UT is served by its closest BS
I distance-based path loss model with path loss exponent α > 2
I total bandwidth W , re-used in each cell
6 / 25
System model: Downlink
Received signal at a tagged UT at the origin:
y =1
rα/20
hH0 x0︸ ︷︷ ︸
desired signal
+∞∑i=1
1
rα/2i
hHi xi︸ ︷︷ ︸
interference
+ n
I hi ∼ CN (0, IN ): fast fading channel vectors
I ri : distance to ith closest BS
I P = E[xH
i xi
]: average transmit power constraint per BS
Assumptions:
I infinitely large network of uniformly randomly distributed BSs and UTswith densities λBS and λUT, respectively
I single-antenna UTs, N antennas per BS
I each UT is served by its closest BS
I distance-based path loss model with path loss exponent α > 2
I total bandwidth W , re-used in each cell
6 / 25
Transmission strategy: Zero-forcing
Assumptions:
I K = λUTλBS
UTs need to be served by each BS on average
I total bandwidth W divided into L ≥ 1 sub-bands
I K = K/L ≤ N UTs are simultaneously served on each sub-band
Transmit vector of BS i :
xi =
√P
K
K∑k=1
wi,k si,k
I si,k ∼ CN (0, 1): message determined for UT k from BS i
I wi,k ∈ CN×1: ZF-beamforming vectors
7 / 25
Transmission strategy: Zero-forcing
Assumptions:
I K = λUTλBS
UTs need to be served by each BS on average
I total bandwidth W divided into L ≥ 1 sub-bands
I K = K/L ≤ N UTs are simultaneously served on each sub-band
Transmit vector of BS i :
xi =
√P
K
K∑k=1
wi,k si,k
I si,k ∼ CN (0, 1): message determined for UT k from BS i
I wi,k ∈ CN×1: ZF-beamforming vectors
7 / 25
Performance metric: Average throughputReceived SINR at tagged UT:
γ =r−α0
∣∣hH0 w0,1
∣∣2∑∞i=1 r−αi
∑Kk=1
∣∣hHi wi,k
∣∣2 + KP
=r−α0 S∑∞
i=1 r−αi gi + KP
Coverage probability:
Pcov(T ) = P (γ ≥ T )
Average throughput per UT:
C =W
L× E [log(1 + γ)] =
W
L×∫ ∞
0
Pcov (ez − 1) dz
Remarks:
I expectation with respect to fading and BSs locations
I S =∣∣hH
0 w0,1
∣∣2 ∼ Γ(N − K + 1, 1), gi =∑K
k=1
∣∣hHi wi,k
∣∣2 ∼ Γ(K , 1)
I K impacts the interference distribution, N impacts the desired signal
I for P →∞, the SINR becomes independent of λBS
8 / 25
Performance metric: Average throughputReceived SINR at tagged UT:
γ =r−α0
∣∣hH0 w0,1
∣∣2∑∞i=1 r−αi
∑Kk=1
∣∣hHi wi,k
∣∣2 + KP
=r−α0 S∑∞
i=1 r−αi gi + KP
Coverage probability:
Pcov(T ) = P (γ ≥ T )
Average throughput per UT:
C =W
L× E [log(1 + γ)] =
W
L×∫ ∞
0
Pcov (ez − 1) dz
Remarks:
I expectation with respect to fading and BSs locations
I S =∣∣hH
0 w0,1
∣∣2 ∼ Γ(N − K + 1, 1), gi =∑K
k=1
∣∣hHi wi,k
∣∣2 ∼ Γ(K , 1)
I K impacts the interference distribution, N impacts the desired signal
I for P →∞, the SINR becomes independent of λBS
8 / 25
A closed-form result
Theorem (Combination of Baccelli’09, Andrews’10)
Pcov(T ) =
∫r0>0
∫ ∞−∞LIr0
(i2πrα0 Ts) exp
(−
i2πrα0 TK
Ps
)LS (−i2πs)− 1
i2πsfr0 (r0)dsdr0
where
LIr0(s) = exp
(−2πλBS
∫ ∞r0
(1−
1
(1 + sv−α)K
)vdv
)
LS (s) =
(1
1 + s
)N−K+1
fr0 (r0) = 2πλBSr0e−λBSπr20
The computation of Pcov(T ) requires in general three numerical integrals.
J. G. Andrews, F. Baccelli, R. K. Ganti, “A Tractable Approach to Coverage and Rate in Cellular Networks” IEEE
Trans. Wireless Commun., submitted 2010.
F. Baccelli, B. B laszczyszyn, P. Muhlethaler, “Stochastic Analysis of Spatial and Opportunistic Aloha” Journal on
Selected Areas in Communications, 2009
9 / 25
Example
I Density of UTs: λUT = 16
I Constant transmit power density: P × λBS = 10
I Number of BS-antennas: N = λUT/λBS
I Path loss exponent: α = 4
I UT simultaneously served on each band: K = λUT/(λBS × L)
⇒ Only two parameters: λBS and L
Table: Average spectral efficiency C/W in (bits/s/Hz)
sub-bands L λBS = 1 λBS = 2 λBS = 4 λBS = 8 λBS = 16
1 0.6209 0.8188 1.1964 1.5215 2.1456
2 1.1723 1.2414 1.3404 1.5068 x
4 0.8882 0.8973 1.1964 x x
8 0.5689 0.5952 x x
16 0.3532 x x x x
Fully distributing the antennas gives highest throughput gains!
10 / 25
Example
I Density of UTs: λUT = 16
I Constant transmit power density: P × λBS = 10
I Number of BS-antennas: N = λUT/λBS
I Path loss exponent: α = 4
I UT simultaneously served on each band: K = λUT/(λBS × L)
⇒ Only two parameters: λBS and L
Table: Average spectral efficiency C/W in (bits/s/Hz)
sub-bands L λBS = 1 λBS = 2 λBS = 4 λBS = 8 λBS = 16
1 0.6209 0.8188 1.1964 1.5215 2.1456
2 1.1723 1.2414 1.3404 1.5068 x
4 0.8882 0.8973 1.1964 x x
8 0.5689 0.5952 x x
16 0.3532 x x x x
Fully distributing the antennas gives highest throughput gains!
10 / 25
First conclusions
I Distributed network densification is preferable over massive MIMO if theaverage throughput per UT should be increased.
I More antennas increase the coverage probability, but more BSs lead to alinear increase in area spectral efficiency (with constant total transmitpower).
I If we use other metrics such as coverage probability or goodput, thepicture might change.
What happens if massively many antennas are used?
11 / 25
Beyond LTE: The 400-Antenna Base Station
Thomas L. Marzetta
Bell Laboratories
Alcatel-Lucent
28 May, 2010
Large Excess of Base Station Antennas Over Terminals Yields Energy Efficiency + Reliably High Throughput
M~400 base station antennas serve K~40 terminals via multi-user MIMO
Doubling M permits a reduction in total transmit power by factor-of-two
Extra base station antennas always help (even with noisy CSI) Eventually produce inter-cellular interference-limited operation: everybody can
now reduce power arbitrarily! reduce effects of uncorrelated noise and fast fading
compensate for poor-quality channel-state information
Multiple Cells: No Cooperation
If we could assign an orthogonal pilot sequence to every terminal in every cell then nothing bad would happen! Ever greater numbers of base station antennas would eventually defeat all
noise, and eliminate both intra- and inter-cell interference
But there aren’t enough orthogonal pilot sequences for everyone! Pilot sequences have to be re-used
Pilot contamination: the base station inadvertently learns the channel to mobiles in other cells Forward link: base station transmits interference to mobiles in other cells Reverse link: base station processing enhances his reception of
transmission from mobiles in other cells
Inter-cell interference due to pilot contamination persists, even with an infinite number of antennas! This is the only remaining impairment
Limiting Case: Infinite Number of Antennas
•Greatly simplifies multi-cellular analysis: all effects accounted for near-analytically• Acquisition of CSI• Imperfections in CSI• Inter-cellular interference• Propagation
• Fast (either line-of-sight, or independent Rayleigh, or something intermediate)
• Slow (geometric, log-normal shadow)
•Far-reaching and comprehensive conclusions ensue•Indicates a new direction in which the macro-cellular world can go: vastly improved energy efficiency and throughput compared with LTE
Summary of Limit Analysis
Multi-cellular TDD scenario, 42 terminals served per cell
500 sec coherence interval (7 OFDM symbols): 3 reverse-link pilots, 1 idle, 3 data
OFDM: 20 MHz bandwidth, cyclic prefix 4.76 sec
Fading: Fast + log-normal shadow (8 dB) + geometric (3.8 power)
No inter-cellular cooperation
Net downlink throughput (comparable uplink) for frequency re-use 7
mean– 730 Mbits/sec/cell– 17 Mbits/sec/terminal
95% likely: 3.6 Mbits/sec/terminal spectral efficiency constant with respect to bandwidth
throughput constant with respect to cell-size
number of terminals per cell proportional to coherence interval
performance independent of power
Cells Operate Independently, Each Serving Single-Antenna Terminals via Multi-User MIMO: TDD Only!
Maximum number of terminals limited by the time that it takes to send reverse pilots: pilot-interval divided by the channel delay-spread
Coherence interval: 500 sec (7 LTE OFDM symbols) – TGV speeds! 3 symbols for reverse-link pilots
3 symbols for data
1 symbol for computations and dead time
42 terminals per cell served simultaneously
Infinitely Many Antennas: Forward-Link Capacity For 20 MHz Bandwidth, 42 Terminals per Cell, 500 sec Slot
Frequency Reuse .95-Likely SIR (dB)
.95-Likely Capacity per
Terminal (Mbits/s)
Mean Capacity per Terminal
(Mbits/s)
Mean Capacity per Cell (Mbits/s)
1 -29 .016 44 1800
3 -5.8 .89 28 1200
7 8.9 3.6 17 730
Interference-limited: energy-per-bit can be made arbitrarily small!
Mean Capacity per Cell (Mbits/s)
LTE Advanced(>= Release 10)
74
Infinitely Many Antennas: Forward-Link Capacity For 20 MHz Bandwidth, 42 Terminals per Cell, 500 sec Slot
Frequency Reuse .95-Likely SIR (dB)
.95-Likely Capacity per
Terminal (Mbits/s)
Mean Capacity per Terminal
(Mbits/s)
Mean Capacity per Cell (Mbits/s)
1 -29 .016 44 1800
3 -5.8 .89 28 1200
7 8.9 3.6 17 730
Interference-limited: energy-per-bit can be made arbitrarily small!
Mean Capacity per Cell (Mbits/s)
LTE Advanced(>= Release 10)
74
Motivation of massive MIMO
Consider a N × K MIMO MAC:
y =K∑
k=1
hkxk + n
where hk , n are i.i.d. with zero mean and unit variance.
By the strong law of large numbers:
1
Nhm
Hya.s.−−−−−−−−−−→
N→∞, K=const.xm
With an unlimited number of antennas,
uncorrelated interference and noise vanish,
the matched filter is optimal,
the transmit power can be made arbitrarily small.
T. Marzetta, “Noncooperative cellular wireless with unlimited numbers of base station antennas” IEEE Trans. Wireless Commun.,
vol. 9, no. 11, pp. 35903600, Nov. 2010.
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 4 / 30
Motivation of massive MIMO
Consider a N × K MIMO MAC:
y =K∑
k=1
hkxk + n
where hk , n are i.i.d. with zero mean and unit variance.
By the strong law of large numbers:
1
Nhm
Hya.s.−−−−−−−−−−→
N→∞, K=const.xm
With an unlimited number of antennas,
uncorrelated interference and noise vanish,
the matched filter is optimal,
the transmit power can be made arbitrarily small.
T. Marzetta, “Noncooperative cellular wireless with unlimited numbers of base station antennas” IEEE Trans. Wireless Commun.,
vol. 9, no. 11, pp. 35903600, Nov. 2010.
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 4 / 30
Motivation of massive MIMO
Consider a N × K MIMO MAC:
y =K∑
k=1
hkxk + n
where hk , n are i.i.d. with zero mean and unit variance.
By the strong law of large numbers:
1
Nhm
Hya.s.−−−−−−−−−−→
N→∞, K=const.xm
With an unlimited number of antennas,
uncorrelated interference and noise vanish,
the matched filter is optimal,
the transmit power can be made arbitrarily small.
T. Marzetta, “Noncooperative cellular wireless with unlimited numbers of base station antennas” IEEE Trans. Wireless Commun.,
vol. 9, no. 11, pp. 35903600, Nov. 2010.
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 4 / 30
About some fundamental assumptions
The receiver has perfect channel state information (CSI).What happens if the channel must be estimated?
The number of interferers K is small compared to N.What does small mean?
The channel provides infinite diversity, i.e., each antenna gives an independent lookon the transmitted signal.
What if the degrees of freedom are limited?
The received energy grows without bounds as N →∞.Clearly wrong, but might hold up to very large antenna arrays if theaperture scales with N.
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 5 / 30
About some fundamental assumptions
The receiver has perfect channel state information (CSI).What happens if the channel must be estimated?
The number of interferers K is small compared to N.What does small mean?
The channel provides infinite diversity, i.e., each antenna gives an independent lookon the transmitted signal.
What if the degrees of freedom are limited?
The received energy grows without bounds as N →∞.Clearly wrong, but might hold up to very large antenna arrays if theaperture scales with N.
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 5 / 30
About some fundamental assumptions
The receiver has perfect channel state information (CSI).What happens if the channel must be estimated?
The number of interferers K is small compared to N.What does small mean?
The channel provides infinite diversity, i.e., each antenna gives an independent lookon the transmitted signal.
What if the degrees of freedom are limited?
The received energy grows without bounds as N →∞.Clearly wrong, but might hold up to very large antenna arrays if theaperture scales with N.
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 5 / 30
About some fundamental assumptions
The receiver has perfect channel state information (CSI).What happens if the channel must be estimated?
The number of interferers K is small compared to N.What does small mean?
The channel provides infinite diversity, i.e., each antenna gives an independent lookon the transmitted signal.
What if the degrees of freedom are limited?
The received energy grows without bounds as N →∞.Clearly wrong, but might hold up to very large antenna arrays if theaperture scales with N.
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 5 / 30
On channel estimation and pilot contamination
1 The receiver estimates the channels based on pilot sequences.
2 The number of orthogonal sequences is limited by the coherence time.
3 Thus, the pilot sequences must be reused.
Assume that transmitter m and j use the same pilot sequence:
hm = hm + hj︸︷︷︸pilot contamination
+ nm︸︷︷︸estimation noise
Thus,1
Nhm
Hya.s−−−−−−−−−→
N→∞,K=const.xm + xj
With an unlimited number of antennas,
uncorrelated interference, noise and estimation errors vanish,
the matched filter is optimal,
the transmit power can be made arbitrarily small (∼ 1/√N [Ngo’11]),
but the performance is limited by pilot contamination.
T. Marzetta, “Noncooperative cellular wireless with unlimited numbers of base station antennas” IEEE Trans. Wireless Commun.,
vol. 9, no. 11, pp. 35903600, Nov. 2010.
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 6 / 30
On channel estimation and pilot contamination
1 The receiver estimates the channels based on pilot sequences.
2 The number of orthogonal sequences is limited by the coherence time.
3 Thus, the pilot sequences must be reused.
Assume that transmitter m and j use the same pilot sequence:
hm = hm + hj︸︷︷︸pilot contamination
+ nm︸︷︷︸estimation noise
Thus,1
Nhm
Hya.s−−−−−−−−−→
N→∞,K=const.xm + xj
With an unlimited number of antennas,
uncorrelated interference, noise and estimation errors vanish,
the matched filter is optimal,
the transmit power can be made arbitrarily small (∼ 1/√N [Ngo’11]),
but the performance is limited by pilot contamination.
T. Marzetta, “Noncooperative cellular wireless with unlimited numbers of base station antennas” IEEE Trans. Wireless Commun.,
vol. 9, no. 11, pp. 35903600, Nov. 2010.
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 6 / 30
On channel estimation and pilot contamination
1 The receiver estimates the channels based on pilot sequences.
2 The number of orthogonal sequences is limited by the coherence time.
3 Thus, the pilot sequences must be reused.
Assume that transmitter m and j use the same pilot sequence:
hm = hm + hj︸︷︷︸pilot contamination
+ nm︸︷︷︸estimation noise
Thus,1
Nhm
Hya.s−−−−−−−−−→
N→∞,K=const.xm + xj
With an unlimited number of antennas,
uncorrelated interference, noise and estimation errors vanish,
the matched filter is optimal,
the transmit power can be made arbitrarily small (∼ 1/√N [Ngo’11]),
but the performance is limited by pilot contamination.
T. Marzetta, “Noncooperative cellular wireless with unlimited numbers of base station antennas” IEEE Trans. Wireless Commun.,
vol. 9, no. 11, pp. 35903600, Nov. 2010.
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 6 / 30
On channel estimation and pilot contamination
1 The receiver estimates the channels based on pilot sequences.
2 The number of orthogonal sequences is limited by the coherence time.
3 Thus, the pilot sequences must be reused.
Assume that transmitter m and j use the same pilot sequence:
hm = hm + hj︸︷︷︸pilot contamination
+ nm︸︷︷︸estimation noise
Thus,1
Nhm
Hya.s−−−−−−−−−→
N→∞,K=const.xm + xj
With an unlimited number of antennas,
uncorrelated interference, noise and estimation errors vanish,
the matched filter is optimal,
the transmit power can be made arbitrarily small (∼ 1/√N [Ngo’11]),
but the performance is limited by pilot contamination.
T. Marzetta, “Noncooperative cellular wireless with unlimited numbers of base station antennas” IEEE Trans. Wireless Commun.,
vol. 9, no. 11, pp. 35903600, Nov. 2010.
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 6 / 30
Uplink
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 7 / 30
System model and channel estimation
Uplink: L BSs with N antennas, K UTs per cell. Received signal at BS j :
yj =√ρ
L∑l=1
Hjlxl + nj
The columns of Hjl (N × K) are modeled as
hjlk = R12jlkwjlk , wjlk ∼ CN (0, IN)
Channel estimation:
yτjk = hjjk +∑l 6=j
hjlk +1√ρτ
njk
MMSE estimate: hjjk = hjjk + hjjk
hjjk ∼ CN (0,Φjjk) , hjjk ∼ CN (0,Rjjk −Φjjk)
Φjlk = RjjkQjkRjlk , Qjk =
(1
ρτIN +
∑l
Rjlk
)−1
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 8 / 30
System model and channel estimation
Uplink: L BSs with N antennas, K UTs per cell. Received signal at BS j :
yj =√ρ
L∑l=1
Hjlxl + nj
The columns of Hjl (N × K) are modeled as
hjlk = R12jlkwjlk , wjlk ∼ CN (0, IN)
Channel estimation:
yτjk = hjjk +∑l 6=j
hjlk +1√ρτ
njk
MMSE estimate: hjjk = hjjk + hjjk
hjjk ∼ CN (0,Φjjk) , hjjk ∼ CN (0,Rjjk −Φjjk)
Φjlk = RjjkQjkRjlk , Qjk =
(1
ρτIN +
∑l
Rjlk
)−1
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 8 / 30
System model and channel estimation
Uplink: L BSs with N antennas, K UTs per cell. Received signal at BS j :
yj =√ρ
L∑l=1
Hjlxl + nj
The columns of Hjl (N × K) are modeled as
hjlk = R12jlkwjlk , wjlk ∼ CN (0, IN)
Channel estimation:
yτjk = hjjk +∑l 6=j
hjlk +1√ρτ
njk
MMSE estimate: hjjk = hjjk + hjjk
hjjk ∼ CN (0,Φjjk) , hjjk ∼ CN (0,Rjjk −Φjjk)
Φjlk = RjjkQjkRjlk , Qjk =
(1
ρτIN +
∑l
Rjlk
)−1
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 8 / 30
System model and channel estimation
Uplink: L BSs with N antennas, K UTs per cell. Received signal at BS j :
yj =√ρ
L∑l=1
Hjlxl + nj
The columns of Hjl (N × K) are modeled as
hjlk = R12jlkwjlk , wjlk ∼ CN (0, IN)
Channel estimation:
yτjk = hjjk +∑l 6=j
hjlk +1√ρτ
njk
MMSE estimate: hjjk = hjjk + hjjk
hjjk ∼ CN (0,Φjjk) , hjjk ∼ CN (0,Rjjk −Φjjk)
Φjlk = RjjkQjkRjlk , Qjk =
(1
ρτIN +
∑l
Rjlk
)−1
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 8 / 30
System model and channel estimation
Uplink: L BSs with N antennas, K UTs per cell. Received signal at BS j :
yj =√ρ
L∑l=1
Hjlxl + nj
The columns of Hjl (N × K) are modeled as
hjlk = R12jlkwjlk , wjlk ∼ CN (0, IN)
Channel estimation:
yτjk = hjjk +∑l 6=j
hjlk +1√ρτ
njk
MMSE estimate: hjjk = hjjk + hjjk
hjjk ∼ CN (0,Φjjk) , hjjk ∼ CN (0,Rjjk −Φjjk)
Φjlk = RjjkQjkRjlk , Qjk =
(1
ρτIN +
∑l
Rjlk
)−1
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 8 / 30
Achievable rates with linear detectorsErgodic achievable rate of UT m in cell j :
Rjm = EHjj[log2 (1 + γjm)]
γjm =
∣∣∣rHjmhjjm
∣∣∣2E[rHjm
(1ρ
IN + hjjmhHjjm − hjjmhH
jjm +∑
l HjlHHjl
)rjm∣∣∣Hjj
]with an arbitrary receive filter rjm.
Two specific linear detectors rjm:
rMFjm = hjjm
rMMSEjm =
(HjjH
Hjj + Zj + NλIN
)−1
hjjm
where λ > 0 is a design parameter and
Zj = E
HjjHHjj +
∑l 6=j
HjlHjl
=∑k
(Rjjk −Φjjk) +∑l 6=j
∑k
Rjlk .
B. Hassibi and B. M. Hochwald, “How much training is needed in multiple-antenna wireless links?” IEEE Trans. Inf. Theory., vol.
49, no. 4, pp. 951–963, Nov. 2003.
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 9 / 30
Achievable rates with linear detectorsErgodic achievable rate of UT m in cell j :
Rjm = EHjj[log2 (1 + γjm)]
γjm =
∣∣∣rHjmhjjm
∣∣∣2E[rHjm
(1ρ
IN + hjjmhHjjm − hjjmhH
jjm +∑
l HjlHHjl
)rjm∣∣∣Hjj
]with an arbitrary receive filter rjm.
Two specific linear detectors rjm:
rMFjm = hjjm
rMMSEjm =
(HjjH
Hjj + Zj + NλIN
)−1
hjjm
where λ > 0 is a design parameter and
Zj = E
HjjHHjj +
∑l 6=j
HjlHjl
=∑k
(Rjjk −Φjjk) +∑l 6=j
∑k
Rjlk .
B. Hassibi and B. M. Hochwald, “How much training is needed in multiple-antenna wireless links?” IEEE Trans. Inf. Theory., vol.
49, no. 4, pp. 951–963, Nov. 2003.
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 9 / 30
Large system analysis based on random matrix theory
Assume N,K →∞ at the same speed. Then,
γjm − γjma.s.−−→ 0
Rjm − log2 (1 + γjm)a.s.−−→ 0
where
γMFjm =
(1N
tr Φjjm
)2
1ρN2 tr Φjjm + 1
N
∑l,k
1N
tr RjlkΦjjm +∑
l 6=j
∣∣ 1N
tr Φjlm
∣∣2
γMMSEjm =
δ2jm
1ρN2 tr ΦjjmT′j + 1
N
∑l,k µjlkm +
∑l 6=j |ϑjlm|2
and δjm, µjlkm, θjlm, T′j can be calculated numerically.
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 10 / 30
Large system analysis based on random matrix theory
Assume N,K →∞ at the same speed. Then,
γjm − γjma.s.−−→ 0
Rjm − log2 (1 + γjm)a.s.−−→ 0
where
γMFjm =
(1N
tr Φjjm
)2
1ρN2 tr Φjjm + 1
N
∑l,k
1N
tr RjlkΦjjm +∑
l 6=j
∣∣ 1N
tr Φjlm
∣∣2
γMMSEjm =
δ2jm
1ρN2 tr ΦjjmT′j + 1
N
∑l,k µjlkm +
∑l 6=j |ϑjlm|2
and δjm, µjlkm, θjlm, T′j can be calculated numerically.
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 10 / 30
A simple multi-cell scenario
intercell interference factor α ∈ [0, 1]transmit power per UT: ρHjl = [hjl1 · · · hjlK ] =
√N/PAWjl
A ∈ CN×Pcomposed of P ≤ N columns of a unitary matrix
Wij ∈ CP×Khave i.i.d. elements with zero mean and unit variance
Assumptions:
P channel degrees of freedom, i.e., rank (Hjl) = min(P,K) [Ngo’11]energy scales linearly with N, i.e., E
[tr HjlH
Hjl
]= KN
only pilot contamination, i.e., no estimation noise:
hjjk = hjjk +√α∑l 6=j
hjlk
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 11 / 30
A simple multi-cell scenario
intercell interference factor α ∈ [0, 1]transmit power per UT: ρHjl = [hjl1 · · · hjlK ] =
√N/PAWjl
A ∈ CN×Pcomposed of P ≤ N columns of a unitary matrix
Wij ∈ CP×Khave i.i.d. elements with zero mean and unit variance
Assumptions:
P channel degrees of freedom, i.e., rank (Hjl) = min(P,K) [Ngo’11]energy scales linearly with N, i.e., E
[tr HjlH
Hjl
]= KN
only pilot contamination, i.e., no estimation noise:
hjjk = hjjk +√α∑l 6=j
hjlk
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 11 / 30
A simple multi-cell scenario
intercell interference factor α ∈ [0, 1]transmit power per UT: ρHjl = [hjl1 · · · hjlK ] =
√N/PAWjl
A ∈ CN×Pcomposed of P ≤ N columns of a unitary matrix
Wij ∈ CP×Khave i.i.d. elements with zero mean and unit variance
Assumptions:
P channel degrees of freedom, i.e., rank (Hjl) = min(P,K) [Ngo’11]energy scales linearly with N, i.e., E
[tr HjlH
Hjl
]= KN
only pilot contamination, i.e., no estimation noise:
hjjk = hjjk +√α∑l 6=j
hjlk
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 11 / 30
Asymptotic performance of the matched filter
Assume that N, K and P grow infinitely large at the same speed:
SINRMF ≈ 1
L
ρN︸︷︷︸noise
+K
PL2︸ ︷︷ ︸
multi-user interference
+ α(L− 1)︸ ︷︷ ︸pilot contamination
where L = 1 + α(L− 1).
Observations:
The effective SNR ρN increases linearly with N.
The multiuser interference depends on P/K and not on N.
Ultimate performance limit:
SINRMF a.s−−−−−−−−−−−→N,P→∞, K=const.
SINR∞ =1
α(L− 1)
J. Hoydis, S. ten Brink, and M. Debbah, “Massive MIMO: How many antennas do we need”, Allerton Conference,
Urbana-Champaing, Illinois, US, Sep. 2011. [Online] http://arxiv.org/abs/1107.1709
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 12 / 30
Asymptotic performance of the matched filter
Assume that N, K and P grow infinitely large at the same speed:
SINRMF ≈ 1
L
ρN︸︷︷︸noise
+K
PL2︸ ︷︷ ︸
multi-user interference
+ α(L− 1)︸ ︷︷ ︸pilot contamination
where L = 1 + α(L− 1).
Observations:
The effective SNR ρN increases linearly with N.
The multiuser interference depends on P/K and not on N.
Ultimate performance limit:
SINRMF a.s−−−−−−−−−−−→N,P→∞, K=const.
SINR∞ =1
α(L− 1)
J. Hoydis, S. ten Brink, and M. Debbah, “Massive MIMO: How many antennas do we need”, Allerton Conference,
Urbana-Champaing, Illinois, US, Sep. 2011. [Online] http://arxiv.org/abs/1107.1709
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 12 / 30
Asymptotic performance of the MMSE detector
Assume that N, K and P grow infinitely large at the same speed:
SINRMMSE ≈ 1
L
ρNX︸ ︷︷ ︸
noise
+K
PL2Y︸ ︷︷ ︸
multi-user interference
+ α(L− 1)︸ ︷︷ ︸pilot contamination
where L = 1 + α(L− 1) and X ,Y are given in closed-form.
Observations:
As for the MF, the performance depends only on ρN and P/K .
The ultimate performance of MMSE and MF coincide:
SINRMMSE a.s−−−−−−−−−−−→N,P→∞, K=const.
SINR∞ =1
α(L− 1)
J. Hoydis, S. ten Brink, and M. Debbah, “Massive MIMO: How many antennas do we need”, Allerton Conference,
Urbana-Champaing, Illinois, US, Sep. 2011. [Online] http://arxiv.org/abs/1107.1709
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 13 / 30
Asymptotic performance of the MMSE detector
Assume that N, K and P grow infinitely large at the same speed:
SINRMMSE ≈ 1
L
ρNX︸ ︷︷ ︸
noise
+K
PL2Y︸ ︷︷ ︸
multi-user interference
+ α(L− 1)︸ ︷︷ ︸pilot contamination
where L = 1 + α(L− 1) and X ,Y are given in closed-form.
Observations:
As for the MF, the performance depends only on ρN and P/K .
The ultimate performance of MMSE and MF coincide:
SINRMMSE a.s−−−−−−−−−−−→N,P→∞, K=const.
SINR∞ =1
α(L− 1)
J. Hoydis, S. ten Brink, and M. Debbah, “Massive MIMO: How many antennas do we need”, Allerton Conference,
Urbana-Champaing, Illinois, US, Sep. 2011. [Online] http://arxiv.org/abs/1107.1709
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 13 / 30
Numerical results
0 100 200 300 4000
1
2
3
4
5
R∞ P = N
P = N/3
ρ = 1, K = 10, α = 0.1, L = 4
Number of antennas N
Erg
odic
achi
evab
lera
te(b
/s/H
z)
MF approx.MMSE approx.Simulations
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 14 / 30
Conclusions (I) - Uplink
Massive MIMO can be seen as a particular operating condition where
noise + interference� pilot contamination.
If this condition is satisfied depends on:
P/K : degrees of freedom per UT
ρN : effective SNR (transmit power × number of antennas)
α : path loss (or intercell interference)
Connection between N and P is crucial, but unclear for real channels.
As N →∞, MF and MMSE detector achieve identical performance. For finite N,the MMSE detector largely outperforms the MF.
The number of antennas needed for massive MIMO depends on all these parameters!
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 18 / 30
Conclusions (I) - Uplink
Massive MIMO can be seen as a particular operating condition where
noise + interference� pilot contamination.
If this condition is satisfied depends on:
P/K : degrees of freedom per UT
ρN : effective SNR (transmit power × number of antennas)
α : path loss (or intercell interference)
Connection between N and P is crucial, but unclear for real channels.
As N →∞, MF and MMSE detector achieve identical performance. For finite N,the MMSE detector largely outperforms the MF.
The number of antennas needed for massive MIMO depends on all these parameters!
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 18 / 30
Conclusions (I) - Uplink
Massive MIMO can be seen as a particular operating condition where
noise + interference� pilot contamination.
If this condition is satisfied depends on:
P/K : degrees of freedom per UT
ρN : effective SNR (transmit power × number of antennas)
α : path loss (or intercell interference)
Connection between N and P is crucial, but unclear for real channels.
As N →∞, MF and MMSE detector achieve identical performance. For finite N,the MMSE detector largely outperforms the MF.
The number of antennas needed for massive MIMO depends on all these parameters!
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 18 / 30
Conclusions (I) - Uplink
Massive MIMO can be seen as a particular operating condition where
noise + interference� pilot contamination.
If this condition is satisfied depends on:
P/K : degrees of freedom per UT
ρN : effective SNR (transmit power × number of antennas)
α : path loss (or intercell interference)
Connection between N and P is crucial, but unclear for real channels.
As N →∞, MF and MMSE detector achieve identical performance. For finite N,the MMSE detector largely outperforms the MF.
The number of antennas needed for massive MIMO depends on all these parameters!
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 18 / 30
Conclusions (I) - Uplink
Massive MIMO can be seen as a particular operating condition where
noise + interference� pilot contamination.
If this condition is satisfied depends on:
P/K : degrees of freedom per UT
ρN : effective SNR (transmit power × number of antennas)
α : path loss (or intercell interference)
Connection between N and P is crucial, but unclear for real channels.
As N →∞, MF and MMSE detector achieve identical performance. For finite N,the MMSE detector largely outperforms the MF.
The number of antennas needed for massive MIMO depends on all these parameters!
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 18 / 30
Downlink
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 19 / 30
System model: Downlink
L BSs with N antennas, K UTs per cell. Received signal at mth UT in cell j :
yjm =√ρ
L∑l=1
hHljmsl + qjm
where
sl =√λl
K∑m=1
wlmxlm =√λlWlxl
λl =1
tr WlWHl
=⇒ E[ρsH
l sl]
= ρ
Channel estimation through uplink pilots (as before):
hjjk = hjjk + hjjk
hjjk ∼ CN (0,Φjjk) , hjjk ∼ CN (0,Rjjk −Φjjk)
Φjlk = RjjkQjkRjlk , Qjk =
(1
ρτIN +
∑l
Rjlk
)−1
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 20 / 30
System model: Downlink
L BSs with N antennas, K UTs per cell. Received signal at mth UT in cell j :
yjm =√ρ
L∑l=1
hHljmsl + qjm
where
sl =√λl
K∑m=1
wlmxlm =√λlWlxl
λl =1
tr WlWHl
=⇒ E[ρsH
l sl]
= ρ
Channel estimation through uplink pilots (as before):
hjjk = hjjk + hjjk
hjjk ∼ CN (0,Φjjk) , hjjk ∼ CN (0,Rjjk −Φjjk)
Φjlk = RjjkQjkRjlk , Qjk =
(1
ρτIN +
∑l
Rjlk
)−1
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 20 / 30
System model: Downlink
L BSs with N antennas, K UTs per cell. Received signal at mth UT in cell j :
yjm =√ρ
L∑l=1
hHljmsl + qjm
where
sl =√λl
K∑m=1
wlmxlm =√λlWlxl
λl =1
tr WlWHl
=⇒ E[ρsH
l sl]
= ρ
Channel estimation through uplink pilots (as before):
hjjk = hjjk + hjjk
hjjk ∼ CN (0,Φjjk) , hjjk ∼ CN (0,Rjjk −Φjjk)
Φjlk = RjjkQjkRjlk , Qjk =
(1
ρτIN +
∑l
Rjlk
)−1
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 20 / 30
Achievable rates with linear precoders
Ergodic achievable rate of UT m in cell j :
Rjm = log2 (1 + γjm)
γjm =
∣∣E [√λjhHjjmwjm
]∣∣21ρ
+ var[√
λjhHjjmwjm
]+∑
(l,k)6=(j,m) E[∣∣∣√λlhH
ljmwlk
∣∣∣2] .
Two specific precoders Wj :
WBFj
4= Hjj
WRZFj
4=(
HjjHHjj + Fj + NαIN
)−1
Hjj
where α > 0 and Fj are design parameters.
J. Jose, A. Ashikhmin, T. Marzetta, and S. Vishwanath, “Pilot contamination and precoding in multi-cell TDD systems,” IEEE
Trans. Wireless Commun., no. 99, pp. 1–12, 2011.
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 21 / 30
Achievable rates with linear precoders
Ergodic achievable rate of UT m in cell j :
Rjm = log2 (1 + γjm)
γjm =
∣∣E [√λjhHjjmwjm
]∣∣21ρ
+ var[√
λjhHjjmwjm
]+∑
(l,k)6=(j,m) E[∣∣∣√λlhH
ljmwlk
∣∣∣2] .
Two specific precoders Wj :
WBFj
4= Hjj
WRZFj
4=(
HjjHHjj + Fj + NαIN
)−1
Hjj
where α > 0 and Fj are design parameters.
J. Jose, A. Ashikhmin, T. Marzetta, and S. Vishwanath, “Pilot contamination and precoding in multi-cell TDD systems,” IEEE
Trans. Wireless Commun., no. 99, pp. 1–12, 2011.
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 21 / 30
Large system analysis based on random matrix theory
Assume N,K →∞ at the same speed. Then,
γjm − γjma.s.−−→ 0
Rjm − log2 (1 + γjm)a.s.−−→ 0
where
γBFjm =
λj
(1N
tr Φjjm
)2
KNρ
+ 1N
∑l,k λl
1N
tr RljmΦllk +∑
l 6=j λj
∣∣ 1N
tr Φljm
∣∣2γRZFjm =
λjδ2jm
KNρ
(1 + δjm)2 + 1N
∑l,k λl
(1+δjm1+δlk
)2
µljmk +∑
l 6=j λl
(1+δjm1+δlm
)2
|ϑljm|2
and λj , δjm, µjlkm and ϑjlm can be calculated numerically.
J. Hoydis, S. ten Brink, M. Debbah, “Comparison of linear precoding schemes for downlink Massive MIMO”, ICC’12, 2011.
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 22 / 30
Large system analysis based on random matrix theory
Assume N,K →∞ at the same speed. Then,
γjm − γjma.s.−−→ 0
Rjm − log2 (1 + γjm)a.s.−−→ 0
where
γBFjm =
λj
(1N
tr Φjjm
)2
KNρ
+ 1N
∑l,k λl
1N
tr RljmΦllk +∑
l 6=j λj
∣∣ 1N
tr Φljm
∣∣2γRZFjm =
λjδ2jm
KNρ
(1 + δjm)2 + 1N
∑l,k λl
(1+δjm1+δlk
)2
µljmk +∑
l 6=j λl
(1+δjm1+δlm
)2
|ϑljm|2
and λj , δjm, µjlkm and ϑjlm can be calculated numerically.
J. Hoydis, S. ten Brink, M. Debbah, “Comparison of linear precoding schemes for downlink Massive MIMO”, ICC’12, 2011.
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 22 / 30
Downlink: Numerical results
−3 −2 −1 0 1 2 3−3
−2
−1
0
1
2
3
Base stationsUser terminals
cell l
UT kdjlk2
cell j
34
7 cells, K = 10 UTs distributed on a circle of radius 3/4
path loss exponent β = 3.7, ρτ = 6 dB, ρ = 10 dB
Two channel models:
I No correlation
I Rjlk = d−β/2jlk [A 0N×N−P ], where A = [a(φ1) · · · a(φP)] ∈CN×P
with
a(φp) =1√P
[1, e−i2πc sin(φ), . . . , e−i2πc(N−1) sin(φ)
]T
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 23 / 30
Downlink: Numerical results
−3 −2 −1 0 1 2 3−3
−2
−1
0
1
2
3
Base stationsUser terminals
cell l
UT kdjlk2
cell j
34
7 cells, K = 10 UTs distributed on a circle of radius 3/4
path loss exponent β = 3.7, ρτ = 6 dB, ρ = 10 dB
Two channel models:
I No correlation
I Rjlk = d−β/2jlk [A 0N×N−P ], where A = [a(φ1) · · · a(φP)] ∈CN×P
with
a(φp) =1√P
[1, e−i2πc sin(φ), . . . , e−i2πc(N−1) sin(φ)
]T
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 23 / 30
Downlink: Numerical results
−3 −2 −1 0 1 2 3−3
−2
−1
0
1
2
3
Base stationsUser terminals
cell l
UT kdjlk2
cell j
34
7 cells, K = 10 UTs distributed on a circle of radius 3/4
path loss exponent β = 3.7, ρτ = 6 dB, ρ = 10 dB
Two channel models:
I No correlation
I Rjlk = d−β/2jlk [A 0N×N−P ], where A = [a(φ1) · · · a(φP)] ∈CN×P
with
a(φp) =1√P
[1, e−i2πc sin(φ), . . . , e−i2πc(N−1) sin(φ)
]T
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 23 / 30
Downlink: Numerical results
0 100 200 300 4000
2
4
6
8
10
12R∞ = 15.75 bits/s/Hz
RZF
BF
Number of antennas N
Ave
rage
rate
per
UT
(bits
/s/H
z)
No CorrelationPhysical ModelSimulations
P = N/2, α = 1/ρ,Fj = 0
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 24 / 30
Conclusions (II) - Downlink
For finite N, RZF is largely superior to BF:A matrix inversion can reduce the number of antennas by one order of magnitude!
Whether or not massive MIMO will show its theoretical gains in practice depends onthe validity of our channel models.
Reducing signal processing complexity by adding more antennas seems a bad idea.
Many antennas at the BS require TDD (FDD: overhead scales linearly with N)
Related work:
Overview paper: Rusek, et al., “Scaling up MIMO: Opportunities and Challengeswith Very Large Arrays”, IEEE Signal Processing Magazine, to appear.http://liu.diva-portal.org/smash/record.jsf?pid=diva2:450781
Constant-envelope precoding: S. Mohammed, E. Larsson, “Single-User Beamformingin Large-Scale MISO Systems with Per-Antenna Constant-Envelope Constraints:The Doughnut Channel”, http://arxiv.org/abs/1111.3752v1
Network MIMO TDD systems: Huh, Caire, et al., “Achieving “Massive MIMO”Spectral Efficiency with a Not-so-Large Number of Antennas”,http://arxiv.org/abs/1107.3862
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 25 / 30
Conclusions (II) - Downlink
For finite N, RZF is largely superior to BF:A matrix inversion can reduce the number of antennas by one order of magnitude!
Whether or not massive MIMO will show its theoretical gains in practice depends onthe validity of our channel models.
Reducing signal processing complexity by adding more antennas seems a bad idea.
Many antennas at the BS require TDD (FDD: overhead scales linearly with N)
Related work:
Overview paper: Rusek, et al., “Scaling up MIMO: Opportunities and Challengeswith Very Large Arrays”, IEEE Signal Processing Magazine, to appear.http://liu.diva-portal.org/smash/record.jsf?pid=diva2:450781
Constant-envelope precoding: S. Mohammed, E. Larsson, “Single-User Beamformingin Large-Scale MISO Systems with Per-Antenna Constant-Envelope Constraints:The Doughnut Channel”, http://arxiv.org/abs/1111.3752v1
Network MIMO TDD systems: Huh, Caire, et al., “Achieving “Massive MIMO”Spectral Efficiency with a Not-so-Large Number of Antennas”,http://arxiv.org/abs/1107.3862
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 25 / 30
Conclusions (II) - Downlink
For finite N, RZF is largely superior to BF:A matrix inversion can reduce the number of antennas by one order of magnitude!
Whether or not massive MIMO will show its theoretical gains in practice depends onthe validity of our channel models.
Reducing signal processing complexity by adding more antennas seems a bad idea.
Many antennas at the BS require TDD (FDD: overhead scales linearly with N)
Related work:
Overview paper: Rusek, et al., “Scaling up MIMO: Opportunities and Challengeswith Very Large Arrays”, IEEE Signal Processing Magazine, to appear.http://liu.diva-portal.org/smash/record.jsf?pid=diva2:450781
Constant-envelope precoding: S. Mohammed, E. Larsson, “Single-User Beamformingin Large-Scale MISO Systems with Per-Antenna Constant-Envelope Constraints:The Doughnut Channel”, http://arxiv.org/abs/1111.3752v1
Network MIMO TDD systems: Huh, Caire, et al., “Achieving “Massive MIMO”Spectral Efficiency with a Not-so-Large Number of Antennas”,http://arxiv.org/abs/1107.3862
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 25 / 30
Conclusions (II) - Downlink
For finite N, RZF is largely superior to BF:A matrix inversion can reduce the number of antennas by one order of magnitude!
Whether or not massive MIMO will show its theoretical gains in practice depends onthe validity of our channel models.
Reducing signal processing complexity by adding more antennas seems a bad idea.
Many antennas at the BS require TDD (FDD: overhead scales linearly with N)
Related work:
Overview paper: Rusek, et al., “Scaling up MIMO: Opportunities and Challengeswith Very Large Arrays”, IEEE Signal Processing Magazine, to appear.http://liu.diva-portal.org/smash/record.jsf?pid=diva2:450781
Constant-envelope precoding: S. Mohammed, E. Larsson, “Single-User Beamformingin Large-Scale MISO Systems with Per-Antenna Constant-Envelope Constraints:The Doughnut Channel”, http://arxiv.org/abs/1111.3752v1
Network MIMO TDD systems: Huh, Caire, et al., “Achieving “Massive MIMO”Spectral Efficiency with a Not-so-Large Number of Antennas”,http://arxiv.org/abs/1107.3862
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 25 / 30
Conclusions (II) - Downlink
For finite N, RZF is largely superior to BF:A matrix inversion can reduce the number of antennas by one order of magnitude!
Whether or not massive MIMO will show its theoretical gains in practice depends onthe validity of our channel models.
Reducing signal processing complexity by adding more antennas seems a bad idea.
Many antennas at the BS require TDD (FDD: overhead scales linearly with N)
Related work:
Overview paper: Rusek, et al., “Scaling up MIMO: Opportunities and Challengeswith Very Large Arrays”, IEEE Signal Processing Magazine, to appear.http://liu.diva-portal.org/smash/record.jsf?pid=diva2:450781
Constant-envelope precoding: S. Mohammed, E. Larsson, “Single-User Beamformingin Large-Scale MISO Systems with Per-Antenna Constant-Envelope Constraints:The Doughnut Channel”, http://arxiv.org/abs/1111.3752v1
Network MIMO TDD systems: Huh, Caire, et al., “Achieving “Massive MIMO”Spectral Efficiency with a Not-so-Large Number of Antennas”,http://arxiv.org/abs/1107.3862
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 25 / 30
Related publications
I T. L. MarzettaNoncooperative cellular wireless with unlimited numbers of base station antennasIEEE Trans. Wireless Commun., vol. 9, no. 11, pp. 3590–3600, Nov. 2010.
I H. Q. Ngo, E. G. Larsson, T. L. MarzettaAnalysis of the pilot contamination effect in very large multicell multiuser MIMOsystems for physical channel modelsProc. IEEE SPAWC’11, Prague, Czech Repulic, May 2011.
I H. Q. Ngo, E. G. Larsson, T. L. MarzettaUplink power efficiency of multiuser MIMO with very large antenna arraysAllerton Conference, Urbana-Champaing, Illinois, US, Sep. 2011.
I J. Hoydis, S. ten Brink, M. DebbahMassive MIMO: How many antennas do we need?Allerton Conference, Urbana-Champaing, Illinois, US, Sep. 2011, [Online]http://arxiv.org/abs/1107.1709.
I J. Hoydis, S. ten Brink, M. DebbahComparison of linear precoding schemes for downlink Massive MIMOICC’12, submitted, 2010.
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 29 / 30
A two-tier network architecture
Massive MIMO base stations (BS) overlaid with many small cells (SCs)BSs ensure coverage and serve highly mobile UEsSCs drive the capacity (hot spots, indoor coverage)
Intra- and inter-tier interference is the main performance bottleneck.
There are many excess antennas in the network which should be exploited!
Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 3 / 23
A two-tier network architecture
Massive MIMO base stations (BS) overlaid with many small cells (SCs)BSs ensure coverage and serve highly mobile UEsSCs drive the capacity (hot spots, indoor coverage)
Intra- and inter-tier interference is the main performance bottleneck.
There are many excess antennas in the network which should be exploited!
Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 3 / 23
A two-tier network architecture
Massive MIMO base stations (BS) overlaid with many small cells (SCs)BSs ensure coverage and serve highly mobile UEsSCs drive the capacity (hot spots, indoor coverage)
Intra- and inter-tier interference is the main performance bottleneck.
There are many excess antennas in the network which should be exploited!
Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 3 / 23
The essential role of TDD
A network-wide synchronized TDD protocol and the resulting channel reciprocity havethe following advantages:
The downlink channels can be estimated from uplink pilots.
→ Necessary for massive MIMO
Channel reciprocity holds for the desired and the interfering channels.
→ Knowledge about the interfering channels can be acquired for free.
TDD enables the use of excess antennas to reduce intra-/inter-tier interference.
Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 4 / 23
An idea from cognitive radio
1 The secondary BS listens to the transmission from the primary UE:
y = hx + n
2 ...and computes the covariance matrix of the received signal:
E[yyH]
= hhH + SNR−1I
Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 5 / 23
An idea from cognitive radio
3 With the knowledge of the SNR, the secondary BS designs a precoder w which isorthogonal to the sub-space spanned by hhH.
4 The interference to the primary UE can be entirely eliminated without explicitknowledge of h.
Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 6 / 23
An idea from cognitive radio
3 With the knowledge of the SNR, the secondary BS designs a precoder w which isorthogonal to the sub-space spanned by hhH.
4 The interference to the primary UE can be entirely eliminated without explicitknowledge of h.
Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 6 / 23
Translating this idea to HetNets
Every device estimates its received interference covariance matrix and precodes (partially)orthogonally to the dominating interference subspace.
Advantages
Reduces interference towards the directions from which most interference is received.
No feedback or data exchange between the devices is needed.
Every device relies only on locally available information.
The scheme is fully distributed and, thus, scalable.
Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 7 / 23
Translating this idea to HetNets
Every device estimates its received interference covariance matrix and precodes (partially)orthogonally to the dominating interference subspace.
Advantages
Reduces interference towards the directions from which most interference is received.
No feedback or data exchange between the devices is needed.
Every device relies only on locally available information.
The scheme is fully distributed and, thus, scalable.
Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 7 / 23
About the literature
Cognitive radioI R. Zhang, F. Gao, and Y. C. Liang, “Cognitive Beamforming Made Practical: Effective
Interference Channel and Learning-Throughput Tradeoff,” IEEE Trans. Commun.,2010.
I F. Gao, R. Zhang, Y.-C. Liang, X. Wang, “Design of Learning-Based MIMO CognitiveRadio Systems,” IEEE Trans. Veh. Tech., 2010.
I H. Yi, “Nullspace-Based Secondary Joint Transceiver Scheme for Cognitive RadioMIMO Networks Using Second-Order Statistics,” ICC, 2010.
TDD Cellular systemsI S. Lei and S. Roy, “Downlink multicell MIMO-OFDM: an architecture for next
generation wireless networks,” WCNC, 2005.
I B. O. Lee, H. W. Je, I. Sohn, O. S. Shin, and K. B. Lee, “Interference-awareDecentralized Precoding for Multicell MIMO TDD Systems,” Globecom. 2008.
Blind nullspace learningI Y. Noam and A. J. Goldsmith, “Exploiting spatial degrees of freedom in MIMO
cognitive radio systems,” ICC, 2012.
and many more...
Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 8 / 23
System model and signaling
Each BS has N antennas and serves K single-antenna MUEs.
S SCs per BS with F antennas serving 1 single-antenna SUE each
The BSs and SCs have perfect CSI for the UEs they want to serve.
Every device knows perfectly its interference covariance matrix and the noise power.
Linear MMSE detection at all devices
The BSs and SCs use precoding vectors of the structure:
w ∼(PHHH + κQ + σ2I
)−1
h
I h channel vector to the targeted UEI H channel matrix to other UEs in the same cellI P, σ2: transmit and noise powersI Q interference covariance matrixI κ: regularization parameter (α for BSs, β for SCs)
About the regularization parameters
For α, β = 0, the BSs and SCs transmit as if they were in an isolated cell, i.e., MMSEprecoding (BSs) and maximum-ratio transmissions (SCs). By increasing α, β, theprecoding vectors become increasingly orthogonal to the interference subspace.
Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 9 / 23
System model and signaling
Each BS has N antennas and serves K single-antenna MUEs.
S SCs per BS with F antennas serving 1 single-antenna SUE each
The BSs and SCs have perfect CSI for the UEs they want to serve.
Every device knows perfectly its interference covariance matrix and the noise power.
Linear MMSE detection at all devices
The BSs and SCs use precoding vectors of the structure:
w ∼(PHHH + κQ + σ2I
)−1
h
I h channel vector to the targeted UEI H channel matrix to other UEs in the same cellI P, σ2: transmit and noise powersI Q interference covariance matrixI κ: regularization parameter (α for BSs, β for SCs)
About the regularization parameters
For α, β = 0, the BSs and SCs transmit as if they were in an isolated cell, i.e., MMSEprecoding (BSs) and maximum-ratio transmissions (SCs). By increasing α, β, theprecoding vectors become increasingly orthogonal to the interference subspace.
Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 9 / 23
Comparison of duplexing schemes and co-channel deployment
time
frequency
SC UL
SC DL
BS DL
BS UL
FDD TDD
SC DL
BS DL
SC UL
BS UL
time
frequency
co-channel TDD
SC DL
BS DL
SC UL
BS UL
time
frequency
co-channel reverse TDD
SC UL
BS DL
SC DL
BS UL
time
frequency
FDD: Channel reciprocity does not hold
TDD: Only intra-tier interference can be reduced
co-channel (reverse) TDD: Inter and intra-tier interference can be reduced
Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 10 / 23
TDD versus reverse TDD (RTDD)
Order of UL/DL periods decides which devices interfere with each other.
The BS-SC channels change very slowly. Thus, the estimation of the covariancematrix becomes easier for RTDD.
Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 11 / 23
Numerical results
1000 m
111 m
SC SUEMUEBS
40 m
3× 3 grid of BSs with wrap around
S = 81 SCs per cells on a regular grid
K = 20 MUEs randomly distributed
1 SUE per SC randomly distributed ona disc around each SC
3GPP channel model with path loss,shadowing and fast fading, N/LOS links
TX powers: 46 dBm (BS), 24 dBm(SC), 23 dBm (MUE/SUE)
20 MHz bandwidth @ 2 GHz
No user scheduling, power control
Averages over channel realizations andUE locations
TDD UL/DL cycles of equal length
Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 12 / 23
Downlink spectral area efficiency regions
0 20 40 60 800
100
200
300
400
Macro DL area spectral efficiency(b/s/Hz/km2
)
SCD
Lar
easp
ectr
alef
ficie
ncy( b/
s/H
z/km
2) FDD (N = 20, F = 1)
Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 13 / 23
Downlink spectral area efficiency regions
0 20 40 60 800
100
200
300
400
FDD regionmore antennas
N = 20 → 100
F=
1→
4
Macro DL area spectral efficiency(b/s/Hz/km2
)
SCD
Lar
easp
ectr
alef
ficie
ncy( b/
s/H
z/km
2) FDD (N = 20, F = 1)
FDD/TDD (N = 100, F = 4)
Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 13 / 23
Downlink spectral area efficiency regions
0 20 40 60 800
100
200
300
400
FDD region
TDD region
less intra-tier interf.α = 0 → 1
more antennasN = 20 → 100
F=
1→
4β
=0→
1
Macro DL area spectral efficiency(b/s/Hz/km2
)
SCD
Lar
easp
ectr
alef
ficie
ncy( b/
s/H
z/km
2) FDD (N = 20, F = 1)
FDD/TDD (N = 100, F = 4)
TDD (N = 100, F = 4, α = 1, β = 1)
Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 13 / 23
Downlink spectral area efficiency regions
0 20 40 60 800
100
200
300
400
FDD region
TDD region
less intra-tier interf.α = 0 → 1
more antennasN = 20 → 100
F=
1→
4β
=0→
1
Macro DL area spectral efficiency(b/s/Hz/km2
)
SCD
Lar
easp
ectr
alef
ficie
ncy( b/
s/H
z/km
2) FDD (N = 20, F = 1)
FDD/TDD (N = 100, F = 4)
TDD (N = 100, F = 4, α = 1, β = 1)
Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 13 / 23
Downlink spectral area efficiency regions
0 20 40 60 800
100
200
300
400
α
FDD region
TDD region
less intra-tier interf.α = 0 → 1
more antennasN = 20 → 100
F=
1→
4β
=0→
1
Macro DL area spectral efficiency(b/s/Hz/km2
)
SCD
Lar
easp
ectr
alef
ficie
ncy( b/
s/H
z/km
2) FDD (N = 20, F = 1)
FDD/TDD (N = 100, F = 4)
TDD (N = 100, F = 4, α = 1, β = 1)
Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 13 / 23
Downlink spectral area efficiency regions
0 20 40 60 800
100
200
300
400
β
α
FDD region
TDD region
less intra-tier interf.α = 0 → 1
more antennasN = 20 → 100
F=
1→
4β
=0→
1
Macro DL area spectral efficiency(b/s/Hz/km2
)
SCD
Lar
easp
ectr
alef
ficie
ncy( b/
s/H
z/km
2) FDD (N = 20, F = 1)
FDD/TDD (N = 100, F = 4)
TDD (N = 100, F = 4, α = 1, β = 1)
Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 13 / 23
Downlink spectral area efficiency regions
0 20 40 60 800
100
200
300
400
β
α
FDD region
TDD region
CoTDD region
less intra-tier interf.α = 0 → 1
more antennasN = 20 → 100
F=
1→
4β
=0→
1
Macro DL area spectral efficiency(b/s/Hz/km2
)
SCD
Lar
easp
ectr
alef
ficie
ncy( b/
s/H
z/km
2) FDD (N = 20, F = 1)
FDD/TDD (N = 100, F = 4)
TDD (N = 100, F = 4, α = 1, β = 1)
Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 13 / 23
Downlink spectral area efficiency regions
0 20 40 60 800
100
200
300
400
β
α
FDD region
TDD region
CoTDD region
less intra-tier interf.α = 0 → 1
more antennasN = 20 → 100
F=
1→
4β
=0→
1
Macro DL area spectral efficiency(b/s/Hz/km2
)
SCD
Lar
easp
ectr
alef
ficie
ncy( b/
s/H
z/km
2) FDD (N = 20, F = 1)
FDD/TDD (N = 100, F = 4)
TDD (N = 100, F = 4, α = 1, β = 1)
Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 13 / 23
Downlink spectral area efficiency regions
0 20 40 60 800
100
200
300
400
β
αα
FDD region
TDD region
CoTDD region
less intra-tier interf.α = 0 → 1
more antennasN = 20 → 100
F=
1→
4β
=0→
1
Macro DL area spectral efficiency(b/s/Hz/km2
)
SCD
Lar
easp
ectr
alef
ficie
ncy( b/
s/H
z/km
2) FDD (N = 20, F = 1)
FDD/TDD (N = 100, F = 4)
TDD (N = 100, F = 4, α = 1, β = 1)
Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 13 / 23
Downlink spectral area efficiency regions
0 20 40 60 800
100
200
300
400
β
αβ
α
FDD region
TDD region
CoTDD region
less intra-tier interf.α = 0 → 1
more antennasN = 20 → 100
F=
1→
4β
=0→
1
Macro DL area spectral efficiency(b/s/Hz/km2
)
SCD
Lar
easp
ectr
alef
ficie
ncy( b/
s/H
z/km
2) FDD (N = 20, F = 1)
FDD/TDD (N = 100, F = 4)
TDD (N = 100, F = 4, α = 1, β = 1)
Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 13 / 23
Downlink spectral area efficiency regions
0 20 40 60 800
100
200
300
400
β
αβ
α
FDD region
TDD region
CoTDD region
less intra-tier interf.α = 0 → 1
more antennasN = 20 → 100
F=
1→
4β
=0→
1
CoRTDD region
Macro DL area spectral efficiency(b/s/Hz/km2
)
SCD
Lar
easp
ectr
alef
ficie
ncy( b/
s/H
z/km
2) FDD (N = 20, F = 1)
FDD/TDD (N = 100, F = 4)
TDD (N = 100, F = 4, α = 1, β = 1)
Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 13 / 23
Downlink SINR distribution
−20 −10 0 10 20 30 400
0.2
0.4
0.6
0.8
1
SINR (dB)
Pr(
SIN
R≤
x)
MUE
SUEα
β
TDD Downlink SINR:
MUE SUEα = 0 α = 1 β = 0 β = 1
Mean 13.11 24.13 23.9 33.7895% 40.38 48.47 40 42.8750% 11.58 22.01 24.65 34.355% −8.48 7.86 6.02 22.62
−20 −10 0 10 20 30 400
0.2
0.4
0.6
0.8
1
SINR (dB)
Pr(
SIN
R≤
x)
MUE
SUE
α,β
α,β
Co-channel TDD Downlink SINR:
MUE SUEα, β = 0 α, β = 1 α, β = 0 α, β = 1
Mean −6.29 9.52 14.33 25.4595% 20.45 35.95 29.88 35.0150% −8.06 6.44 15.49 26.055% −26.64 −6.82 −6.51 13.6
Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 14 / 23
Uplink spectral area efficiency regions
0 20 40 60 800
100
200
300
400
α
more antennasN = 20 → 100
F=
1→
4
Macro UL sum-rate(b/s/Hz/km2
)
Smal
lce
llU
Lsu
m-r
ate( b/
s/H
z/km
2)FDD/TDD (N = 20, F = 1)
FDD/TDD (N = 100, F = 4)
co-channel TDDco-channel reverse TDD
Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 15 / 23
Observations
With the proposed precoding scheme, a TDD co-channel deployment of BSs andSCs leads to the highest area spectral efficiency (α = β = 1, 20 MHz BW):
DL UL
Area throughput 7.63 Gb/s/km2 8.93 Gb/s/km2
Rate per MUE 38.2 Mb/s 25.4 Mb/sRate per SUE 84.8 Mb/s 104 Mb/s
Even a few “excess” antennas at the SCs lead to significant gains.
As the scheme is fully distributed and requires no data exchange between thedevices, the rates can be simply increased by adding more antennas to the BSs/SCsor increasing the SC-density.
Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 16 / 23
Discussion
Channel reciprocity requires:
I Hardware calibrationI Scheduling of UEs on the same resource blocks in subsequent UL/DL cycles
The network-wide TDD protocol requires tight synchronization of all devices:I GPS (outdoor)I NTP/PTP (indoor)I BS reference signals
Channel estimation will suffer from interference and pilot contamination.
Covariance matrix estimation becomes difficult for large N.
We have considered a worst-case outdoor deployment scenario with fixed cellassociation, no power control or scheduling. Location-dependent user scheduling andinterference-temperature power control could further enhance the performance.
Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 17 / 23
Massive MIMO for wireless backhaul
small cellwireless backhaul
wireless datawired backhaul
user equipment
massive MIMO base station
Core network
The unrestrained SC-deployment “where needed” rather than “where possible”requires a high-capacity and easily accessible backhaul network.
Already for most WiFi deployments, the backhaul capacity (10–100 Mbit/s) and notthe air interface (54–600 Mbit/s) is the bottleneck.
Why not provide wireless backhaul with massive MIMO?3
3T. L. Marzetta and H. Yang, “Dedicated LSAS for metro-cell wireless backhaul - Part I: Downlink,” Bell Laboratories, Alcatel-Lucent,
Tech. Rep., Dec. 2012.
Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 18 / 23
Massive MIMO for wireless backhaul: Advantages
No standardization or backward-compatibility required
BS-SC channels change very slowly over time:
I Complex transmission/detection schemes (e.g., CoMP) can be easily implemented.
I Even FDD might be possible due to reduced CSI overhead.
Provide backhaul where needed:
I Adapt backhaul capacity to the load (support highly variable traffic)
I Statistical multiplexing opportunity to avoid over-provisioning of backhaul
I Enable user-centric small-cell clustering for virtual MIMO
SCs require only a power connection to be operational
Line-of-sight not necessary if operated at low frequencies
Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 19 / 23
Massive MIMO for wireless backhaul: Is it feasible?
How many antennas are needed to satisfy the desired backhaul rates with a giventransmit power budget?
Assumptions:
Every BS knows the channels to all SCs.
The BSs can exchange some control information.
Full user data sharing between the BSs is not possible.
Single-antenna SCs, BSs with N antennas
TDD operation on a separate band (2/3 DL, 1/3 UL)
Same modeling assumptions as before
Find the smallest N such that the power minimization problem with target SINRconstraints for the multi-cell multi-antenna wireless system is feasible.4,5
4H. Dahrouj and W. Yu, “Coordinated beamforming for the multicell multi-antenna wireless system,” IEEE Trans. Wireless Commun.,
vol. 9, no. 5, pp. 1748–1759, May 2010.5
S. Lakshminarayana, J. Hoydis, M. Debbah, and M. Assaad, “Asymptotic analysis of distributed multi-cell beamforming, in IEEEInternational Symposium in Personal Indoor and Mobile Radio Communications (PIMRC), Istanbul, Turkey, Sep. 2010, pp. 2105–2110.
Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 20 / 23
Massive MIMO for wireless backhaul: Numerical results
0 20 40 60 80 1000
100
200
300
400
500
Downlink backhaul rate (Mbit/s)
Req
uire
d#
ofB
S-an
tenn
as
S = 81
S = 40
S = 20
0 10 20 30 40 50Uplink backhaul rate (Mbit/s)
Average minimum number of required BS-antennas N to serve S ∈ {20, 40, 81} randomly chosen
SCs with the same target backhaul rate.
Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 21 / 23
Summary
Massive MIMO and SCs have distinct advantages which complement each other:
I Massive MIMO for coverage and mobility support
I SCs for capacity and indoor coverage
TDD and the resulting channel reciprocity allow every device to fully exploit itsavailable degrees of freedom for intra-/inter-tier interference mitigation.
A TDD co-channel deployment of massive MIMO BSs and SCs can achieve a veryattractive rate region.
Massive MIMO BSs can provide wireless backhaul to a large number of SCs. Theslowly time-varying nature of the BS-SC channels might allow for complex precodingand detection schemes.
For more details:
J. Hoydis, K. Hosseini, S. ten Brink, and M. Debbah, “Making Smart Use of Excess Antennas:Massive MIMO, Small Cells, and TDD,” Bell Labs Technical Journal, vol. 18, no. 2, Sep. 2013.
Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 22 / 23
Thank you!
Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 23 / 23
Thank you!
Jakob Hoydis (Supelec) Massive MIMO: How many antennas do we need? 30 / 30