MIMO Transmission with Rank Adaptation for Multi-Gigabit 60GHz Wireless

Abstract

In this paper, we propose a practical and systematic approach to implement the MIMO transmission with rank adaptation for 60 GHz systems. In the 60 GHz system with multiple antennas, the transmit and receive (Tx-Rx) antenna arrays are grouped into a number of subarrays with a predetermined subarray separation based on the derived geometrical criteria of creating high rank MIMO in LoS environments. We first apply an enhanced blind beamforming technique based on a stochastic gradient algorithm (SGA) for the inner-subarray antennas, which does not require channel state information (CSI) at either the transmitter or the receiver. Secondly, the composite MIMO channel, as a joint effect of Tx-Rx beamforming and the channel impulse response, can be estimated with much reduced complexity. Finally, the MIMO transmission with rank adaptation is performed by adaptively selecting the better scheme out of the high-rank spatial multiplexing and the rank-1 beamforming whichever gives higher system throughput. Simulation results show that high-rank spatial multiplexing and rank-1 beamforming outperform each other at different geometrical placements and transmit power settings. The proposed MIMO transmission with rank adaptation offers significant performance gain especially at high signal-to-noise ratio (SNR) regions.

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Page 1

MIMO Transmission with Rank Adaptation for
Multi-Gigabit 60GHz Wireless
Meilong Jiang, Guosen Yue and Sampath Rangarajan
NEC Laboratories America, Inc.
{meilong,yueg,sampath}@nec-labs.com
Abstract—In this paper, we propose a practical and systematic
approach to implement the MIMO transmission with rank
adaptation for 60 GHz systems. In the 60 GHz system with
multiple antennas, the transmit and receive (Tx-Rx) antenna
arrays are grouped into a number of subarrays with a prede-
termined subarray separation based on the derived geometrical
criteria of creating high rank MIMO in LoS environments. We
first apply an enhanced blind beamforming technique based on
a stochastic gradient algorithm (SGA) for the inner-subarray
antennas, which does not require channel state information (CSI)
at either the transmitter or the receiver. Secondly, the composite
MIMO channel, as a joint effect of Tx-Rx beamforming and
the channel impulse response, can be estimated with much
reduced complexity. Finally, the MIMO transmission with rank
adaptation is performed by adaptively selecting the better scheme
out of the high-rank spatial multiplexing and the rank-1 beam-
forming whichever gives a higher system throughput. Simulation
results show that high-rank spatial multiplexing and rank-1
beamforming outperform each other at different geometrical
placements and transmit power settings. The proposed MIMO
transmission with rank adaptation offers significant performance
gain especially at high signal-to-noise ratio (SNR) regions.
I. INTRODUCTION
Recently, there have been extensive advancements in re-
search and standardization to realize multi-Gigabit wireless
transmission over the 60GHz carrier. In the standards [1],
[2], beamforming is exclusively considered due to the fact
that LoS channels are in general rank deficient. Some recent
investigations show that the spatial multiplexing gain can be
obtained in LoS channels by employing specifically designed
antenna arrays to preserve the orthogonality between antenna
signatures [3], [4]. Briefly, high rank or full rank MIMO chan-
nel can be created by increasing inter-element antenna spacing
and assuming particular geometrical setting (Tx-Rx distance
and antenna array orientation). However, the knowledge of the
exact geometrical placement is very difficult to obtain and the
antenna spacing usually cannot be dynamically adjusted. Thus
the above systems are quite sensitive to the geometrical change
and misplacement in practice.
In a 60GHz system, the number of uniform linear array
(ULA) antennas can be as large as 8, 16 or even more
[1]. This provides an advantage to exploit the processing
gain from the spatial domain. In this paper, we propose a
novel method that can obtain the optimal transmission mode
and adaptively adjust the transmission scheme for any given
transceiver placement without requiring the actual geometrical
information. The proposed method consists of three proce-
dures, namely, the blind subarray beamforming, the composite
channel estimation and the transmission mode adaptation.
In what follows, section II introduces the 60GHz wireless
channel model. Section III derives a geometrical criteria for
high rank MIMO transmission in LoS channel. In section IV,
a systematic approach to realize adaptive high rank MIMO
transmission and rank-1 beamforming is proposed. Section V
provides the performance results and concluding remarks are
made in Section VI.
II. CHANNEL MODEL
We consider a 60GHz MIMO system with Nt transmit
antennas and Nrreceive antennas. The radio wave propagation
at 60GHz is featured by the co-existence of a strong LoS
component and the scattered non-LoS multipath components.
In this paper, we consider the Rician channel formulated by
the weighted sum of the free-space and the scattered signal
response matrices given by [3]
?
where the Rician K-factor is defined as the power ratio
between the HLOS and HNLOS to indicate the relative
strength. Practical measurements indicate that K could range
from 6 to 15dB for a typical 60GHz wireless channel [5].
The free-space channel response HLOSis deterministic and
can be written as [3] HLOS=
⎡
⎣
where dij is the distance between the j-th Tx antenna and
the i-th Rx antenna and k = 2π/λ is the wave number cor-
responding to the carrier wavelength λ (λ = 5mm for 60GHz
carrier). The channel responses for the scattered components
HNLOS can be modeled as an Nr× Nt matrix with each
entry hn,mbeing an i.i.d. complex Gaussian random variable,
i.e., hn,m ∼ CN(0,σ2
scattered channel response.
H =
K
K + 1HLOS+
?
1
K + 1HNLOS,
(1)
⎢⎢⎢⎢
1
d11e−jkd11
1
d21e−jkd21
...
1
dNr1e−jkdNr1
1
d12e−jkd12
1
d22e−jkd22
...
1
dNr2e−jkdNr2
...
...
...
...
1
d1Nte−jkd1Nt
1
d2Nte−jkd2Nt
...
1
dNrNte−jkdNrNt
⎤
⎦
⎥⎥⎥⎥
, (2)
H), where σ2
His the variance of the
III. GEOMETRICAL CRITERIA FOR HIGH RANK MIMO IN
LOS CHANNEL
We first derive the geometrical criteria of high rank trans-
mission in LoS channel for an Nt×2 MIMO system. As shown
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Fig. 1.60G Hz Transceiver with 2 × Nt antennas.
in Fig. 1, the Nttransmit antennas are divided into two sub-
arrays each with
2
simple spatial filtering scheme, namely delay-and-sum (DAS)
beamforming [6], [7] for the transmit subarrays. With the DAS
beamforming, each element of the subarray is multiplied by a
complex weight, corresponding to a delay, so that each element
adds completely in phase in the desired direction. Specifically
for the system under investigation, the two transmit subarrays
steer two directional beams towards the receiver antennas, i.e,
in the direction of θ11 and θ22. The DAS beamformers w1
and w2 for subarray 1 and 2 respectively can be expressed
as [6] w1=
ejk(Nt
?
where d =λ
θ11is the direction seen from subarray 1 to the first receive
antenna and θ22 the direction seen from subarray 2 to the
second receive antenna.
It can be shown that the optimal transmit inter-subarray
spacing sT and the receive antenna spacing sRto achieve a
capacity-maximizing rank-2 MIMO transmission is given by
Nt
λ
2-spaced antenna elements. We apply a
?
1,ejkdsinθ22,ejk2dsinθ22,...,ejk(Nt
2−1)dsinθ11,...,ejk2d sinθ11,ejkdsinθ11,1
?
,
and w2 =
2−1)dsinθ22?
2is the inter-element spacing within the subarrays.
sR≈ (2p + 1)
Dλ
2− 1?λ.
2sT+?Nt
(3)
The proof is given in Appendix 1.
Thus it is potentially feasible to create high rank MIMO
over LoS channel through geometrical configurations. How-
ever, in practice it is not possible to know in advance the
geometrical settings in terms of Tx-Rx distance and subarray
orientation. And usually the antenna/subarray spacing cannot
be dynamically adjusted once it is deployed.
IV. MIMO TRANSMISSION WITH RANK ADAPTATION
We now propose a scheme with which we can obtain the op-
timal transmission mode without the knowledge of the actual
geometrical information and adaptively adjust the transmission
scheme for any given transceiver placement. We first apply an
enhanced blind beamforming technique for the inner-subarray
antennas, which does not require CSI at the transmitter or the
receiver. Secondly, the composite (M × M) MIMO channel
with much reduced size can be estimated. Finally, the MIMO
transmission with rank adaptation is performed.
For simplicity, we consider forming a practical MIMO
system with rank-2 transmission. Both the Tx and Rx arrays
are grouped into 2 subarrays, i.e, M = 2. Each subarray is
a ULA with
antenna spacing.
Nt
2Tx elements (Nr
2Rx elements) andλ
2inter-
A. Blind Subarray Beamforming
Since it is impractical to obtain the actual channel matrix
for the 60GHz wireless channel because of the large antenna
array size, we introduce a blind beamforming scheme based
on a stochastic gradient algorithm (SGA) [8] for the subarrays.
For any given selected pair of Tx-Rx subarrays, the Tx
and Rx beamformers can be independently determined by
a criteria maximizing the received SNR or signal power.
Specifically, for the j-th Tx subarray, the Tx beamfomer wj=
[wj,1,wj,2,...,wj,Nt
Similarly, for the i-th Rx subarray, we have the Rx beamformer
as ui= [ui,1,ui,2,...,ui,Nr
For the j-th transmit and the i-th receive subarrays, the
received signal at the receiver can be written as
√Pu†
2]T, with ?wj? = 1,j = 1,2, is applied.
2]T, with ?ui? = 1,i = 1,2.
yi,j=
iHijwjx + u†
in,
(4)
where P denotes the transmit power, Hij ∈ C
channel matrix formed by the j-th transmit and the i-th
receive subarrays, x the normalized transmitted symbol and
n ∈ C
(·)†denotes matrix Hermitian and C denotes complex spaces.
The Tx beamformer wj
∈ C
ui∈ C
beamformer output in (4), i.e.,
Nr
2×Nt
2
the
Nr
2 the noise vector with Gaussian distributed elements.
Nt
2
and Rx beamformer
Nr
2 are chosen to maximize the power at the receive
(ˆ wj, ˆ ui) = arg max
Nt
2 ,ui∈C
wj∈C
Nr
2
yi,jy∗
i,j.
(5)
We now resort to a blind stochastic gradient method to
determine the optimal Tx-Rx beamformers for the selected
subarray pair. The SGA-based beamforming procedure is
elaborated in Algorithm 1. For practical implementations, a
low rate ?logKt?-bit feedback channel is needed to inform
the transmitter about the selected transmit beamformer.
Note that the generation of normalized perturbation vectors
is critical to the performance and convergence of the Stochastic
Gradient Algorithm [9]. We now propose an efficient way to
generate the perturbation vectors set, which can approach the
optimal beamformers with a very few number of iterations
with the use of any random beamformer as the seed.
1) Generation of Perturbation Vectors: Considering the
vector space with unit norm ΩN, the perturbation vectors
{pj: pj∈ ΩNt} and {qj: qj∈ ΩNr} are line vectors with
the ending points located at a unit complex sphere. To achieve
better perturbation for the input vector w in either transmit or
receive beamforming, it is desired to separate any two vectors
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Algorithm 1 Stochastic gradient algorithm for blind subarray
beamforming
1: Initialize two random unitary vectors: u(0)∈ C
2: Generate Kt and Kr normalized vectors respectively as the Tx
and Rx beamformer perturbation vectors, i.e, pi∼ CN(0,I),i =
1,....,Kt and qj ∼ CN(0,I),j = 1,....,Kr. Set the total
number of iterations to be N.
3: for iteration index n = 0,··· ,N − 1 do
4:
For the current beamformers u(n)and w(n); Generate Ktnew
Tx beamformers and Kr new Rx beamformers respectively
using the perturbation vectors, i.e. w(n)
u(n)+βqj
?u(n)+βqj?,j = 1,...,Kr.
5:
Compute the received power |y|2for each one of the KtKr
new beamformer pairs.
6:
Find the ˆ piand ˆ qjgiving the largest received power and
update the beamformers as w(n+1)
u(n)+βˆ qj
?u(n)+βˆ qj?.
7: end for
Nr
2 , w(0)∈ C
Nt
2 .
i
=
w(n)+βpi
?w(n)+βpi?,i =
1,...,Kt and u(n)
j
=
=
w(n)+βˆ pi
?w(n)+βˆ pi?and
u(n+1)=
as far as possible, i.e., maximize the distance between any two
vectors.
Denote PK
search of transmit and receive beamforming vectors used in
Algorithm 1 where ?pj?2= 1. Hence, we want to design the
vector set P to maximize the minimal distance of any pair of
vectors (pi,pj), i.e.,
P∗
PK
where d(pi,pj) denotes the chordal distance, dc(pi,pj) =
?
timization in (6) is essentially the Grassmannian line packing
problem for Kt>Nt
We now iteratively search for the solutions of Grassmannian
line packing in (6) based on the following two steps. First, for
a given perturbation set PK, the optimal partition for the space
ΩN is given by
Vj=?v ∈ ΩN: dc(v,pj) ≤ dc(v,pi) ∀ i ?= j?.
Then for each partition, we find the solution to satisfy the
centroid condition, given by
?
= {pj}K
j=1as the set of K vectors for gradient
K= argmax min
pi,pj∈PKd(pi,pj),
(6)
1 − ?pH
ipj?2, between piand pj. We can see that the op-
2[10].
(7)
pj= arg min
p∈ΩN
E{dc(p,v)|v ∈ Vj},
(8)
which can be solved numerically using the gradient search
algorithm. So far we have obtained the Tx and Rx beamform-
ers through the blind SGA method, i.e., ˆ wj and ˆ ui, which
can be applied to the Tx and Rx subarrays before actual data
transmissions.
B. Composite Channel Estimation
Instead of estimating the original Nt×Nrchannel matrix, an
estimation of the equivalent 2×2 channel matrix is needed with
much reduced complexity. Denote˜hij = ui†Hijwj as the
composite channel gain between the i-th receive subarray and
the j-th transmit subarray. The composite channel?
channel impulse response, can be expressed as
?˜h11
At the transmitter, the known pilot signals xp are sent
through each subarray in a predefined order for channel
estimation at the receiver. For the j-th Tx and the i-th Rx pair,
the received signal at the i-th Rx subarray output is given by
√Pu†
H among
the subarrays, as a joint effect of Tx-Rx beamforming and the
?
H ?
˜h12
˜h22
˜h21
?
=
?
u†
u†
1H11w1
2H21w1
u†
u†
1H12w2
2H22w2
?
.
(9)
yp=
iHijwjxp+ u†n =
√P˜hijxp+ u†n.
(10)
Assuming unit transmission power, the estimate of the
composite channel˜hijbased on minimum mean square error
(MMSE) estimator can be found as [11]
?
p
where xpis the pilot symbols for channel estimation, E[yp]
and E?|yp|2?can be obtained in the training stage when the
step described in Section IV-A.
ˆ˜hij=
E
E?ypy∗
y∗
p˜hij
?
? yp=
|E[yp]|2
E [|yp|2]xpyp,
(11)
optimal beamformers uiand wjare converged in the previous
C. Rank Adaptation
We now apply the rank adaptation based transmission for the
60GHz system. With the composite channel gain?
chosen to be either rank-2 spatial multiplexing or rank-1
beamforming, whichever gives a higher maximum achievable
data rate. In practice, the selected transmission mode can be
informed to the transmitter through a feedback channel.
For the rank-2 spatial multiplexing, assuming equal power
allocation among the subarrays, the maximum achievable rate
for rank-2 transmission is given by
?
where I2corresponds to a 2×2 identity matrix and ρ the total
transmit power.
For the rank-1 beamforming, the beamformer weights can
be obtained based on singular value decomposition (SVD) of
the composite channel (9). Assuming ˜ u and ˜ w respectively
the right and left singular vectors of?
for rank-1 beamforming can be obtained by
?
Now the optimal transmission scheme can be adaptively
chosen as the scheme that maximizes the achievable rate, i.e.,
H obtained
at the receiver, the transmission scheme can be adaptively
CSM= log2
det
?
I2+ρ
2
?
H?
H
†??
,
(12)
H corresponding to the
H), the maximum achievable rate
principal singular value Λ1(?
CBF= log2
1 + ρ
???˜ u†?
H ˜ w
???
2?
.
(13)
COPT= max(CSM,CBF).
(14)
V. SIMULATION RESULTS
We consider a 60GHz MIMO system with Nt= Nr= 8
and M = 2 subarrays, as shown in Fig. 2. Let Δy denote
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Fig. 2.Antenna layout model.
the Y -axis shift and θ the angular rotation. Notice that a 3-
dimension (3-D) setting in practice can be easily converted to
such 2-D model. The Rician K-factor is set as K = 10 dB.
Figure 3 shows the optimal inter-subarray spacing at the
transmitter and receiver to form a rank-2 MIMO channel
with maximum capacity. By antenna grouping and subarray
beamforming, the inter-element spacing required to create a
full rank channel is reduced as Nt increases. We choose
sT= sR= 10cm in the proposed system, which is a practical
operating point to offer high rank transmission capability.
The performance of the blind subarray beamforming al-
gorithm is illustrated in Fig. 4. The number of perturbation
vectors can be Kt = Kr = 16, Kt = Kr = 8 or Kt =
8 with Kr= 16, which requires 4-bit, 3-bit or 3-bit feedback
correspondingly. Note that, with the efficiently designed per-
turbation vectors, the beamformer converges to the optimal
performance within only a few number of iterations.
In Fig. 5, the performance of maximum achievable rate is
compared between the rank-1 beamforming and the rank-2
MIMO transmission for a system illustrated in Fig. 2. The
maximum achievable rate or capacity is shown for different
geometrical settings, which include Tx-Rx distance (D), y-
axis shift Δy and angular rotation θ respectively. It can be seen
that rank-1 beamforming and rank-2 transmission outperforms
each other in different geometrical configurations. This clearly
demonstrates that the high rank transmission in 60GHz system
is quite sensitive to geometrical movement and misplacement,
which necessitates the rank adaptation transmission in practice.
Figure 6 illustrates the average capacity of the 60GHz
transceiver in random geometrical settings. The geometrical
settings in terms of D, Δy and θ are randomly chosen from the
uniformly distributed sets give by D ∈ [0.1 5], Δy ∈ [−2 2]
and θ ∈ [−π
Ndrop= 8000 random drops of the geometrical placement of
transmitter and receiver pairs. It is shown that the proposed
optimum transmission scheme offers huge performance gain
over rank-1 beamforming at moderate and high SNR scenarios.
2
π
2]. Each point is obtained by averaging over
0 0.05 0.10.150.2 0.25 0.30.35
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Tx inter−subarray/inter−element spacing sT (m)
Rx inter−subarray/inter−element spacing sR (m)


2 × 2 system with omni−directional antennas
2 × 8 system with 2 subarrays and beamforming
2 × 32 system with 2 subarrays and beamforming
Fig. 3.
Δy = 0.
Optimal inter-subarray spacing for rank 2 with D = 5m, θ = 0,
01020304050
0
0.5
1
1.5
2
2.5
3
3.5
Number of iterations
Recived power |y|2


optimal beamforming
Peturbation vector set Kt= Kr = 16
Peturbation vector set Kt=8, Kr = 16
Peturbation vector set Kt= Kr = 8
Fig. 4.Blind beamforming performance.
VI. CONCLUSION
We have proposed a technique to realize high rank MIMO
transmission for LoS 60GHz wireless systems. The technique
is based on the optimization of inner-subarray beamforming
and inter-subarray spatial multiplexing at both transmitter and
receiver. With the proposed scheme, practical spatial multi-
plexing transmission in 60GHz wireless systems is justified
and provides significant capacity gain over rank-1 beamform-
ing, which is highly desired for multi-Gigabit applications in
60GHz systems. In addition, the proposed scheme is robust to
the geometrical misplacement and human blockage effect.
APPENDIX 1: HIGH RANK CRITERIA FOR Nt× 2 SYSTEM
WITH SUBARRAY BEAMFORMING
The equivalent channel gain after applying the transmit
DAS beamforming can be expressed as (15), in which α2?
sinθ11− sinθ21 and α1 ? sinθ22− sinθ12. The sufficient
condition to create a rank 2 MIMO channel maximizing
capacity from?
H is to let R ??
H?
H
†
= ξI, where ξ is
a constant. The solution is given by setting the off-diagonal
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?
H =
⎡
⎣
Nt
2e−jkd11
?
1 + ejkdα1+ ejk2dα1+ ... + ejk(Nt
2−1)dα1?
e−jkd12
?
1 + ejkdα2+ ejk2dα2+ ... + ejk(Nt
2−1)dα2?
e−jkd21
Nt
2e−jkd22
⎤
⎦. (15)
012345
0
5
10
15
20
D (m)
Capacity (bit/s/Hz)
Capacity over D, SNR = 0, Δ y = 0, θ =0


−2−1.5−1−0.500.511.52
2
4
6
8
Capacity over Δ y, D=1.5m, SNR = 0, θ=0
Y−axis shift Δ y (m)
Capacity (bit/s/Hz)
−100−50050100
4
6
8
10
capacity over θ, D=1m, SNR = 0, Δ y=0
Rotation θ (degree)
Capacity (bit/s/Hz)
rank 2 transmission
rank 1 beamforming
Fig. 5.
geometrical settings, K = 10dB.
Capacity variation of rank-1 and rank-2 transmission at different
elements of R to be zeros, i.e., R(1,2) = R(2,1) = 0.
R(1,2) =Nt
1 + e−jψ+ e−j2ψ+ ... + e−j(Nt
2e−jkd0?
= 2Ntcos1
?
where d0 ? d21− d11 = d12− d22, ψ ? kdα2 = kdα1.
Considering the symmetric structure and the fact that the
distance D is much larger than sT and sR, we have α1 =
α2 ≈ −sR
R(1,2) = 0 is to let cos1
2
met by
1
22
From the geometry of the arrays we know that [3]
2ejkd0?
+Nt
2−1)ψ?
1 + ejψ+ ej2ψ+ ... + ej(Nt
?
2ψ + cos3
2−1)ψ?
− 1)ψ
2
2kd0− (Nt
2
?
·
cos1
2ψ + ... + cos(Nt
2
− 1)ψ
?
,
Dand ψ ∼ −sR
Dπ. Thus a sufficient condition of
?2kd0− (Nt
=π
2+ pπ, p = 0,±1,±2,... (16)
2− 1)ψ?= 0, which is
?
2kd0− (Nt
− 1)ψ
?
sTsR= (d21− d11)(d21+ d11).
We can also assume that (d11+ d12) ≈ 2D without loss
of accuracy. Taking d0=sTsR
2D
full rank criterion with maximum capacity becomes
(17)
and ψ = −sR
Dπ into (16), the
2sTsR+ (Nt
2
− 1)sRλ = (2p + 1)Dλ.
(18)
−10−50510
0
1
2
3
4
5
6
7
8
9
10
Transmit power SNR
Capacity (bit/s/Hz)


Optimal transmission
Rank 2 spatial multiplexing
Rank 1 beamforming
Fig. 6.
[−2 2] and θ ∈ [−π
Average capacity of the proposed scheme (D ∈ [0.1 5], Δy ∈
2
π
2], K = 10dB).
Thus we have
sR≈ (2p + 1)
Dλ
2sT+ (Nt
2− 1)λ.
(19)
Notice that this solution also satisfies R(2,1) = 0.
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Multi-GigabitWirelessSpecification,
WPANStandardizationwithinIEEE802.15.3c,
978-1-4244-5637-6/10/$26.00 ©2010 IEEE
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE Globecom 2010 proceedings.