Doubly-Massive MIMO Systems at mmWave Frequencies: Opportunities and Research Challenges

Doubly-Massive MIMO Systems at mmWave Frequencies:
Opportunities and Research Challenges
Stefano Buzzi, University of Cassino and Lazio Meridionale Doubly-massive MIMO at mmWave Frequencies

Copyright Information
If you use concepts and ideas from these slides, please acknowledge it by citing:
S. Buzzi, “Doubly-massive MIMO systems at mmWave frequencies:
Opportunities and research challenges,” IEEE WCNC’2016 Workshop on Green
and Sustainable 5G Wireless Networks, keynote talk, Doha (Qatar), April 2016
Bibtex entry:
@Conference{buzziWCNC2016keynote,
Title = {{Doubly-massive MIMO systems at mmWave frequencies:
Opportunities and research challenges}},
Author = {S. Buzzi},
Booktitle = {IEEE WCNC’2016 Workshop on Green and Sustainable 5G
Wireless Networks},
Year = {2016},
Address = {Doha, Qatar},
Month = {April},
Note = {keynote talk}
}

Millimeter Waves (mmWaves)
One of the ”key pillars” of 5G networks
Refers to above-6Ghz frequencies
Regulators worldwide are starting releasing spectrum chunks at frequencies
up to 100GHz
The main beneﬁt here is the availability of large bandwidths

The Path-Loss Challenge...
- Friis’ Law: PR = PT GT GR
λ
4πd
2
- We may have heavy shadowing losses:
brick, concrete > 150 dB
Human body: Up to 35 dB
NLOS propagation mainly relies on reﬂections

And there is also increased atmospheric absorption...

The Path-Loss: a not-so-hard challenge...
However...
- For a constant physical area, GT and GR ∝ λ−2
- Otherwise stated, the number of antennas that can be packed in a given
area increases quadratically with the frequency
- The free-space path loss is well-compensated by the antenna gains =⇒
mmWaves must be used in conjunction with MIMO

The case for doubly massive MIMO at mmWaves
- At fc = 30GHz, the wavelength λ = 1cm
- Assuming λ/2 spacing, ideally, more than 180 antennas can be placed in
an area as large as a credit card
The number climbs up to 1300 at 80GHz!!

Some words of wisdom...
We have some serious/challenging practical and physical impairments:
- The MIMO channel at mmWaves is not so generous as in sub-6GHz bands
- ADC bottleneck: forget all-digital beamforming
- Power consumption issues
- Low eﬃciency of power ampliﬁers

The MIMO Eldorado...
MIMO communications have been around for more than two decades.

The MIMO Eldorado...
...started with these landmark papers:
References
[2] J. H. Winters, J. Salz, and R. D. Gitlin, “The impact of antenna diversity on the capacity of wireless
communication systems,” IEEE Transactions on Communications, vol. 42, no. 234, pp. 1740–1751, 1994
[3] G. J. Foschini, “Layered space-time architecture for wireless communication in a fading environment
when using multi-element antennas,” Bell labs technical journal, vol. 1, no. 2, pp. 41–59, 1996
[4] P. W. Wolniansky, G. J. Foschini, G. Golden, and R. A. Valenzuela, “V-blast: An architecture for realizing
very high data rates over the rich-scattering wireless channel,” in 1998 URSI International Symposium
on Signals, Systems, and Electronics, 1998. ISSSE 98. IEEE, 1998, pp. 295–300
[5] V. Tarokh, N. Seshadri, and A. R. Calderbank, “Space-time codes for high data rate wireless communi-
cation: Performance criterion and code construction,” IEEE Transactions on Information Theory, vol. 44,
no. 2, pp. 744–765, 1998
The main and striking result was that capacity increased linearly with
min{NT , NR }.

But for mmWaves...
Many of the results that hold for sub-6Ghz frequencies do not
translate to mmWave frequencies

The clustered channel model
- The rich scattering environment assumption typically assumed for sub-6
GHz does not hold at mmWaves. The following no longer holds:
Channel matrix with i.i.d. entries
Channel matrix with full rank with probability 1
At mmwaves, a “clustered” channel model is more representative of the
physical propagation mechanism
Ncl scattering clusters
Each cluster contributes with Nray propagation paths
The clustered channel model has an implication on the maximum rank of
the channel matrix

Just a sample of recent papers - by diﬀerent set of authors - that have
embraced the clustered channel model:
References
[6] O. El Ayach, S. Rajagopal, S. Abu-Surra, Z. Pi, and R. W. Heath, “Spatially sparse precoding in
millimeter wave MIMO systems,” IEEE Transactions on Wireless Communications, vol. 13, no. 3, pp.
1499–1513, 2014
[7] A. Alkhateeb, O. El Ayach, G. Leus, and R. W. Heath, “Channel estimation and hybrid precoding for
millimeter wave cellular systems,” IEEE Journal of Selected Topics in Signal Processing, vol. 8, no. 5,
pp. 831–846, 2014
[8] S. Haghighatshoar and G. Caire, “Enhancing the estimation of mm-Wave large array channels by ex-
ploiting spatio-temporal correlation and sparse scattering,” in Proc. of 20th International ITG Workshop
on Smart Antennas (WSA 2016), 2016
[9] S. Buzzi, C. D’Andrea, T. Foggi, A. Ugolini, and G. Colavolpe, “Spectral eﬃciency of MIMO millimeter-
wave links with single-carrier modulation for 5G networks,” in Proc. of 20th International ITG Workshop
on Smart Antennas (WSA 2016), 2016
[10] T. E. Bogale and L. B. Le, “Beamforming for multiuser massive MIMO systems: Digital versus hybrid
analog-digital,” in 2014 IEEE Global Communications Conference (GLOBECOM). IEEE, 2014, pp.
4066–4071
[11] L. Liang, W. Xu, and X. Dong, “Low-complexity hybrid precoding in massive multiuser MIMO systems,”
IEEE Wireless Communications Letters, vol. 3, no. 6, pp. 653–656, 2014
[12] J. Lee, G.-T. Gil, and Y. H. Lee, “Exploiting spatial sparsity for estimating channels of hybrid MIMO sys-
tems in millimeter wave communications,” in 2014 IEEE Global Communications Conference (GLOBE-
COM). IEEE, 2014, pp. 3326–3331
[13] C.-E. Chen, “An iterative hybrid transceiver design algorithm for millimeter wave MIMO systems,” IEEE
Wireless Communications Letters, vol. 4, no. 3, pp. 285–288, 2015

Our clustered channel model...
- Detailed in [14], in the clustered channel model used here...
- the departure and arrival angles of the rays are tied by the geometry of the
system;
- The number of clusters is not ﬁxed a-priori but is a function of the link
length;
- The multipath delays also descend from the system geometry;
- We include in the model a distance-dependent loss;
- We account for a non-zero probability that a Line-of-Sight (LOS) link exists
between the transmitter and the receiver;
- The proposed statistical channel model also accommodates time-varying
scenarios (not considered in this talk).
References
[14] S. Buzzi and C. D’Andrea, “A clustered statistical MIMO millimeter wave channel model,” IEEE Wireless
Communications Letters, submitted., 2016

H(τ) = γ
Ncl
i=1
Nray
l=1
αi,l Λr (φr
i,l , θr
i,l )Λt (φt
i,l , θt
i,l )×
L(ri,l )ar (φr
i,l , θr
i,l )aH
t (φt
i,l , θt
i,l )h(τ − τi,l ) + HLOS(τ) . (1)

γ
Ncl
i=1
Nray
l=1
αi,l Λr (φr
i,l , θr
i,l )Λt (φt
i,l , θt
i,l )L(ri,l )ar (φr
i,l , θr
i,l )aH
t (φt
i,l , θt
i,l )h(τ − τi,l )
αi,l ∼ CN(0, 1) complex path gain
L(ri,l ) path loss
ri,l link length
τi,l = ri,l /c propagation delay
Λr (φr
i,l , θr
i,l ) receive antenna element gains
ar (φr
i,l , θr
i,l ) normalized receive array response vectors
γ =
NR NT
NclNray
normalization factor

Number of clusters depending on the TX-RX distance
Ncl(d) =



Nmin
cl +
Nmax
cl − Nmin
cl
ˆd3
d3
d ≤ ˆd ,
Nmax
cl d > ˆd ,
(2)
Suggested values are Nclmin
= 10, Nmax
cl = 50 and ˆd = 200m. The ﬁxed value
Nray = 8 is used.
The angles φt
i,l , l = 1, . . . , Nray have a Laplacian distribution whose mean
φt
i ∼ U[0, 2π], and with standard deviation σφ = 5deg.
The angles, θt
i,l are again conditionally Laplacian with a mean θt
i uniformly
distributed in [−π/2, π/2] and variance σθ = 5deg.

- For the path loss L(ri,l ) we have [15]:
L(ri,l )dB = β + 10α log10(ri,l ) , (3)
with values β = 50 dB and α = 3.3.
- Transmitter’s and receiver’s antenna element are modeled as being ideal
sectored elements, so Λr (φr
i,l , θr
i,l ) and Λt (φt
i,l , θt
i,l ) are expressed as
Λx (φx
i,l , θx
i,l ) =
1 φx
i,l ∈ [φx
min, φx
max], θx
i,l ∈ [θx
min, θx
max],
0 otherwise ,
(4)
where x may be either r or t.
References
[15] S. Singh, M. N. Kulkarni, A. Ghosh, and J. G. Andrews, “Tractable model for rate in self-backhauled
millimeter wave cellular networks,” IEEE Journal on Selected Areas in Communications, vol. 33, no. 10,
pp. 2196–2211, 2015

For a planar array with YZ antennas, the array response vectors ar (φr
i,l , θr
i,l )
and at (φt
i,l , θt
i,l ) are
ax (φx
i,l , θx
i,l ) =
1
√
Yx Zx
[1, . . . , e−jk˜d(m sin φx
i,l sin θx
i,l +n cos θx
i,l )
,
. . . , e−jk˜d((Yx −1) sin φx
i,l sin θx
i,l +(Zx −1) cos θx
i,l )
] , (5)
- x may be either r or t
- k = 2π/λ
- ˜d is the inter-element spacing

The LOS component...
- Let φr
LOS, φt
LOS, θr
LOS, and θt
LOS be the departure angles corresponding to
the LOS link
- We have
HLOS(τ) = ILOS(d)
√
NR NT ejδ
ar (φr
LOS, θr
LOS)aH
t (φt
LOS, θt
LOS)h(τ − τLOS)
with
δ ∼ U(0, 2π)
ILOS(d) is a random variate indicating if a LOS link exists between
transmitter and receiver
We assume that ILOS(d) = 1 with probability 0.5 for d < 5m, and with
probability 0.11 for d < 100m, while being zero in all the remaining cases

Channel Generation routine available
Matlab scripts for generating the described clustered channel model are
available here
https://github.com/CarmenDAndrea/mmWave Channel Model Link

mmWave MIMO is not like sub-6GHz MIMO
H(τ) = γ
Ncl
i=1
Nray
l=1
αi,l Λr (φr
i,l , θr
i,l )Λt (φt
i,l , θt
i,l )×
L(ri,l )ar (φr
i,l , θr
i,l )aH
t (φt
i,l , θt
i,l )h(τ − τi,l ) + HLOS(τ) .
- Neglecting the LOS component, the channel has at most rank NclNray
- The channel rank depends by the geometry, but is independent of the
number of antennas
- This has an impact on the multiplexing capabilities of the channel

Impact of increasing NT and NR
H(τ) = γ
Ncl
i=1
Nray
l=1
αi,l Λr (φr
i,l , θr
i,l )Λt (φt
i,l , θt
i,l )×
L(ri,l )ar (φr
i,l , θr
i,l )aH
t (φt
i,l , θt
- The array response vectors
ax (φx
i,l , θx
i,l ) =
1
Nx
[1, . . . , e−jk˜d(m sin φx
i,l sin θx
i,l +n cos θx
i,l )
,
. . . , e−jk˜d((Yx −1) sin φx
i,l sin θx
i,l +(Zx −1) cos θx
i,l )
] , (6)
for increasing number of antennas, tend to an orthogonal sets.
- Otherwise stated, for large NT , the vectors at (φt
i,l , θt
i,l ), for all i and l,
provided that the departure angles are diﬀerent, converge to an
orthogonal set.
- The same applies to the vectors ar (φr
i,l , θr
i,l ) for large values of NR .

Impact of increasing NT and NR
H(τ) = γ
Ncl
i=1
Nray
l=1
αi,l Λr (φr
i,l , θr
i,l )Λt (φt
i,l , θt
i,l )×
L(ri,l )ar (φr
i,l , θr
i,l )aH
t (φt
i,l , θt
For large NT and NR , and distinct arrival and departure angles, the array
response vectors become the right and left singular vectors of the matrix
channel.
Matrix Algebra
Recall indeed that H = UΛVH
=
i
λi ui vH
i

Take-Home Points
- The number of clusters and rays has an impact on the channel rank (and,
hence, multiplexing and diversity channel capabilities)
- Large values of NT and NR just help in increasing the received power
(scales linearly with the product NT NR ), and in sharpening the beams of
the radiation patterns
- For large values of NT and NR , and separate departure angles, the transmit
and receive array responses tend to be orthogonal. The most favourable
channel eigen-direction is the one pointing to the strongest scatterer

Transceiver model with TDE
r(n) = DH
y(n) =
eP−1
=0
DH
H( )Q˘s(n − ) + DH
w(n) . (7)
A block linear MMSE equalizer is applied to remove intersymbol interference.
˘s(n) = EH
reP (n) , (8)

Transceiver model with FDE
yCP
(n) = H(n) xCP
(n) + w(n) , n = 1, . . . , k (9)
RCP
(n) = H(n)XCP
(n) + W(n) , (10)
ZCP
(n) = EH
(n)RCP
(n) = SCP
(n) + (H(n)Q)−1
W(n) .

Considerations on Complexity
TDE structure: the computation of the equalization matrix E requires the
inversion of the covariance matrix of the vector reP (n), with a
computational burden proportional to (PM)3
; then, implementing Eq. (8)
requires a matrix vector product, with a computational burden
proportional to (PM2
); this latter task must be made k times in order to
provide the soft vector estimates for all values of n = 1, . . . , k.
FDE structure: 2M FFTs of length k are required, with a complexity
proportional to 2Mk log2 k; in order to compute the zero-forcing matrix,
the FFT of the matrix-valued sequence H(n) must be computed, with a
complexity proportional to MNt T(k log2 k); computation of the matrix
(H(n)Q) and of its inverse, for n = 1, . . . , k, ﬁnally requires a
computational burden proportional to k(NT M2
+ M3
).

Hybrid precoding and decoding
We use here hybrid digital/analog beamforming
The number of RF chains is equal to the multiplexing order
The used algorithm is the Block Coordinate Descent for Subspace
Decomposition [16]
References
[16] H. Ghauch, M. Bengtsson, T. Kim, and M. Skoglund, “Subspace estimation and decomposition for
hybrid analog-digital millimetre-wave mimo systems,” in 2015 IEEE 16th International Workshop on
Signal Processing Advances in Wireless Communications (SPAWC). IEEE, 2015, pp. 395–399

ASE with QPSK inputs
Multiplexing order M = 2; d = 30m; SRRC pulses with roll-oﬀ 0.22.

ASE with QPSK inputs
Multiplexing order M = 2; PT = 0dBW; SRRC pulses with roll-oﬀ 0.22.

ASE with Gaussian inputs
By means of an horizontal shift, the curves can be made (almost) perfectly
overlapping!

ASE with Gaussian inputs
The curve corresponding to the conﬁguration 50 × 100 has been shifted to the
left of 10 log10(10)
The curve corresponding to the conﬁguration 10 × 50 has been shifted to the
left of 10 log10(30)

ASE with Gaussian inputs: impact of number of clusters
NR × NT = 50 × 100

What about energy efficiency?
- Dividing the ASE by the consumed power we obtain a measure of energy
efficiency, which we nickname the spectral energy efficiency [bit/J/Hz]
- Multipliying the spectral EE by the signal bandwidth we obtain the
conventional EE (measured in bit/J)
Spectral EE =
ASE
NT Pc + ηPT
Remarks
1 We are considering the energy consumed at the transmitter only
2 EE heavily depends on Pc

Spectral EE with Gaussian inputs

Spectral EE with QPSK inputs
Remark: Very similar behaviour to the case of Gaussian inputs

Spectral EE
BIG QUESTION:
Can we ﬁnd antenna arrays with sub-linear power consumption?

Conclusions
- Mmwaves are an exciting field for wireless research
- They promise to make true the multi-gigabit experience for everyone
- Their use implies radically new ways of leveraging the performance
benefits granted by the use of multiple antennas
- Hardware/Complexity/Energy constraints are to be seriously taken into
account
- There is need for accurate energy consumption models
- There is need of extensive measurements campaign (already ongoing from
a while) to validate the clustered model
Acknowledgement
Special thanks to Ms. Carmen D’Andrea, Ph.D. student at UNICAS, for
producing most of the figures shown here.

THANK YOU!!
Stefano Buzzi, Ph.D.
University of Cassino and Lazio Meridionale
buzzi@unicas.it

Doubly-Massive MIMO Systems at mmWave Frequencies: Opportunities and Research Challenges

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