Chapter 2 System Model
2.4 Summary
eigenvalue of A . With Uk obtained from previous step, each precoders Vk is calculated based on virtual DL system model by the algorithm:
Leakage-IA is listed in Table 2-1.2.4 Summary
To cope with the interference issues in modern mobile communication systems and to further enhance the system performance, CoMP has been proposed as a key
technique. In this chapter, the infrastructure and classification of CoMP are firstly provided, and then the closed loop centralized UL CoMP system adopted in this thesis and its associated mathematical system model are introduced. Moreover, the sum-rate as the performance index is described as well. Finally, a promising technique, interference alignment, aiming at interference mitigation in K-user interference channel is illustrated. The basic idea of IA will be incorporated into one of our proposed transceiver designs.
Chapter 3
Interference Alignment (IA) Aided Transceiver Design
The interference from other cells which severely degrade the system performance is a crucial factor in modern wireless cellular communication systems and should be carefully managed. To cope with the issues caused by interference such as inconsistent service quality at cell-edge, poor cell coverage, and inferior throughput and to further improve the system efficiency, a promising technique, coordinated multipoint (CoMP) transmission and reception, is developed. In such scenario, the transceiver design based on the full BS cooperation is a critical issue.
In this thesis, two centralized UL CoMP transceiver schemes with multiple transmit antennas, receive antennas, and transmit layers are proposed; the one which incorporates the idea of interference management is provided in this chapter. Interference alignment is a new emerging interference management technique which is developed based on K-user interference channel structure, and its superior advantage for interference mitigation has been widely evaluated and discussed in K-user interference channel.
The organization of this chapter is shown below. The motivation of the proposed IA aided UL CoMP transceiver scheme is given in section 3.1. In section 3.2, we introduce the incorporation of IA in UL CoMP based on two popular iterative IA
algorithms, Min Leakage-IA and Max SINR-IA provided in [9], [12], and their performances will be evaluated. After the investigation in section 3.2, we propose an IA aided UL CoMP transceiver scheme based on the full cooperation at BSs in section 3.3.
Then the numerical evaluation and discussion are provided in section 3.4. Finally, we summarize this chapter in section 3.5
3.1 Motivation
In an interference limited communication environment, there are two typical interference management methods: 1) to decode the desired signal and interference simultaneously and 2) to separate the desired signal from interference by allocating orthogonal/independent physical resource (time, frequency, space, etc.). It is reasonable to infer that incorporating the concept of second approach into the first one can have great potential for dealing with the interference issues.
The inter cell interference which is often treated as noise in the case without BS cooperation is now decodable along with the desired signal at CU owing to the full BS cooperation provided by centralized UL CoMP as illustrated in (2.3). That is the first interference management method mentioned above is provided by centralized UL CoMP. On the other hand, interference alignment is belonging to the second interference management method, and it tries to align the interference into some limited subspace that is independent to the desired signal.
Considering the capability for interference mitigation provided by the two typical interference management methods, we combine the two methods in our first transceiver design which leads to equivalent channel matrix (2.5) reformulation in our work. Hence we aim to capture the basic idea of IA in our precoder and decoder design so that a well-behaved equivalent channel matrix can be obtained.
3.2 Incorporation of IA in UL CoMP
In K-user interference channel, IA intends to align interference at each terminal that inter-user/inter-cell interference can be separated from desired signal and then be alleviated successfully. In this work, we attempt to incorporate IA in our UL CoMP transceiver design (precoder and decoder design as illustrated in section 2.2) where the interference is aligned and then suppressed at the output of joint decoder UH based on two popular iterative IA algorithms, Min Leakage-IA and Max SINR-IA provided in [9], [12]. Owing to the intention of interference alignment and mitigation, the residual interference for each layer/user at the output of decoder will be minimized, and a near diagonal /block diagonal effective channel matrix in (2.3) and (2.4) is formed.
According to the system model of centralized UL CoMP depicted in (2.3) and the design principle of IA in K-user interference channel demonstrated in (2.11) and (2.12), the UL CoMP transceiver design which incorporates IA is based on the criteria shown below (taking kth BS for example, k {1,2, , }K ): K-user interference channel and IA in centralized CoMP is that the latter incorporates full cooperation between BSs for computing the decoders at the BSs. In order to achieve these criteria, we embrace the basic idea of the following two iterative IA approaches developed in K-user interference channel: Min Leakage-IA and Max
SINR-IA [9], [12]. In the rest of this thesis, the UL CoMP transceiver schemes assisted with Min Leakage-IA and Max SINR-IA are called Min Leakage-UL CoMP and Max SINR-UL CoMP, respectively. The two UL CoMP transceiver schemes both involve an iterative procedure based on UL-DL duality, and each iteration consists of two stages: 1) to calculate the joint decoder and 2) to compute the precoders according to the corresponding virtual DL CoMP system.
In regard to Min Leakage-IA aided Uplink CoMP (Min Leakage-UL CoMP) we obtain the modified optimization problem for joint decoder U from Min Leakage-IA depicted in (2.19) (taking kth BS for example, k {1,2, , }K ): interference leakage at the UE in kth cell gives
H U HV. The iterative procedure of Min Leakage-UL CoMP is listed in Table 3-1.
On the other hand, Max SINR-IA aided Uplink CoMP (Max SINR-UL CoMP) try
to maximize the SINR corresponding to different layers (data streams) at the output of decoder. Taking into account system model provided by (2.3) and the basic idea of Max SINR-IA, we reformulate (2.13) into the following objective function which aims at
(2.3). For the precoder design, we consider the corresponding virtual DL system model with which SINRik is maximized: i {1,2, , }d , k {1,2, , }K
SINR-IA algorithm plays an importance role to convert the original channel into a more tractable effective channel, HU HVH , which is nearly diagonal. The detail of this iterative algorithm is summarized in Table 3-1.Table 3-1: Iterative procedure of Min Leakage-UL CoMP and Max SINR-UL CoMP Step 1. Start with arbitrary precoders Vk, k {1, 2, …, K}
Step 2. Compute the joint decoder U using Min Leakage-UL CoMP (3.4) or Max SINR-UL CoMP (3.9) with Vk obtained from previous step, k {1, 2, …, K} .
Step 3. Based on virtual DL system model, compute precoder Vk using Min Leakage-UL CoMP (3.6) or Max SINR-UL CoMP (3.12) with U obtained from previous step, k {1, 2, …, K} .
Step 4. Go back to Step 2 unless the number of iterations reaches a predefined limit.
After the derivation of the two IA aided Uplink CoMP schemes, the achievable sum-rate performance comparison is provided by numerical simulation as shown in Figure 3-1. In our simulation, linear MMSE receiver is adopted, and sum-rate performance is calculated according to (2.7) as mentioned in section 2.2. The simulation results in this section are obtained by averaging over 100 independent channel realizations, and 20 iterations were performed for each iterative algorithm. The entries of the associated channel matrix are assumed i.i.d. complex Gaussian with unit
variance. Three BSs in one cooperative group and one UE in the coverage of each BS (K = 3, u = 1) are considered. All BSs are equipped with Mr = 4 antennas, and all UEs are equipped with Mt = 4 antennas. All UEs have equal number of transmit signals, i.e., d = 2.
Figure 3-1: Sum-rate performance of Min Leakage-UL CoMP and Max SINR-UL CoMP with K=3, Mt=4, Mr=4, d=2, and no. of iterations=20
The simulation result shows that Max SINR-UL CoMP significantly outperforms Min Leakage-UL CoMP. The major reason is that Min Leakage-UL CoMP mechanism tries to minimize the interference leakage but assumes (3.2) is automatically satisfied.
That is only the interference effect is considered, and there is no guarantee for the detection quality of the desired signal. On the other hand, the Max SINR-UL CoMP algorithm preserves a good compromise between interference and received power of desired signal because it takes both into account. As a potential solution to manage the interference issue and to further improve the system performance, the basic idea of Max SINR-ULCoMP is embraced in our proposed IA aided UL CoMP transceiver
scheme in section 3.3.
3.3 Proposed IA Aided Transceiver in UL CoMP
According to the discussion and simulation result in section 3.2, it is found that Max SINR-UL CoMP achieves better sum-rate performance compared to Min Leakage-UL CoMP, because the first one aided by Max SINR-IA preserves a good compromise between interference and received power of desired signal. In terms of effective channel matrix H , a near diagonal effective channel matrix is accomplished by Max SINR-ULCoMP, since the SINR maximization will somehow suppress the off-diagonal terms of the effective channel matrix. However, since the SINR maximization is executed layer by layer, the SINR performance achieved by each layer might be highly diverse leading to a poor-conditioned effective channel matrix. To improve the condition of the effective channel matrix, it is desired to further balance the layer SINR at the decoder output. Therefore we attempt to propose an IA aided UL CoMP transceiver that can achieve good trade-off between interference issue and received power of desired signal by SINR maximization, and can balance the SINR of each layer at the output of decoder.
The proposed IA aided UL CoMP transceiver is achieved by maximizing the product of instantaneous SINRs for each layer (per-layer SINR), which in turn attempts to increase each per-layer SINR and to reduce the difference between the per-layer SINRs at the output of decoder. Namely, the proposed IA aided UL CoMP scheme aims at maximizing the function shown below:
(( 1) ) ( ) ( ) (( 1) )
where SINRikis the SINR corresponding to the ith layer of the kth user at the output of
decoder as illustrated in Figure 3-2 ( i
1, 2, ,d
, k
1, 2, ,K
). Theproposed IA aided UL CoMP transceiver scheme involves an iterative procedure as shown in Figure 3-3, and each iteration consists of two stages: 1) to calculate the joint decoder and 2) to compute the precoders.
In the first stage, each column of the joint decoder is computed successively by the algorithm shown below: above is equal to the criterion,
(( 1) )
Figure 3-2: Illustration of centralized UL CoMP transceiver scheme, SINRik, and ki
which yields the same results as obtained in Max SINR-UL CoMP:
Figure 3-3: Flow chart of the proposed IA aided UL CoMP scheme
In the second stage, each column of the precoders is computed successively by the above is equal to the one shown below:
( )
The result of (3.25) implies:
max, max max, max max, max max, max max, max
1
max, max max, max max, max max, max max, max
1
Based on the discussion above, we can approximate (3.27) as
( )
max, max max, max max, max max, max max, max
1
summarized in Table 3-2.
Table 3-2: Iterative procedure for the proposed IA aided UL CoMP transceiver design Step 1. Start with arbitrary precoders Vk, k {1, 2, …, K}
Step 2. Compute the joint decoder U column by column using (3.18) to achieve better SINR performance with Vk obtained from previous step, k {1, 2, …, K} .
Step 3. Compute precoder Vk column by column by equation (3.31) to achieve better SINR performance with U obtained from previous step, k {1, 2, …, K} .
Step 4. Go back to Step 2 unless the number of iterations reaches a predefined limit.
3.4 Computer Simulations
The convergence behavior and sum-rate performance evaluations are presented for comparison between the UL CoMP transceiver scheme assisted with Min Leakage-IA, the UL CoMP transceiver scheme assisted with Max SINR-IA, and the proposed IA aided UL CoMP transceiver design which are called “Min Leakage-UL CoMP”, “Max SINR-UL CoMP”, and “IA aided UL CoMP”, respectively. The achievable sum-rate is calculated based on (2.7) mentioned in chapter 2 because a linear MMSE receiver is adopted in our work. ki involved in (2.7) is illustrated in Figure 3-2. Furthermore, sum capacity of UL CoMP with full BS cooperation also exhibits as a performance upper bound [15]. The simulation parameters chosen in this section are listed in Table 3-3.
Table 3-3: Simulation parameters
Parameter Value
Channel i.i.d. Rayleigh fading channel
Number of BSs / UEs (K) 3
Number of transmit antennas (Mt) 4
Number of receive antennas (Mr) 2, 4
Number of transmitted signal layers (d) 2, 3
Number of channel realizations 100 (sum-rate performance) 5000 (convergence behavior) Number of iterations for each algorithm 20 (sum-rate performance)
The convergence behavior are provided in Figure 3-4 and Figure 3-5 both of which are evaluated at SNR = 10 dB and at SNR = 30 dB. Figure 3-4 is simulated in the case with Mt=4, Mr=2, K=3, d=2; Figure 3-5 is simulated in the case with Mt=4, Mr=4, K=3, d=3. The simulation results show that Min Leakage-UL CoMP, Max SINR-UL CoMP, and IA aided UL CoMP have superior convergence behavior in all cases especially for Min Leakage-UL CoMP. However, large rate degradation occurs when Min Leakage-UL CoMP is adopted which is consisted with the numerical evaluation in section 3.2. This is because Min Leakage-UL CoMP mechanism makes all its effort to minimize the interference leakage but assumes (3.2) is automatically satisfied; hence there is no assurance that the received power of desired signal can achieve an acceptable level as mentioned in section 3.2.
Figure 3-4: Rate convergence behavior of Min Leakage-UL CoMP, Max SINR-UL CoMP, and IA aided UL CoMP with Mt=4, Mr=2, K=3, d=2, and SNR = 10/30 (dB)
Figure 3-5: Rate convergence behavior of Min Leakage-UL CoMP, Max SINR-UL CoMP, and IA aided UL CoMP with Mt=4, Mr=4, K=3, d=3, and SNR = 10/30 (dB)
SNR = 30 dB
SNR = 10 dB SNR = 30 dB
SNR = 10 dB
In Figure 3-6 and Figure 3-7, sum-rate performance comparisons between Min Leakage-UL CoMP, Max SINR-UL CoMP, and IA aided UL CoMP are displayed.
Figure 3-6 is simulated in the case with Mt=4, Mr=2, K=3, d=2; Figure 3-7 is simulated in the case with Mt=4, Mr=4, K=3, d=3. In all cases, it is found that Min Leakage-UL CoMP has substantial rate degradation compared to other two UL CoMP transceiver schemes due to its poor ability to maintain the received power of desired signal as mentioned above. The simulations also show that Max SINR-UL CoMP can achieve acceptable sum-rate performance as expected, and the proposed IA aided UL CoMP can reach even better sum-rate performance than Max SINR-UL CoMP. This is because that the proposed IA aided UL CoMP has the effect of balancing the SINR of each layer at the decoder output to improve the condition of the effective channel matrix. The sum capacity is provided here as a performance upper bound. We can find that the achievable sum-rate of IA aided UL CoMP is sufficiently close to the sum capacity especially for the case with Mt=4, Mr=2, K=3, d=2.
Figure 3-6: Sum-rate performance of Min Leakage-UL CoMP, Max SINR-UL CoMP, and IA aided UL CoMP with Mt=4, Mr=2, K=3, and d=2
Figure 3-7: Sum-rate performance of Min Leakage-UL CoMP, Max SINR-UL CoMP, and IA aided UL CoMP with Mt=4, Mr=4, K=3, and d=3
3.5 Summary
Interference alignment assisted UL CoMP is discussed and evaluated comprehensively in this chapter. First, two popular interference alignment algorithms, Min Leakage-IA and Max SINR-IA [9], [12], developed in K-user interference channel are incorporated in the UL CoMP transceiver designs which are called Min Leakage-UL CoMP and Max SINR-UL CoMP, respectively. Their sum-rate performance are evaluated and it is demonstrated that Max SINR-UL CoMP has better sum-rate performance since a good compromise between interference and received power of desired signal can be preserved. Hence Max SINR-UL CoMP is regarded as a highly potential interference mitigation scheme. According to the study in the first stage, an IA aided UL CoMP transceiver scheme that incorporates the basic idea of Max SINR-UL CoMP and further balances the SINR of each layer at the output of decoder is proposed. The simulation results show that the proposed IA-aided UL CoMP transceiver can achieve superior sum-rate and convergence performance.
Chapter 4
Channel Condition Enhanced Transceiver Design
In the thesis, two centralized UL CoMP transceiver schemes are introduced and both of which are established based on the joint processing nature provided by full BS cooperation. One of the UL CoMP transceiver schemes aided by IA is presented in Chapter 3. The other one aiming at enhancing the condition of the effective channel is given in this chapter.
The proposed channel condition enhanced UL CoMP transceiver scheme involves an iterative procedure which is similar to the iterative procedure included in IA aided UL CoMP transceiver design mentioned in Chapter 3, and each iteration consists of two stages: 1) to calculate the joint decoder and 2) to compute the precoders. But unlike IA aided UL CoMP transceiver, the precoders in the channel condition enhanced scheme is obtained by exploiting the UL-DL duality where the centralized UL CoMP (MAC-like structure) is dual to the virtual centralized DL CoMP (broadcast channel-like structure, BC-like structure) by reversing the direction of communication.
The arrangement of this thesis is as follows. In section 4.1, the motivation of the proposed channel condition enhanced UL CoMP transceiver scheme is provided. Then the problem formulation and design procedure of the proposed channel condition
enhanced scheme are described in section 4.2. Next, we analyze the complexity behavior of the two proposed transceiver schemes in section 4.3, which is followed by the numerical simulations including evaluations of convergence behavior, achievable sum-rate performance, sensitivity to the initial value in the iterative procedure, and the fairness between different users in section 4.4. Last of all, we summarize this chapter in section 4.5.
4.1 Motivation
Due to full BS cooperation, a MAC-like structure and an effective channel matrix as shown in (2.5) are formed in centralized UL CoMP. The state of the effective channel matrix is a crucial factor in transceiver design and can significantly affect the system performance; hence we attempt to properly design the precoders and the joint decoder to induce a well-behaved effective channel matrix. In this thesis, two UL CoMP transceiver schemes for creating a well-behaved effective channel are proposed.
In Chapter 3, an IA-aided UL CoMP transceiver is proposed from the viewpoint of interference alignment and interference mitigation. The algorithm tries to reduce the residual interference and to increase the received power of the desired signal for each layer at the output of decoder. Then a near diagonal effective channel matrix is accomplished since the algorithm will somehow enlarge the ratio of diagonal terms to off-diagonal terms. On the other hand, in this chapter, we endeavor to develop a UL CoMP transceiver scheme which tries to enhance the effective channel condition.
It is well known that the effective channel matrix in a good condition must have small condition number and large singular values. Therefore, we try to develop a transceiver design criterion that can minimize the condition number and can maximize the singular values simultaneously. The proposed channel condition enhanced
transceiver is described in section 4.2.
4.2 Proposed Channel Condition Enhanced Transceiver
The proposed channel condition enhanced transceiver provided in this section attempts to properly design the precoders and the joint decoder such that a
The proposed channel condition enhanced transceiver provided in this section attempts to properly design the precoders and the joint decoder such that a