1. Priori-Aided Channel Tracking for Millimeter-Wave Beamspace Massive MIMO Systems
Linglong Dai and Xinyu Gao
Good afternoon, everyone! I’m Linglong Dai from Tsinghua University. The title of my presentation is priori-aided channel tracking for millimeter-wave beamspace massive MIMO systems. As we know, the high energy consumption caused by the huge number of RF chains is a bottleneck problem for mmWave massive MIMO systems, and the beamspace MIMO with lens antenna array can be considered as a promising solution. However, beamspace MIMO requires the information of beamspace channel of large size which is challenging in practice, since the user mobility at mmWave frequency band leads to the fast variation of the beamspace channel, thus the real-time channel estimation involves unaffordable pilot overhead. In this work, we aim to solve this problem.
Department of Electronic Engineering,
Tsinghua University, Beijing , China
August 25, 2016

2. Contents 1 Technical Background 2 Beamspace MIMO 3 PA channel tracking
This presentation consists of 5 parts. At the beginning, let’s have a view of the technical background 4
Simulation Results 5
Conclusions

3. Advantages of mmWave massive MIMO
High frequency ( GHz)
Larger bandwidth: 20MHz → 2GHz
Short wavelength (1-10 mm)
Enable large antenna array (massive MIMO): 1~8 → 256~1024
Higher array and multiplexing gains to improve spectral efficiency
Serious path-loss
Avoid multi-cell interference, more appropriate for small cell
As we can see from the figure, there are three special properties of mmWave. The first one is the high frequency around and above 30GHz, where the spectrum is less crowded, so we can provide much larger bandwidth for communication, e.g., the bandwidth can be increased from 20MHz to 2GHz, 100 times larger. The second property is the short wavelength, which enables a large antenna array to be arranged in a small area. That means we can achieve higher array gain and multiplexing gain to significantly improve the spectral efficiency. The last property is the serious path-loss, which can efficiently avoid multi-cell interference, which is attractive for the dense deployment of small cells. In conclusion, mmWave massive MIMO is able to combine the roadmaps of 5G in an unified way to achieve 1000 times capacity increase in the future.
mmWave
High frequency
Short wavelength
Serious path-loss
Spectrum expansion
Large antenna array
Small cell
1000x capacity increase!

4. Challenges of mmWave massive MIMO
Traditional MIMO: one dedicated RF chain for one antenna
Enormous number of RF chains due to large antenna array
Unaffordable energy consumption (250 mW per RF chain at 60 GHz)
MmWave massive MIMO BS with 256 antennas → 64 W (only RF)
Micro-cell BS in 4G → several W (baseband + RF + transmit power)
However, realizing mmWave massive MIMO in practice is not a trivial task. One key challenge is that each antenna in MIMO systems usually requires one dedicated RF chain including high-speed ADC, power amplifier, etc. This results in unaffordable hardware cost and energy consumption in mmWave massive MIMO systems, as the number of antennas becomes huge and the energy consumption of RF chain in mmWave band is high. For example, at 60 GHz, one RF chain will consume 250 mW. If we consider a mmWave massive MIMO base station (BS) with 256 antennas, the RF chains will consume 64 Watts, which is much higher than the total power consumption of current 4G micro-cell BS. This problem is considered as “the death of 5G” by some experts. Therefore, it is urgent for us to find out an efficient solution to reduce the number of required RF chains.
How to reduce the number of required RF chains?

5. Contents 1 Technical Background 2 Beamspace MIMO 3 PA channel tracking4
Simulation Results 5
Conclusions

6. Beamspace MIMO with lens antenna array
Basic idea [Brady’13]
Concentrate the signals from different directions (beams) on different antennas by lens antenna array
Transform conventional spatial channel into beamspace (spatial DFT)
Limited scattering at mmWave→ beamspace channel is sparse
Select dominant beams to reduce the dimension of MIMO system
Negligible performance loss→ significantly reduced number of RF chains
To solve this problem, beamspace MIMO with lens antenna array has been recently proposed. By using the lens antenna array, beamspace MIMO can transform the conventional spatial channel into beamspace channel by concentrating the signals from different directions (beams) on different antennas. Since the scattering at mmWave frequencies is not rich, the number of effective prorogation paths is quite limited, which means we have only a small number of beams. Therefore, the beamspace channel is sparse in nature, and we can select a small number of dominant beams to significantly reduce the dimension of MIMO system and thus the number of RF chains without obvious performance loss.
Beamspace MIMO
Conventional MIMO
[Brady’13] J. Brady, et al., “Beamspace MIMO for millimeter-wave communications: System architecture, modeling, analysis, and measurements,” IEEE Trans. Ant. and Propag., Jul

7. Beamspace channel Spatial channel Beamspace channel
In this slide, we give some figures to explain beamspace MIMO more clearly. The figure in the top left corner is the prototype of beamspace MIMO built by Nokia. The figure in the top right corner shows the concentrating function of lens. The figure in the bottom left corner is the power distribution of the traditional spatial channel, while the last figure is the one of the beamspace channel. Obviously, with the help of lens antenna array, the beamspace channel becomes sparse.

8. Challenges of beamspace MIMO
1st : Beamspace channel estimation
Traditional algorithms, such as LS and LMMSE can be used
With limited number of RF chains, the pilot overhead is high
Support detection (SD)-based beamspace channel estimation [Gao’16]
Fully utilize the sparsity to significantly reduce the pilot overhead
2nd : Beamspace channel tracking
Fast time-varying channel
Real-time channel estimation requires
high pilot overhead
No paper on this topic
However, although beamspace MIMO can significantly reduce the number of RF chains, it still need to acquire the information of beamspace channel of large size, which is challenging in practice.
Firstly, since we cannot sample the signals on all antennas simultaneously with limited number of chains, the traditional algorithms, such as LS, will involve unaffordable pilot overhead. To solve this problem, in our previous work, we proposed a support detection based channel estimation scheme, which can fully utilize the sparsity of mmWave channel to reduce the pilot overhead.
Secondly, since the user mobility usually leads to the fast variation of mmWave beamspace channels. If we adopt the real-time channel estimation, the pilot overhead will also be quite high. Therefore, more efficient beamspace channel tracking schemes exploiting the temporal correlation of time-varying channels is preferred. Unfortunately, there are quite few works on this topic.
[Gao’16] X. Gao, L. Dai, et al., “Beamspace channel estimation for millimeter-wave massive MIMO systems,” IEEE/CIC ICCC, Jul

9. Contents 1 Technical Background 2 Beamspace MIMO 3 PA channel tracking
To solve this problem, in this work, we propose a priori-aided (PA) channel tracking scheme. 4
Simulation Results 5
Conclusions

10. Motion of the kth user : speed : sampling period : direction of motion
Our target is to find the relationship of the beamspace channels of user k in sequential time slots. To achieve this goal, we first consider a practical linear user motion model as shown in this slide. Note that the our scheme can be also employed in nonlinear motion model as will be discussed later. Here, v_k and phi_k are the motion speed and motion direction respectively, which are assumed to keep fixed over time, T is the sampling period, d_k_t and theta_k_t is the distance and physical direction between user k and the base station at time slot t. From this figure, we can observe that the motion of user k can be described only by four parameters, that are d_k_t, theta_k_t, phi_k and v_k.
: speed
: sampling period
: direction of motion
: distance at time t
: physical direction at time t
The motion of user k can be described by four parameters:

11. Motion state of the kth user
Target
Predict according to
Solution
Define an auxiliary parameter
Define the motion state of the kth user at time t
Proposition 1. The relationship between and is
As the mmWave channel is dominated by the LoS path, we can observe that the physical direction theta_k of the LoS path is a crucial parameter. Therefore, we can try to exploit the temporal variation law of the physical direction for beamspace channel tracking. This means that we need to use the physical directions at the previous t time slots to predict the one at the next time slot t+1. To achieve this goal, we first define a auxiliary parameter lemada_k_t as this, which can be considered as the angular speed. Then, we define the motion state of user k at time slot t as this. With some mathematical derivations, the motion states at different time slots have the following relationship. This relationship indicates that once the motion state m_k_t has been estimated, the physical direction at time slot t+N can be predicted accordingly.
Corollary 1. The relationship between and is
After has been estimated, can be predicted accordingly

12. How to estimate the motion state?
Observations
Consider the triangle with green lines and utilize the law of sine
Consider the triangle with red lines and utilize the law of sine
Our next work is to estimate the motion state m_k_t. To do this, we can observe the red and green triangles as shown in this figure. Using the law of sine, we can obtain two groups of equations as listed in this slide.

13. How to estimate the motion state?
Solutions
Estimate , , and by regular channel estimation
Use the observations
where
The motion state at time t can be estimated as
One step prediction
Why one step ?
, , and may be not accurate enough
A miss is as good as a mile
According to Proposition 1
Solving these two groups of equations jointly, we can estimate two parameters in motion state, that are phi_k and lemda_k_t by these two equations. This indicates that we can estimate the physical direction in time slots t, t-1 and t-2. Then, the motion state at time slot t can be obtained accordingly. Based on the motion state, the physical direction at time slot t+1 can be predicted by the equation in blue color. Note that, in our scheme, we only adopt one step prediction. This is due to the fact that the estimations of the physical direction in time slots t, t-1 and t-2 may be inaccurate. A miss at the beginning may lead to a destructive error in the end.

14. The priori information of
After has been predicted
Use to obtain the priori information of the beamspace channel
How to fully exploit
Resort to the special structural property of beamspace channels
Proposition 2. Consider the beamspace channel of the kth user. The ratio between the power of V strongest elements of and the total power of the channel can be lower-bounded by
The position of the strongest element of is determined by Besides, once is detected, other V-1 strongest elements will uniformly locate around it.
After we have predicted the physical direction in time slot t+1, we can use it to obtain the priori information of the beamspace channel. Specifically, we can resort to the special structural property as shown in Proposition 2. It shows that the ratio between the power of the V strongest elements of the channel and the total channel power can be lower bounded by this equation. And once the strongest element is determined, the other V-1 elements will uniformly locate around it.

15. The priori information of
Insights of Proposition 2
can be well-approximated by a sparse vector
The support (positions of nonzero elements) of is determined by ( )
This figure gives a more intuitive explanation of Proposition 2. The red line is the best case where all the channel power is concentrated on one nonzero element, while the blue line presents the worst case where power diffusion is most serious. From this figure and propostion 2, we can observe that the beamspace channel can be well-approximated as a sparse vector with the sparsity V. And the support of the sparse beamspace channel is uniquely determined by the position of the strongest element, which is only related to the physical direction. Therefore, once we can predict the physical direction, we can directly obtain the support of the beamspace channel in the next time slot.
We can directly obtain the support of at time t+1 according to

16. Priori-aid (PA) channel tracking
Regular channel estimation
for
1. Estimate by SD-based channel estimation
2. Detect the physical direction according to the position of the strongest element
end
Channel Tracking
3. Estimate the motion state
4. Predict the physical direction
5. Detect the support of based on
6. Estimate the nonzero elements of by LS algorithm
7. Form the estimated channel
8. Refine according to the position of the strongest element
Based on the observations above, we propose a PA channel tracking scheme. The flow chart of our scheme is provided at the top of this slide, following with the pseudo-code. At the first 3 time slots, we adopt the regular channel estimation, and estimated the physical directions in time slot 1,2,3. Then, we execute the channel tracking. Firstly, we estimate the motion state in time slot t-1 using the physical directions in time slot t-1,t-2,t-3. Then, we predict the physical direction in time slot t, and use it to obtain the support of sparse beamspace channel directly. After the support has been obtained, we can utilize the classical LS algorithm to estimate the nonzero elements of the beamspace channel with low pilot overhead. In the end, we use the position of the strongest element of the estimated channel to refine the physical direction.

17. Some explanations Step 2: how detect Step 5: how detect the support
Find the predefined spatial direction based on
Step 5: how detect the support
Based on , reversely compute the position of the strongest elements
Obtain the support
Step 6: how realize LS & why it can save pilot overhead
LS can be simply realized by the selecting network of beamspace MIMO
The size of support is small, pilot overhead can be saved even with limited number of RF chains
Next, we will explain some key steps of the proposed PA channel tracking scheme. In step 2, we can use the position of the strongest element to estimate the physical direction, which follows the one-to-one relationship like this. In step 5, based on proposition 2, we can obtain the support of beamspace channel by this equation. In step 6, we can use LS algorithm to estimate the beamspace channel. This procedure involves quite low pilot overhead even with limited number of RF chains, since size of support is small as we have proved. In step 8, we refine the predicted physical direction to improve its accuracy. This is due to the fact that the predicted physical direction may not accurate enough, leading to the following prediction imprecise. Moreover, when users move nonlinearly, this step enables us to track the physical direction adaptively.
Step 8: why refine
Due to error, may be inaccurate, leading to the following predict imprecise
When users move nonlinearly, can be tracked adaptively

18. Contents 1 Technical Background 2 Beamspace MIMO 3 PA channel tracking
Next, we provide the simulation results to show the advantages of our scheme. 4
Simulation Results 5
Conclusions

19. Simulation setup Channel parameters Motion state Algorithms
Channel model: Saleh-Valenzuela model
MIMO configuration:
Antenna array: ULA at BS, with antenna spacing
One LoS path with gain
Length of one period
Motion state
User 1:
User 2:
User 3:
User 4: , (nonlinear)
The simulation parameters are set as follows. The mmWave channel is assumed to follow the classical Saleh-Valenzuela multi-path model. The BS employs a lens antenna array with 256 elements to serve 4 moving users. The number of RF chains is also set as 4. The initial motion states of four users are set as this, where user 4 moves nonlinearly. For the initial regular channel estimation, we employ our proposed SD-base algorithm, where the number of pilots is 128 per period. For the PA channel tracking, the number of pilots is 16 per period.
Algorithms
Regular channel estimation: SD-based algorithm, pilots/period
Channel tracking: PA channel tracking, pilots/period

20. Physical direction prediction
Observations
SNR = 10 dB
PA channel tracking can always track the physical direction accurately
Even for user 4 who moves nonlinearly, the performance is satisfying
This figure shows the physical direction tracking accuracy of the proposed PA channel tracking scheme, where the SNR is set as 10 dB. We can observe that the proposed PA channel tracking can always track the physical direction accurately. Even for user 4 who moves nonlinearly, the performance is still satisfying.

21. NMSE of channel tracking
Observations
PA channel tracking can much higher accuracy
The pilot overhead can be significantly reduced (16 instead of 128)
This figure compares the normalized mean square error performance between the proposed PA channel tracking scheme, the red line, and the conventional real-time OMP channel estimation scheme, the blue line. Both schemes use 16 pilots per period for fair comparison. From this figure, we can observe that the proposed PA channel tracking can achieve much higher accuracy than conventional schemes but with significantly reduced pilot overhead.
[Mendez-Rial’15] R. Mendez-Rial, et al “Channel estimation and hybrid combining for mmWave: Phase shifters or switches?” ITA Workshops, Feb

22. Contents 1 Technical Background 2 Beamspace MIMO 3 PA channel tracking
In the end, we make a brief summary of this presentation. 4
Simulation Results 5
Conclusions

23. Conclusions Proposed PA channel tracking Advantages
Designed for beamspace mmWave massive MIMO systems
May be the first work to solve this problem
Consider a practical user motion model
Temporal variation law of the physical direction → Predict
Structural properties of the beamspace channel → Priori information
In this presentation, we propose a PA channel tracking scheme for beamspace mmWave massive MIMO systems, which may be the first work to solve the channel tracking problem. The key idea of our scheme is to consider a practical user motion model to derive the temporal variation law of the physical direction. Then, based on this law and the structural property of mmWave beamspace channel, we can utilize the obtained beamspace channels in the previous time slots to predict the prior information of the beamspace channel in the following time slot without channel estimation. Simulation results show that our scheme can track the time-varying beamspace channel with quite low pilot overhead. Moreover, it enjoys satisfying accuracy even for the user who moves nonlinearly.
Advantages
Track the beamspace channel with quite low pilot overhead
Enjoy satisfying NMSE performance
Efficient even for the nonlinear motion

24. Thanks http://oa.ee.tsinghua.edu.cn/dailinglong/
Simulation codes for most papers are provided for reproducible research !