CHAPTER 2 BACKGROUND AND RELATED WORK
2.2 Related Work
2.2.3 Machine Learning based Link Adaption
Recently, there has been a growing interest in the applications of machine learning. In the communication field, the capability of machine learning to deal with the complicated parameters catch many researchers’ eyes.
[16] implemented online AMC with support vector machines to capture the channel effect in real time and found out the proper mapping from SNR to MCS.
Unfortunately, this method is not suitable while the mapping is not one-to-one.
Also, the training set is still too large to converge fast. [17] proposed a low dimen-sional feature set to increase the AMC accuracy while operating in MIMO. This research simply adopted k-NN. The method showed good performance. However, this method may suffer from excessive training memory and processing time.
Reinforcement learning is one of the machine learning techniques. It is suitable for a goal-oriented game, training the agent to learn how to act to achieve a higher cumulative reward. Several researches paid attention to this method because one of the advantages of reinforcement learning is that it can train online and save memory in comparison to supervised learning. Reinforcement learning can collect the data in a more efficient way because exploration and exploitation is a widely studied issue in this field [27]. [18, 19] adopted Q-learning and showed better per-formance in comparison with a supervised learning based method. Although the researches have shown the positive results and the potential, the applied reinforce-ment learning techniques are not efficient enough. Moreover, these methods did not focus on optimizing the convergence strategy, which is an important issue in a practical environment.
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CHAPTER 3
SCENARIO AND PROBLEM FORMULATIONS
In this section, we first introduce the system model in LTE/LTE-A. And then, the encountered problems when implementing NOMA+MU-MIMO in cur-rent LTE/LTE-A are presented clearly. In the end, we introduce the problem formulation.
Notations: We use upper-case boldface letters for matrices and lower-case boldface for vectors. The operation (·)−1, (·)T and (·)H denote the inverse, the transpose and the conjugate transpose of matrix respectively. E(·) stands for the expectation operator, and C represent the complex value. |S| denote the size of set S.
3.1 Network Model of NOMA+MU-MIMO
When the base station uses NOMA technique to transmit signal, they allocate the users with the different power to utilize the power-domain. The receivers adopt SIC to eliminate the interference from the other users. When it comes to MU-MIMO, the based station uses the precoding technique to encode the transmitted signal, exploiting the spatial-domain to superpose multiple users’ messages in the same resource block. With the combination of NOMA and MU-MIMO, the base stations transmit the signals with different power allocation and precoders for different receivers. In this thesis, different precoder means different beam. The transmitted signal, which is denoted as y, can be written as
y =
Nb
X
b=1
fb X
u∈Kb
ab,usb,u, (3.1)
where Nbis the maximum number of beams. sb,u is the desired data which receiver U Eu in beam b desires to receive. Also, to apply the NOMA, the users have to be in the same beam.
In order to retrieve the desired signal, the receiver have to decode the received signal successfully. In the communication environment, the channel responses for different users are various so the received signal for each users are different. The
15
3.1. NETWORK MODEL OF NOMA+MU-MIMO 16
Table 1: Notation Table Type Symbols Definition
Parameters
NB The maximal number of beams M The number of antenna transmitter Nr The number of antenna receiver
Nc The number of vectors in the codebook P Power constraint on the transmitted signals
Sets
C Set of codebook U Set of UEs
S Set of scheduled UEs
Kb Set of shceduled UEs served in beam b T Set of RBs
M Set of MCSs
Variables
xu The signal received by UEu.
xk,b The signal received by UEk in beam b.
y The transmitted signal
sb,u The desired signal of UEu in beam b.
Hk,b The channel matrix of UEk in beam b.
hk,b The channel vector of UEk in beam b.
bhk,b The quantized channel vector returned by UEk in beam b.
ehk,b The normalized channel response of UEk in beam b.
cj The codebook vector j in codebook.
fb The precoding vetor of beam b.
ab,k The power of UEk in beam b.
ek The error vector for UEk.
eek The normalized error vector for UEk. U Eb,k The UEk in beams b.
γef f The effective SINR estimated by BS based on the mapping.
γef f0 The effective SINR modified by BS.
θ The angle betweenehk,b and bhk,b.
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3.1. NETWORK MODEL OF NOMA+MU-MIMO 17
Beamforming
Figure 5: Overall System in NOMA+MU-MIMO
received signal for U Eu’s in beam b is denoted by xb,u. xb,u is represented as
Also, the user implements spatial filter to enhance the desired signal and sup-press the interference including undesired signals.
Thus, the received signal can be rewritten as
x = vu,bHu,b where vu,b is denoted by equalization of receiver.
The effective channel response denoted as gu,b can be represented as
gu,b = vu,bHu,b. (3.4)
3.2. COMMUNICATION SYSTEM IN LTE/ LTE-A 18
Zero-forcing beamforming is a useful technique to mitigate the interference from the other beam so we implement is as the precoding mechanism. We choose the fborthogonal to the other beams. Theoretically, if the channel information can be fully obtained, the received signal with zero-forcing precoding can be rewritten as
x = vu,bHu,bFb X
u∈Kb
ab,usb,u+ n. (3.5)
The overall system in NOMA+MU-MIMO is illustrated in Fig. 5.
3.2 Communication System in LTE/ LTE-A
In a practical communication system, the channel information returned by UE is limited. It includes CQI, PMI, and RI. CQI implies the magnitude of the chan-nel. PMI indicates the direction of the chanchan-nel. RI indicates the number of layers the UE preferred. In LTE/LTE-A, the PMI is chosen from the LTE codebook.
Assuming that the number of layers is 1, and the LTE codebook composed of the quantized vector is given by
C = {c1, ....cNc} , (3.6)
where C denotes the set of the codebook. Nc denotes the number of vectors in the codebook.
The chosen PMI is the best choice among the code book to represent the channel. The chosen PMI, which is denoted by hu , can be represented as
chu = arg max
cj∈C|Huc∗j|, (3.7) where chu is best chosen PMI among the codebook.
With zero-forcing beamforming, fu satisfies
fubh∗j = 0, if user i is not allocated in the same beam as user j. (3.8)
The received signal of UE u in beam b is
xu = vu,bGu,bfb X
u∈Kb
ab,usb,u+ vu,bHu,b
Nb
X
j=1,j /∈b
fj X
u∈Kj
aj,usj,u+ n. (3.9)
The term F = vu,bHu,bPNb
j=1,j /∈bfjP
u∈Kjaj,usj,u is regarded as undesired signal for UE u. While the perfect CSI is available, F would be 0. Otherwise, F would be larger than zero.
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3.2. COMMUNICATION SYSTEM IN LTE/ LTE-A 19
Tx
𝑈𝐸1,1
𝑈𝐸𝐵,1
𝑈𝐸𝐵,2
SINR N𝑟
low N𝑟
N𝑟
beam1
beamB
intra-interference
inter-interference
N𝑡
𝑈𝐸1,2 N𝑟
Figure 6: Operate NOMA+MU-MIMO in Nt × Nr MIMO. Inter-interference indicates the interference caused by the other beams. Intra-interference indicates the interference caused by the other user in the same beam.
ILLA
preprocessingCQI
OLLA
UE eNB
CQI
MCS ACK/NACK 𝛾𝛾𝑒𝑒𝑒𝑒𝑒𝑒
𝛾𝛾′𝑒𝑒𝑒𝑒𝑒𝑒
Figure 7: Operation Diagram in Downlink
3.3. SCENARIO IN LTE/LTE-A 20
In Fig. 7, the link adaption scheme is separated into two part: one is the inner loop link adaption (ILLA), the other is outer loop link adaption(OLLA).
ILLA is designed to assign the most suitable MCS based on the estimation of link quality. The purpose of OLLA is to correct the reporting inaccuracies. Thus, it modifies the estimated link quality based on the ACK and NACK instead of merely depending on reporting CQI.
3.3 Scenario in LTE/LTE-A
Base station
UE
Figure 8: Deployment of NOMA+MU-MIMO
Fig. 8 illustrates the deployment of NOMA+MU-MIMO. The number of trans-mitters’ antenna Nt = 4, the number of receivers’ antenna Nr = 1. The assump-tions are shown as following:
1. The number of transmit beams is fixed over all RBs.
2. The power allocated among beams is equal.
3. The number of multiplexed users within a beam is smaller than 2.
4. The maximal number of data streams each user received do not exceed.
5. The PMI is chosen from the LTE codebook.
These assumptions allow us to optimize the system performance without losing generality.
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3.4. PROBLEMS FORMULATION 21
3.4 Problems Formulation
3.4.1 Observation of NOMA+MUMIMO and MUMIMO
Firstly, we ran simulations with different the setting of estimation of SINR in order to analyze the the difference between perfect CSI and limited CSI. If the base station can obtain full feedback, it can estimate SINR correctly. By contrast, if the feedback is limited, the base station can only approximate the SINR. The format of limited follows the standard of the LTE\LTE-A. The results are shown in Fig. 9. From Fig. 9, there is almost no throughput gain between NOMA+MUMIMO and MUMIMO. In addition, NOMA+MUMIMO is supposed to be better than MU-MIMO in terms of cell-edge due to the characteristic of NOMA. Unfortunately, the expected results can not be seen from Fig. 9. That is, Fig. 9 indicates that the performance fails to be further improved as long as the estimation is not accurate enough.
(a) Throughput. (b) Cell-edge Throughput.
Figure 9: Comparison between MU-MIMO and NOMA+MU-MIMO with correct Estimation of SINR or not
The previous observations imply that CSI integrity is crucial to the improve-ment. The feedback adopted in VIENNA is the lower bound of the expectation of SINR, but the inaccuracy of the estimated SINR and real SINR have not analyzed well in [3]. The feedback has an impact on the estimation of SINR so we analyze the variation of real SINR for estimation of SINR based on limited feedback [3].
It is noticing in Fig. 10 that the variation of real SINR for a returned CQI is extremely large. It implies that the returned CQI from UE is very inaccurate.
The loss of accuracy of SINR might be acceptable while operating in MU-MIMO.
Nevertheless, in the case that taking NOMA into account, the inaccuracy becomes an important issue. Additionally, lots of researches [5,6] have shown that the power allocation and paring is a key problem as operating in NOMA. And the paring mainly depends on the difference of channel gain between the UEs, which receive
3.4. PROBLEMS FORMULATION 22
−10 −5 0 5 10 15 20 25
−8
−6
−4
−2 0 2 4 6 8 10 12
Estimated SINR
Real SINR
Figure 10: Comparison between estimated SINR and real SINR in terms of Throughput. Estimated SINR is the SINR estimated by limited CSI. Real SINR is SINR that UE actually suffers.
the data encoded with NOMA. The wrong estimation of channel gain difference leads to the wrong power allocation, causing the loss of performance.
Furthermore, the wrong paring and power allocation cause the UE to decode the signal unsuccessfully since the degradation of the signal is more than expected.
In other words, the SIC receiver may fail to decode the signal due to the unexpected interference.
3.4.2 The Impact of CSI on SINR
The impact of the inaccurate CSI on SINR will be further discussed.
Assuming that the number of beams is 2, 4x1 MIMO, beamforming is zero-forcing, and the receiver is perfect SIC receiver, which implies that the near user can successfully eliminate the intra-interference. Therefore, the intra-interference can be neglected, the inter-interference is the major topic to be discussed in the following. These assumptions allow us to analyze the problem without losing generality.
If the perfect CSI is available, the relationship between precoder fiand channel hi is demonstrated in Fig. 11. After passing the channel, the signal that UE
doi:10.6342/NTU201900453
3.4. PROBLEMS FORMULATION 23
𝑓1
ℎ1
𝑓2 ℎ2
Figure 11: Relationship of fi and hi under perfect CSI
ℎ1 = 𝑐1
ℎ2=c2 ℎ2 𝜃1
𝜃2 𝑓1
𝑓2 ℎ1
𝑒1
𝑒2
Figure 12: Relationship of fi and hi under limited CSI
3.4. PROBLEMS FORMULATION 24
Eq. (3.10) shows that the interference from the other beam can be eliminated perfectly with the precoding. However, the situation under the limited feedback is changed.
The relationship of precoder fi and channel hi is demonstrated in Fig. 12. The channel vector is hk = khkk (| ehkhbk|Hhbk+ ek). ek is denoted by the error vector.
hbk and ehk are denoted by the quantized channel vector and normalized channel vector, respectively. The received signal of UE is expressed as
Z1 = h1y limited feedback causes precoding, f2, to be chosen wrongly because the real chan-nel vector, h1, is unknown. In this situation, the base station could only choose the precoding orthogonal to bh1 instead of h1. As a result, the messages encoded by the precoding of the other beams cannot be eliminated naturally after going through h1.
Thus, the SINR of U Ek under limited feedback is
SIN Rk,real =
The interference, F = P
i∈S\k deter-mined by base station and the co-scheduled UE. Different co-scheduled UEs lead to different F, which could even range from 0 to 1. On the other hand, the ek is unknown at the base station due to the quantized PMI. As a result, the base station and UE can not get the accurate estimation of SINR, if the information
doi:10.6342/NTU201900453 3.5. ANALYSIS OF THE CONVERGENCE FORMULATION 25
Table 2: Objective Function Objective function:
maxπEπ
hPT
k=0rt+k | sti (3.13)
π is the strategy of selecting MCS.
st is the observable information for base station.
rt=
0, if the base station knows that it has assigned the suitable MCS
−1, otherwise
.
between the base stations and UE can not be exchanged completely. The base station may fail to estimate SINR for proper scheduling.
3.4.3 Convergence Formulation
Estimation of SINR is highly dependent on the CQI and PMI returned by UE in LTE. On the condition that reporting CSI is unable to represent the real SINR accurate enough due to the quantization error and limited feedback, changing the MCS based on the HARQ information have to be taken into consideration. Chang-ing MCS dynamically based on HARQ is so-called OLLA mechanisim. The preva-lence of short connection in LTE network [11] enforces the conventional OLLA to take convergence into consideration. As a result, convergence speed issue is our major goal in the thesis. Mathematically, the objective function is shown in Table 3.4.3.
Eq. (3.13) depicts the convergence problem mathematically.
The larger the Eq. (3.13) is, the quicker the base stations are able to assign the suitable MCS within a period time T . In other words, optimizing the objective function is to fulfill the requirement of the short connections in LTE. The base station can respond to the inaccurate reporting SINR more quickly, achieving better performance in scheduling with the corrected suitable estimation of SINR.
Thus, our aim is to design a strategy of modifying the MCS so the base stations can obtain the suitable estimation of SINR as quick as possible.
3.5 Analysis of the Convergence Formulation
To solve the optimization problem, the first step is to analyze the parameters associated with the rt. rt is an indicator that whether the base station finds the proper estimated SINR or not. The proper SINR indicates that the base station
3.5. ANALYSIS OF THE CONVERGENCE FORMULATION 26
real SINR of far user
real SINR of near user
Far user fail
is the SINR of near and far user that the base station approximate
Figure 13: Condition that the receivers of far and near user fail or success to decode the signal
is able to find maximal available MCS for the specified UEs. The base station can judge whether the MCS is maximal available MCS or not by the ACK\NACK.
Intuitively, the historical data about the success and failure of the assigned MCS is associated the outcome of the rt. In addition, we have known the base station chooses the MCS according to the estimated SINR. It decides the MCS based on a map, which suggests the appropriate MCS so the UE can receive the data efficiently, to transform the estimated SINR to MCS. We observed from Fig. 13 that the assigned MCSs only fail on the condition that the estimated SINR is larger than real SINR. That is to say, the probability of the outcome of rt is associated with not only historical data but also the distribution of SINR. Also, as shown in the previous chapter, the variation of the distribution of SINR is mostly caused by inter-interference. Eq. (3.12) shows all the parameters related to SINR. Therefore, we focus on analyzing the parameters of SINR in terms of PMI, CQI, and co-scheduled PMI.
3.5.1 Analysis of the SINR in MU-MIMO
Assuming the number of the beam is 2, 4x1 MIMO and zero-forcing beam-forming. SINR can be written as
SIN Rk,real =
Assuming that the co-scheduled UEs are orthogonal, the term ekfek will be 0
doi:10.6342/NTU201900453 3.5. ANALYSIS OF THE CONVERGENCE FORMULATION 27
with zero-forcing; thus, the real SINR of U Ek can be represented as
SIN Rk,real =
Since the base station can only estimate the SINR by PMI and CQI, we replace the parameters in Eq. (3.15) with PMI and CQI. Through the replacement, the relationship between CSI and SINR is more clear. The distribution of SINR can be observed in a easier way. Knowing that SIN R2 = | bhkeel|2, cos2θ = 1 − sin2θ, the SINR can be rewritten as
SIN Rk,real =
We can conclude from Eq. (3.16) that the ek is a random variable, which is related to P M Ik and CQIk. The inner product of ek and P M Ii can affect the SIN Rk. Also, it can be observed that the interference is caused by fkeek and ekfi. The fi and fk are precoding vectors for U Ei and U Ek respectively. That is to say, if the UE knows its co-scheduled user in advance, it could return the perfect estimation of CQI; or, if the base station is able to get the information of ek, the perfect estimation of SINR can be achieved. Nevertheless, the additional feedback would bring more burden on the channel because the channel has to give more space for transmitting control signal instead of the data. It is a trade-off
3.5. ANALYSIS OF THE CONVERGENCE FORMULATION 28
between the bits of feedback and the accuracy of the estimation. Furthermore, the additional feedback has to change the current LTE feedback standard. The target of this thesis is to assign a suitable MCS in order to achieve a better performance following the LTE feedback standard. Thus, the target of analyzing the SINR is to improve the design of the mechanism to find the proper MCS dynamically. As a result, we focus on the analysis of random variable in Eq. (3.16) for the reason that the probability of whether the transmission is failed or successful is highly associated with these parameters.
3.5.2 Observation of SINR in different CQI and PMI
In the previous subsection, we learned that the distribution of SINR is asso-ciated with the PMI, CQI, and co-scheduled CQI mathematically, but the actual distributions are still unknown. As a result, we run the simulations for different CQI and PMI to observe the pattern of the distribution.
5 10 15
Figure 14: Real CQI and estimated CQI. Real CQI is calculated by h, the esti-mated CQI is the CQI returned by UE.
doi:10.6342/NTU201900453 3.5. ANALYSIS OF THE CONVERGENCE FORMULATION 29
In Fig. 14, only four different PMI cases are presented for the convenience of observation. The x-axis is the real CQI value calculated based on real channel response. The y-axis is the estimated CQI value calculated based on limited feedback. The color represents the number of the pair of certain estimated CQI and real CQI out of the overall cases. Basically, if the point tends to be red, it implies such a pair appears more frequently. This figure indicates that what is the possible real value of CQI corresponding to the estimated value. Thus, the pattern of the distribution of estimated CQI and real CQI are able to be observed
In Fig. 14, only four different PMI cases are presented for the convenience of observation. The x-axis is the real CQI value calculated based on real channel response. The y-axis is the estimated CQI value calculated based on limited feedback. The color represents the number of the pair of certain estimated CQI and real CQI out of the overall cases. Basically, if the point tends to be red, it implies such a pair appears more frequently. This figure indicates that what is the possible real value of CQI corresponding to the estimated value. Thus, the pattern of the distribution of estimated CQI and real CQI are able to be observed