{'fraction_non_alphanumeric': 0.03505000162871755, 'fraction_numerical': 0.005993680575914525, 'mean_word_length': 4.640271908873783, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 5, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
A Covariance-Based Hybrid Channel Feedback in FDD Massive MIMO Systems

In this paper, a novel covariance-based channel feedback mechanism is investigated for frequency division duplexing (FDD) massive multi-input multi-output (MIMO) systems. The concept capitalizes on the notion of user statistical separability which was hinted in several prior works in the massive antenna regime but not fully exploited so far. We here propose a hybrid statistical-instantaneous feedback mechanism where the users are separated into two classes of feedback design based on their channel covariance. Under the hybrid framework, each user either operates on a statistical feedback mode or quantized instantaneous channel feedback mode depending on their so-called statistical isolability. The key challenge lies in the design of a covariance-aware classification algorithm which can handle the complex mutual interactions between all users. The classification is derived from rate bound principles. A suitable precoding method is also devised under the mixed statistical and instantaneous feedback model. Simulations are performed to validate our analytical results and illustrate the sum rate advantages of the proposed feedback scheme under a global feedback overhead constraint.

However, the large number of antennas brings up new challenges, one of which is the acquisition of accurate instantaneous channel state information (CSI), especially the downlink CSI. To counteract this effect, a majority of works considered the time-division duplex (TDD) mode where downlink instantaneous CSI is obtained by estimating uplink CSI via channel reciprocity [6], although the downlink CSI is not always accurate in practice due to calibration error in baseband-to-radio frequency chains [7]. While the bulk of available systems today is frequency division duplex (FDD) based, a successful deployment of massive MIMO in the FDD setting hinges on an ever bigger problem: The uplink feedback overhead for downlink channel acquisition increases linearly with the number of antennas, hence may quickly grow prohibitive. In practice, feedback channel estimates are quantized and subject to a uplink bit resource constraint [8]. This unfortunately leaves the system designer with a tough dilemma: Allow precise feedback at the unbearable cost of uplink bit resources or keep quantizing rough at the risk inducing undue downlink interference.
To solve this well recognized problem, a large array of strategies have been proposed in the last years to reduce MIMO feedback overhead, including recent efforts tackling massive MIMO specifically, such as advanced trellis-extended codebook design [9], compressive sensing based channel feedback reduction [10], [11], antenna grouping based feedback reduction technique [12], frequency-independent parameter extraction and downlink channel reconstruction [13], [14], angular domain energy distribution based channel estimation [15], [16] etc. Moreover, the channel limited feedback issue was also tackled by exploiting user cooperation via device-to-device communications [17], [18]. The authors in [18] adopted cooperative precoder feedback scheme among users to further improve system performance. Quite notably, some works took advantage of special low-rank channel covariance exhibited in the large array regime first characterized in [19], [20] to reduce feedback information [11], [19]- [23]. The key principle is that the lowrank covariance behavior that stems from finite scattering channel models can be used to project channel information into a lower dimensional space with little or no loss of information. In turn, a two-stage precoding structure was presented in [19] where the first-stage precoding is the key step to reduce the cost of downlink training and uplink feedback through user grouping.
Interestingly, this result prompted a series of subsequent studies on the problem of user grouping itself, such as agglomerative clustering method [24], density-based clustering [25], [26] etc.
Note that, while the above-mentioned works do capitalize on the low rank aspect of the covariance, they fail to exploit fully the mutual inter-covariance orthogonality aspect that inherently comes along with it, and not for the purpose of feedback reduction. To further build up intuition into this issue, consider the following two examples: First, the case of two closely spaced users whose channels undergo scattering over a limited radius around them (e.g. under the famed one ring model [19]). In this case, while the users' channels can be equivalently represented by their low-rank covariance's signal space projections, (reduced) instantaneous feedback is required by the BS to design an interference canceling precoder. In other words, the low rank property does not facilitate spatial separation in this case because the signal subspaces happen to mostly coincide among the two users. However in a second example, consider those same users to move apart from each other in such a way that their intervals of multpath angles becomes distinct, hence their signal subspaces cease to overlap. In this case, it is well known that an interference canceling precoder can be designed based on covariance signal subspace projection alone, making instantaneous feedback completely unnecessary [19], [21], [27]! In other words, inter-user signal subspace orthogonality can be leveraged for the purpose of feedback reduction. Interesting results were earlier reported about the impact of spatial statistics on feedback overhead [28]. Elsewhere, the allocation of feedback bits was even designed as a function of transmit covariance matrix information [29]. While that and other existing work exploits finely the per-user covariance properties, the inter-user orthogonality remained ignored. For example, this can be best seen from the fact: the existing work leads to an identical feedback bit allocation to all the users when the users have roughly the same covariance rank and eigenvalues. In contract, this work highlights the fact that even in such symmetric cases, much feedback overhead can be saved by not allocating feedback in symmetric ways across users. To the best of our knowledge, the pairwise degree of orthogonality among users has not yet been exploited for feedback bit allocation.
While the above phenomenon will make intuitive sense to most readers, a possible reason for this effect to not have been pointed or analyzed is the irregularity of the phenomenon: Random channel statistical behavior causes a variety of ranks to be observed in channel covariances as well as highly diverse "degrees" of orthogonality between pairs of users, making it very difficult in practice to assign a rate-optimal amount of instantaneous feedback to each user.
In this paper, we counteract this issue by proposing a new simplification strategy for the feedback assignment policy, while retaining the essential non-symmetric user-dependent design idea. Our basic concept lies in a binary version of the hybrid statistical-instantaneous feedback scheme alluded to above. Under this feedback concept, each user will be classified either as an instantaneous feedback user (labeled as class-I user) or a statistical feedback user (labeled as class-S user). Hybrid classes could be considered in principle but are in fact fairly challenging and left out for further studies. The classification is assumed to be carried out as a preamble on the basis of statistical information alone (covariance matrices). The challenge lies in the task of coming up with an optimal classification algorithm capable of processing the complex mutual interactions that users exhibit via their covariance matrices.
The solution of this problem is carried out in two steps. First, we articulate a precoder design capable of handling the mixed statistical-instantaneous type of feedback information, which can be seen as a relatively straightforward extension of both the statistical signal-to-leakage-and-noise ratio (SLNR) [31] and instantaneous SLNR precoders [30]. Second, we present a rate bound analysis predicting the rate performance under the above precoder and any classification solution.
Finally, while the optimal classifier is computationally complex, the rate bound is exploited to guide the derivation of a suboptimal greedy classifier with good performance-complexity tradeoff. Critically, the classifier is designed to operate under the same feedback resource constraint as a conventional feedback scheme, allowing to observe substantial spectral efficiency gains, on a fair feedback rate basis. For ease of exposition, our results are mainly presented in a single-cell setting (interference of intra-cell nature only). The accounting of the multi-cell case is discussed in Section VI.
Note that above ideas have been presented in our previous conference paper [32]. There are clear differences however. First, the full rate analysis is explicit here while only a sketch was given before. Secondly, the number of BS antennas was ideally assumed to be infinite in the analysis carried out in the conference paper, leading to the ignorance of inter-user interference when any two users lie in non-overlapping but adjacent subspaces. Here, we consider a more practical assumption on the number of antennas which accounts for finite-antenna regime interuser interference. Furthermore, the multi-cell scenario is touched upon in this paper.
The rest of the paper is organized as follows. In Section II, the system and channel models are described. In Section III, the SLNR-based precoder is proposed for both class-I and class-S users. The system sum rate bound is derived based on channel covariance in Section IV. A user classification method is elaborated under the criterion of system sum rate maximization in Section V. The user classification for multi-cell scenario is given in Section VI. The simulation results and conclusions are presented in Section VII and VIII, respectively.
Notations: Boldface lowercase (uppercase) letters denote column vectors (matrices). The superscripts (·) H represents conjugate transpose and E {·} denote expectation operation. The notation C m×n represents a set of m × n matrices with complex entries and is used to denote a definition. An n×n identity matrix is denoted as I n and A = diag(a 1 , . . . , a l , . . . , a M ) denoted a diagonal matrix whose l-th diagonal element is [A] l = a l . The notations ⌊x⌉, ⌊x⌋ and ⌈x⌉ imply rounding a decimal number to its nearest, nearest lower and nearest higher integers, respectively.
The notation z ∼ CN (0, Σ) means z is a complex Gaussian random vector with zero mean and covariance matrix Σ. In addition, we use X = {x 1 , . . . , x N } and |X | = N to denote a set and its cardinal number, respectively.

A. Channel Model
A single-cell massive MIMO system is first considered where the BS is equipped with M antennas and simultaneously serves K single-antenna users labeled as user set K = {1, . . . , K}.
For each user k ∈ K, a physical channel model which describes the multiple paths propagation is exploited and given classically as [10], [20] where P is the number of independent, identically distributed (i.i.d.) paths, γ kp represents the complex gain of the p-th ray, a (θ kp ) is the steering vector. For tractability, we consider a uniform linear array (ULA) and the steering vector is given as where θ kp is the random angle of arrival (AoA) corresponding to the p-th path, d is the antenna spacing at the BS and λ is wavelength. The AoA of the P paths are assumed to be uniformly distributed over θ k − θ ∆ /2, θ k + θ ∆ /2 where θ k ∈ − π 2 , π 2 is the mean AoA and θ ∆ is spread AoA (SAoA).
We assume that the BS holds the statistical information of users, such as channel covariance Compared to instantaneous CSI, accurate estimation of channel covariance is much easier to obtain by long-term statistics. Furthermore, downlink channel covariance estimation for FDD systems can be estimated from uplink channel covariance matrix through certain frequency calibration processing [35].

B. Feedback Model
Under the proposed hybrid statistical-instantaneous feedback scheme, the K users are classified into K S so-called statistical feedback users (labeled class-S users) and K I instantaneous feedback users (labeled class-I users). The user sets are denoted as K S = {1, . . . , K S } and K I = {1, . . . , K I }, respectively. Different from conventional channel feedback schemes where all the users need to feed back quantized instantaneous channel, only the class-I users feed their quantized channel back to the BS after pilot-based channel estimation. In contrast, the class-S users are assigned zero bit towards instantaneous feedback, as shown in Fig. 1. As a result, if the total feedback bit budget is B total , each class-I user can use B  Throughout the paper, we use subscript (·) I,i and (·) S,n to denote the notations for the i-th class-I and n-th class-S users, respectively. The quantized channel vector h B I,i for the i-th class-I user is selected based on its codebook C I,i {c 1 , . . . , c X } with X = 2 B and obtained as [9] h B I,i = arg max where h I,i ∈ C M ×1 represents the downlink instantaneous CSI. Thus, the BS holds the quantized channel matrix of all the class-I users as H B covariance matrix only Φ k , k ∈ K of all the users for downlink data transmission. Note that our analysis does not account for the cost related to collecting covariance information, which is left out for future studies.

C. Proposed Downlink Data Transmission
As we are interested in downlink design, a first challenge is how the BS can serve class-I and class-S users simultaneously while managing inter-user interference and despite the lack of instantaneous CSI related to class-S users. To go around this problem, we first characterize the received signals y I,i and y S,n at an arbitrary i-th class-I user and n-th class-S user as where p d is downlink transmit power to each user, h S,n ∈ C M ×1 represents the downlink channel vector of the n-th class-S user, The received signal y I,i and y S,n are further expressed as Expected signal Interference from the other class-I users Interference from class-S users Interference from the other class-S users Interference from class-I users Thus, the signal-to-interference-plus-noise ratio (SINR) r I,i for the i-th class-I user is given as Following a similar approach, the SINR of the n-th class-S user r S,n can be derived as 8 Based on the assumption of block fading channel model, the downlink ergodic achievable rate of the i-th class-I and the n-th class-S users are obtained as respectively. The system sum rate under feedback bit constraint B total is Clearly, the system sum rate is highly influenced by the user classification decisions and by the accuracy of class-I users' quantized channel. Hence, the challenge behind this approach is to find the optimal classifier capable of leveraging the complex mutual interactions among users's channel statistics. To solve this problem, we propose below a precoder design in the next section to handle the mixed statistical-instantaneous feedback information and then derive a sum rate bound to evaluate the performance of different user classification results.

III. SLNR-BASED DOWNLINK PRECODER DESIGN
Precoding methods with mixed utilization of statistical and instantaneous CSI have been studied in [33], where the interference between two user classes is canceled by removing the common channel existing in the overlapping subspaces. To minimize the loss, a SLNR-based downlink precoder is designed in this paper with the mixed statistical-instantaneous feedback information introduced in Section II. The motivation to use SLNR precoder is twofold. First, the leakage-based criterion leads to a decoupled optimization problem and gives an analytical closed-form solution which is critical to derive the rate bounds needed for the classification algorithm. Secondly, SLNR precoder takes the Gaussian noise into consideration and has been illustrated to achieve identical performance to minimum mean square error precoder [30], [36].
With the coexistence of class-I and class-S users, the SLNR expressions of the i-th class-I and the n-th class-S users are respectively. Since the BS only has the statistical information of class-S users, we will bound  and E Γ LB S,n , the closed-form precoding vectors are straightforwardly obtained as It can be seen that the proposed SLNR-based precoder is an extension of both the statistical SLNR and instantaneous SLNR precoders. When all the users are selected as class-I users, the proposed precoder becomes the classical instantaneous SLNR precoder [30], likewise for class-S users, the proposed precoder becomes the statistical SLNR precoder [31].

IV. SYSTEM SUM RATE BOUND ANALYSIS
Under the proposed feedback framework, the BS needs to classify the users in the first place.
After that, the class-I users are able to quantize their instantaneous CSI according to the assigned feedback bits and pre-defined codebooks. In other words, the BS has no any instantaneous CSI of class-I users when it performs user classification. Therefore, system performance prediction is necessary at the BS to evaluate different user classification solutions. In this section, we present a rate bound derived from covariance matrices alone to predict the rate performance under the proposed SLNR-based precoder and any classification solution. The objective behind the rate bound is less to characterize precisely the system throughput as it is to drive the design of a classification algorithm with satisfactory properties and performance.
In the following subsections, so-called beam domain channel and beam domain covariance are first introduced to rewrite the actual channel and covariance in form of discrete Fourier transform (DFT) matrix. Secondly, a prediction method for quantized instantaneous channel of class-I users is presented exploiting the beam domain representation and DFT matrices. Note that the quantized instantaneous channel prediction is one-off operation and is only used for rate bound derivation. Once the rate bound is obtained, the BS can directly use the closed-form rate bound to evaluate system performance under any user classification.

A. Beam Domain Channel and Covariance
Channel vectors can be equivalently presented in virtual angular domain by simply sampling at equi-spaced angular intervals at the BS side. Then, the multipath channel vector h k , k ∈ K, can be approximately rewritten as a beam domain channel and given as [34] h . . , M, and the t-th column of matrix V is given as Thus, the p-th path of the k-th user can be presented with virtual beams as where h BD kp t denotes the gain of the p-th path in the t-th virtual beam given as where β t kp = sin(θ kp ) − 2t M + 1. Then, the beam domain gain of the k-th user in the t-th beam is given as The beam domain channel covariance matrix is given as . For the simplicity of notations, we assume the complex gain of each path satisfies γ kp ∼ CN (0, 1). Thus, the t-th diagonal element of Φ BD k is given as It can be seen that the beam domain channel covariance is only related to the number of paths and antennas, and the AoAs of paths which can be obtained via long-term statistics.

B. Quantized Instantaneous Channel Prediction
To derive a rate bound, the BS needs to know the quantized instantaneous channel of class-I users which influences the downlink precoder design. However, the quantized instantaneous channel of class-I users cannot be fed back before user classification operation. One possible solution for the BS is to predict the quantized instantaneous channel and then to derive the rate bound. The prediction method is given as follows.
The users usually feed back the codewords which are most similar to their channel directions.
The codebook size decides the number of predefined spatial directions and impacts the accuracy of quantized channel. Although the instantaneous channel gain of class-I users is unavailable at the BS, the BS is assumed to know the beam domain channel covariance. Therefore, the BS can predict the channel direction (quantized channel) of class-I users based on beam gain variance under a given feedback bit budget and user classification.
Since the users lie in low-dimension subspaces due to limited scatterers, the codebook design for spatially correlated channel usually takes the subspaces into account [39]. Therefore, we first present approximate subspaces of users with virtual beams. Due to the limited angular spread of multipaths, the dominant nonzero elements in Φ BD I,i are limited and assumed to be distributed between indices x I,i,min and x I,i,max 1 . Then, the dominant subspace of the i-th class-I user can 1 The parameters xI,i,min and xI,i,max are influenced by the number of BS antennas M and SAoA of users [38]. It is difficult to determine the parameters in theoretical analysis, while they can be obtained from long-term statistics or off-line tables at the BS.
be presented as The predicted codewords are simply considered to be isotropically distributed in subspace S I,i .
Thus, the codewords c I,i,u ∈ C I,i , u = 1, . . . , X, is created as where η I,i (u) is given as Thus, the codebook is also presented in form of DFT vectors. Given feedback bits B (X = 2 B ) for each class-I user, the codebook and quantized channel of the i-th class-I user can be predicted based on its channel statistics. The codeword index and quantized channel are respectively given as The proof of Equation (29) and (30) is given in Appendix A.
Although the channel quantization given in (30) is not obtained from instantaneous CSI, the predicted channel can be accurate in direction based on statistical information. Note that the quantized channel prediction is one-off operation at the BS and is only used for rate bound derivation.

C. Lower Bound Analysis of System Sum Rate
After quantized channel of class-I users is predicted and known by the BS, the BS can forecast the system sum rate under the proposed SLNR-based precoder.
First, the downlink SLNR-based precoding vectors for the i-th class-I and the n-th class-S users can be approximately obtained as w S,n = V(:, l * S,n ), respectively, where the index m I,i is with the l-th diagonal element of matrix Σ S,n given as The proof of Equation (31) and (32) is given in Appendix B.
Next, with the predicted quantized channel of class-I users and the approximate SLNR-based precoding vectors, a lower bound of system sum rate can be obtained as where E r LB I,i and E r LB S,n denote the effective SINR and are respectively given as The proof of Equation (36) is given in Appendix C.
Note that the rate bound is computed based on channel statistics alone and can be directly used to predict system performance under any user classification. A greedy user classification algorithm using the bound is presented in the next section.

V. GREEDY USER CLASSIFICATION
The optimal classifier for the proposed feedback scheme to maximize the system sum rate is computationally complex. Therefore, the rate bound obtained in Section IV is exploited to obtain a suboptimal greedy classifier with good performance-complexity trade-off. The user classification problem can be formulated as where the system sum rate in the objective function (39a) is given in (52), the constraints (39b) and (39c) is to make sure all the K users are classified and each user only belongs to one user class, and the constraint (39d) indicates that class-I users share the total feedback bit budget B total evenly.
To find the solution for problem (39)

VI. USER CLASSIFICATION FOR MULTI-CELL SCENARIO
Different from the single-cell setting, the multi-cell scenario will give rise to inter-cell interference, especially for the users located in the edge of cells. Thus, any user classification algorithm should consider all the users in the multi-cell network to maximize the system sum rate. In this section, we introduce the system model, precoding design, a lower bound for the system sum rate and user classification for a multi-cell network. Note that the principles are easily derived from the single cell setting, hence only sketches of results are detailed below.
An L-cell massive MIMO network is considered serving K users simultaneously. We use K where ς l,j,k is large-scale fading and h l,j,k is fast fading given in Eq.
respectively. Exploiting the same idea given in Section III to maximize the lower bound of average SLNR with the quantized channel of class-I users and the channel covariance matrices of the remaining users, the precoding vectors for the users in the l-th cell are obtained as l,l,q + j =l k∈K j Φ l,j,k + 1 where H l,l,i . Each user in the network suffers intra-cell and inter-cell interference (from both class-I and class-S users). Take class-I user i as an example, its SINR is l,l,n to derive a lower bound of multi-cell sum rate. To achieve this goal, we first calculate the predicted quantized channel for class-I users following the similar approach of Equation (29) and (30), and denote the feedback codeword index as u [I] l,l,i for the class-I user i in the l-th cell. Then, by exploiting the predicted channels and beam domain covariance matrices, approximate precoding vectors of the users in the l-th cell are obtained with the similar procedure given in Equation (31) and (32), and presented as w l,l,k = V (:, m l,l,k ) , k ∈ K l . Due to the limited space, we omit the details to obtain m l,l,k and directly present the result for a class-I user as m l,l,k = x I,i,min + l,l,i . For a class-S user, we have where Σ l,l,k is a diagonal matrix and its x-th element is given as Replacing the sum rate expression as R net,LB sum and inputting the beam domain channel covariance Φ BD l,j,k of this network into Alg. 1, we can get the user classification result for multicell network.

VII. SIMULATION RESULTS
In this section, the analytical rate bound and the performance of the proposed hybrid statisticalinstantaneous channel feedback mechanism 2 are evaluated. For any user k, we set the number of multipaths P = 20, SAoA θ ∆ = 10 • , x k,min = 1 and x k,max = M for channel feedback prediction. For conventional feedback schemes, we assume all the K users evenly share the feedback budget and SLNR precoder is adopted [30]. Moreover, two types of codebook with and without channel covariance are considered for the simulations, i.e., DFT-based codebook and skewed codebook:

1) DFT-based codebook:
The DFT-based codebook does not take channel statistics into consideration. When the codebook size is X, the u-th codeword c u is defined as 2) Skewed codebook: For class-I user i , the codebook with size X is given as where f u ∈ C M ×1 is isotropically distributed on the unit-sphere. This codebook is more efficient for spatially correlated channel than DFT-based codebook [39].     proposed feedback scheme keeps growing with K increasing. When K = 20, the system sum rate under the proposed feedback scheme is more than 20 times larger than the conventional one with DFT-based codebook and 1.4 times larger with skewed codebook.    can always achieve much better system performance even when the feedback bit budget is very limited, i.e., 10 bits in total for 20 users. With the increasing of feedback bit budget, the performance of the proposed feedback scheme with skewed codebook keep rising, while the performance with DFT-based codebook slightly decreases. When feedback bit budget is extremely large, the performances of the conventional and the proposed scheme will be identical.

A. Evaluation for Single-cell Scenario
The system sum rate under different channel correlation is shown in Fig. 6. When SAoA becomes larger, users have stronger channel correlation with the others and suffer more interinterference. Then, the system performance decreases under identical feedback bit budget. However, the performance of the proposed feedback scheme outperforms the conventional scheme and achieves more stable system sum rate with the increasing SAoA.

B. Evaluation for Multi-cell Scenario
We consider L = 3 cells with the radius of 500 meters and each BS is equipped with M = 128 antennas. We assume that the users are randomly distributed in the adjacent three sectors of the cells and no user is closer to the BSs than r h = 100 meters. The topology of the system is shown in Fig. 7. The large-scale fading is modelled as ς l,j,k = z/(d l,j,k /r h ) ν , where z is a log-normal random variable with standard deviation σ shadow , the variable d l,j,k is the distance between user k in the j-th cell to the BS in the l-th cell and ν is the path loss exponent. For fair comparison, the inter-cell interference suppression is also considered in conventional SLNR precoding scheme  which is taken as a special case of (45) and (46) with K [S] l = ∅, l = 1, 2, 3. Fig. 8 illustrates that the system sum rate of the proposed feedback scheme outperforms the conventional scheme, especially when DFT-based codebook is used.

VIII. CONCLUSIONS
In this paper, a hybrid statistical-instantaneous channel feedback scheme was proposed for FDD massive MIMO systems, where only class-I users need to estimate downlink CSI and feed back the quantized instantaneous channel to the BS by sharing the feedback bit budget evenly.
Enabling downlink data transmission with hybrid statistical-instantaneous feedback information, we proposed a SLNR-based precoder. Then, we presented a rate bound analysis which is only based on channel covariance of users and can be exploited to predict the system performance under any user classification solution and feedback bit overhead constraint. To balance the computational complexity of user classification and system performance gain, a sub-optimal classifier was elaborated with the purpose of maximizing the analytical rate bound. Furthermore, we analyse the user classification for multi-cell case. Finally, simulations illustrated that the proposed channel feedback scheme significantly improves system sum rate over the conventional schemes under global feedback bit constraint, especially when the feedback bit budget is deficient.
Similarly, an approximate SLNR-based precoding vector for the n-th class-S user is where Σ S,n = The vector in matrix V corresponding to the largest Σ S,n l is selected as w S,n and the index of the largest diagonal element is labeled as l * S,n , such that l * S,n = arg max Since the BS only holds channel statistics, effective SINR are considered and given as Thus, the effective achievable sum rate is obtained as