Comparative study of various multiuser detection and base-station cooperation schemes for uplink multicell systems
© Ju et al.; licensee Springer. 2013
Received: 11 July 2012
Accepted: 5 February 2013
Published: 15 March 2013
In this contribution, we investigate and compare the spectral-efficiency of uplink multicell systems, when various BS cooperation strategies and detection schemes are employed. Associated with our studies, three base-station (BS) operational schemes are considered, which are the ideal BS cooperation, data exchange only and no BS cooperation, in conjunction with four multiuser detection (MUD) schemes, including the optimum MUD (OMUD), OMUD with parallel interference cancellation (OMUD-PIC), linear minimum mean-square error MUD (MMSE-MUD) and the MMSE-based successive interference cancellation (MMSE-SIC). Their spectral-efficiency is evaluated either by simulations for the multicell systems of limited size or based on the formulas derived by asymptotic analysis. In this article, the asymptotic spectral-efficiency (ASE) of multicell systems with various BS cooperation and MUD schemes is derived based on the asymptotic analysis of the channel autocorrelation matrix’s eigenvalue distribution or of the signal-to-interference-plus-noise ratio (SINR) attained by a concerned scheme. The impacts of system load, signal-to-noise ratio (SNR) and intercell interference strength on the spectral-efficiency are demonstrated. Our studies and performance results show that, when taking into account of the trade-off between complexity and performance, the MMSE-SIC supported by data exchange among BSs may constitute a promising multicell processing (MCP) scheme that is beneficial for implementation in practical systems.
KeywordsMulticell cooperation Multiuser detection Optimum multiuser detection Minimum mean-square error Interference Cancellation Spectral-efficiency Asymptotic spectral-efficiency
With the increasing scarcity of spectrum, universal frequency reuse has been recognized as one of the important techniques in the future generations of cellular communication systems. In this case, intercell interference may become a dominant factor, which limits the spectral-efficiency of cellular communication systems. In order to circumvent this problem, base-station (BS) cooperation has been introduced to suppress or even exploit intercell interference [1, 2]. Usually, BS cooperation is achieved via exchanging some information, including channel state information (CSI) or/and user data, among the BSs involved with the aid of backhaul systems.
The spectral-efficiency of cellular systems with/without BS cooperation has been widely investigated in literature, see  and the references therein, in order to quantify how efficient the spectrum resource is utilized and how much performance gain can be obtained by BS cooperation. Specifically, related to our studies in this contribution, in , the single-cell processing (SCP), which uses the detection based on the principles of minimum mean-square error and successive interference cancellation (MMSE-SIC), has been investigated in the context of the Wyner’s infinite linear model . The studies demonstrate that intercell interference has a dramatic effect on the achievable spectral-efficiency. Then, the studies in  have been extended to a more general model, which employs joint multicell processing (MCP) . In , the infinite number of cells are assumed to be divided into clusters, where each cluster has M cells and their M BSs are assumed to cooperate ideally. In , the ‘soft-handoff’ scenario has been considered, where every mobile user simultaneously communicates with two BSs and is jointly controlled by the two BSs. The spectral-efficiency of both uplink and downlink has been analyzed under the assumption of ideal BS cooperation.
In the above-mentioned references, either no BS cooperation or ideal BS cooperation is assumed across the BSs involved. As the implementation of ideal BS cooperation usually requires a backhaul system with extremely high complexity, recently, BS cooperation supported by limited backhaul resources has been studied. Assuming a constrained backhaul system, in [6, 7], the authors have investigated two BS cooperation schemes, namely, the distributed interference subtraction (DIS) and compressed interference forwarding (CIF), which only require to exchange the decoded user data or compressed user data among the involved BSs. However, in [6, 7], each cell is assumed to support only one user. In , the capacity region has been studied, which is under the assumption of optimum multiuser detection (OMUD). The authors in  have considered the MCP based on the group MMSE-SIC, when assuming that each BS has multiple antennas but supports only one user. Most recently, a joint detection scheme has been investigated in , which turns an interference-limited system into a noise-limited system. Accordingly, intercell interference is exploited by acquiring the knowledge about the modulation formats of interfering users.
Against the background, in this article, we investigate and compare the achievable spectral-efficiency of the uplink multicell systems, which are modeled by the Wyner’s infinite linear model , when various MUD and BS cooperation schemes are assumed. In contrast to the assumption of one user per cell that is usually used in the existing references, we assume that each BS employs multiple antennas and covers multiple users of each having a single transmit antenna, in order to study the impact of system load on the achievable spectral-efficiency of multicell systems. Associated with our studies, three levels of BS cooperation are considered, which are a) no BS cooperation, b) data exchange only and c) ideal BS cooperation, and four types of MUDs are addressed, which include a) optimum MUD (OMUD), b) OMUD with parallel intercell interference cancellation (OMUD-PIC), c) MMSE-MUD and d) MMSE with successive intracell/intercell interference cancellation (MMSE-SIC). We first make use of the equivalent channel model to derive the formulas for the spectral-efficiency of multicell systems with various MUD and BS cooperation schemes. The requirements for carrying out BS cooperation are explained and the trade-off among the computational complexity, achievable spectral-efficiency and consumption of resources is discussed. Then, the asymptotic spectral-efficiency (ASE) of the multicell systems with fixed load-factors is analyzed with the aid of random matrix theory [10–14], also when the various MUD and BS cooperation schemes are considered. Furthermore, the special cases with the load-factor tending to zero, which are coincidence with the concept of massive MIMO [15–17], are analyzed. Finally, the spectral-efficiency performance of the multicell systems associated with the considered MUD and BS cooperation schemes is investigated via both the simulation results and the numerical results evaluated from the derived asymptotic formulas. Our studies and performance results show that, in general, using the OMUD with ideal BS cooperation is capable of attaining some extra spectral-efficiency against the other schemes considered, but at the cost of bandwidth and complexity for CSI exchange among BSs. In the heavily loaded multicell systems, the scheme of MMSE-SIC with data exchange stands above the other schemes that do not use CSI exchange. By contrast, when a multicell system is lightly loaded, making the load-factor approximately zero, which corresponds to the scenario of massive MIMO, all the schemes except the OMUD with ideal BS cooperation achieve a similar spectral-efficiency, which equals the spectral-efficiency achieved by an isolate cell with OMUD.
The rest of this article is structured as follows. Section 2 presents the system model. The spectral-efficiency of different schemes is derived in Section 3. In Section 4, we analyze the ASE, while in Section 5, the special cases with the load-factor tending to zero are considered. Performance results and discussions are provided in Section 6. Finally, in Section 7, we summarize the contributions and findings of this article.
2 System model
where y i is an N-length complex-valued observation vector, x i = [xi 1, xi 2, …, x i K ] T contains the baseband symbols transmitted by the K users controlled by BS i, while Hi(i + j) (j = -1, 0, +1) is an (N × K) channel matrix, the elements of which obey the complex Gaussian distribution with zero mean and a common variance of 1 / N for j = 0, which corresponds to the intracell users, or α2 / N for j = -1, + 1, which corresponds to the users in the two adjacent cells. We assume that the CSI is only available to the receivers at the BSs, while the mobile users only make use of the channel distribution information (CDI) for signal transmission. In (1), n i is an N-length complex-valued noise vector, which obeys the complex Gaussian distribution with zero mean and a covariance matrix of σ2I with σ2 the noise variance.
Based on the above system model, let us now consider the spectral-efficiency of the uplink multicell SDMA systems, when various BS cooperation and multiuser detection schemes are assumed.
In this section, the spectral-efficiency of uplink multicell SDMA systems is investigated, when various multicell cooperation and detection strategies are considered. The spectral-efficiency is expressed in terms of bits per second per hertz per user(bits/s/Hz/User). Let us first consider the OMUD with ideal BS cooperation.
3.1 Optimum multiuser detection with ideal BS cooperation
where E[·] denotes the expectation with respect to the channel matrix, while M → ∞ indicates that an infinite number of BSs are invoked.
Since the OMUD with ideal BS cooperation is considered, explicitly, the spectral-efficiency evaluated from (6) is an upper bound for all the other BS cooperation schemes associated with various BS detection schemes. The ideal BS cooperation exploits the intercell interference positively rather than eliminates it. However, the complexity for implementation of ideal BS cooperation, especially, with OMUD is extreme. Furthermore, exchanging both the CSI and the observations of many invoked BSs requires a backhaul system having huge bandwidth and, possibly, spending a lot of energy. In the following sections, more practical BS cooperation and detection schemes are considered, which usually have significantly lower complexity than the OMUD with ideal BS cooperation. Furthermore, the bandwidth and energy required for information exchange among BSs by the backhaul system can also be significantly reduced.
3.2 Optimum multiuser detection with ideal data exchange
To reduce the bandwidth and energy required by the backhaul system for implementing ideal BS cooperation, BSs may refrain from sharing CSI, but only exchange their data received from mobile users. In this case, when the OMUD is employed, PIC can be carried out after a BS obtains the data detected by the other BSs. This scheme is referred to as the OMUD-PIC, which is implemented as follows.
It can be seen that, under the OMUD-PIC, one cell only needs to send its detected data to one of its two neighbors. Hence, in comparison with the ideal BS cooperation, as discussed in Section 3.1, the requirements imposing on the backhaul system can be significantly relaxed. However, the OMUD, such as, the maximum likelihood detector , is still very high-complexity, which usually becomes extreme when the number of users supported per cell is relatively high. Therefore, we below consider a range of suboptimum MUD schemes that are more practical.
3.3 MMSE-MUD without BS cooperation
In order to illustrate the performance enhancement by BS cooperation, we first give the spectral-efficiency of two related MUD benchmark schemes without employing BS cooperation. The first one is the MMSE-MUD, which is discussed in this section, and the other one is the MMSE-SIC, which is addressed in Section 3.4.
represents the covariance matrix of the interference (both intracell and intercell) plus noise, represents the covariance matrix of the overall intercell interference plus noise, while h11,1 is the first column of H11, as seen in (7).
where E[ ·] takes the expectation with respect to γ1.
3.4 MMSE-SIC without BS cooperation
It is well-known that the SIC assisted MUDs (SIC-MUDs) constitute a class of detectors, which are capable of achieving the sum capacity  and, in principle, approximate the ML-MUD . Among the SIC-MUDs, the MMSE-SIC is the one that has been widely studied. It can be shown that, when the system size is relatively large, the MMSE-SIC is capable of achieving the near optimum error performance, even when symbol-by-symbol detection is considered . In this section, we first illustrate how the MMSE-SIC achieves the sum capacity. Then, some discussion about the detection procedure is provided.
Since no BS cooperation is assumed, the MMSE-SIC of a BS detects the K user signals using K stages, detecting one at each stage. Specifically for Cell 1, in the first stage, the first user is detected in the same way as the MMSE-MUD considered in Section 3.3, yielding the SINR as shown in (11). Hence, the spectral-efficiency of user 1, which is expressed as C1, is given by (13).
where the interference cancellation is ideal, as the error probability of user 1 is zero, provided that its information rate does not exceed C1. In the following stages, the other users are detected in the same way as user 1; one user is detected at every stage and, then, its interference on those having not been detected is canceled. This process is repeated until all the K users are detected.
It can be readily observed that (21) has the same form as (8), which is the spectral-efficiency of the optimum detector analyzed in  when there exists interference. This explains that the MMSE-SIC without BS cooperation is capable of achieving the same capacity as the optimum MUD without BS cooperation. Note that, the reason behind this conclusion is that, according to (, 8.3.4), the MMSE processing is information-lossless. Hence, the spectral-efficiency achieved at each stage is precisely the maximum mutual information between the detected symbol and the received signal. Consequently, the total spectral-efficiency is just the channel capacity.
In order to achieve the spectral-efficiency given by (21), the BS of a cell requires to inform its K mobile users at which rates they should transmit. A user detected at an earlier stage must transmit at a lower rate than a user detected at a later stage, as the SINR of a later detected user is higher than that of an earlier detected one, owing to the interference cancellation. This detection process explicitly results in unfairness. In order to enhance the fairness, the detection order may be updated periodically. However, in this case, extra resource is required to inform the mobile users the change of ordering. Moreover, joint coding that considers different data rates is required by each user.
In order to make the communication fair for all the mobile users, alternatively, every mobile user may transmit at the same rate, such as at C given in (21). According to , channel reliability knowledge can be exploited by the receiver to improve the error performance. Specifically, at the BS receiver, the detection is carried out in the order from the more reliable ones to the less reliable ones. By doing this, the users detected at earlier stages benefit from the high channel reliability, making their channel capacities higher than their transmission rates. Hence, they can be reliably detected. By contrast, the later detected users can benefit from the interference cancellation operations. Owing to the interference cancellation, the SINR of later detected users improves, which in turn results in improved channel capacities. Hence, the detection reliabilities of the later detected users will also improve. This in fact explains why in , when multiuser diversity is exploited for detection, the MMSE-SIC is capable of achieving the near optimum error performance, especially in the cases when the system is relatively large.
3.5 MMSE-SIC with ideal data exchange
The MMSE-SIC without BS cooperation is capable of achieving the spectral-efficiency of the optimum MUD without BS cooperation. However, the intercell interference significantly degrades the achievable spectral-efficiency. With the aid of BS cooperation by exchanging the data detected by adjacent BSs at different detection stages, the spectral-efficiency of multicell systems employing the MMSE-SIC can be significantly increased. Below we consider this scenario.
When operated under the scheme of MMSE-SIC with ideal data exchange, multiple stages of detection in the principles of the MMSE-SIC are exploited, so that the data detected at a stage can be shared by the BSs, in order to cancel their interference on the following stages of detection. To be more specific, under the MMSE-SIC with ideal data exchange, at every stage of detection, each of the three BSs detects one user. Then, the detected symbol is sent via the backhaul-links to the other two BSs. Simultaneously, it also receives the two symbols detected by the other BSs. In the next stage of detection, the interference imposed by these three symbols is canceled. The above process is continued until all the users in each cell are detected.
Let us now analyze the asymptotic spectral-efficiency of the BS cooperation and detection schemes considered in this contribution.
4 Analysis of asymptotic spectral-efficiency
where is the asymptotic probability density function (PDF) of the eigenvalues of , here is an (N × K) random matrix characterizing an equivalent channel model considered. With the aid of (29), analytical results for different scenarios have been derived in , some of which will be introduced for the OMUD with ideal BS cooperation in Section 4.1.
where γ k denotes the SINR of the k th (1 ≤ k ≤ K) user and γ(x) is the corresponding asymptotic SINR with uniformly distributed in (0,1].
Let us now consider the ASE of the OMUD with ideal BS cooperation.
4.1 Optimum multiuser detection with ideal BS cooperation
where J is an (N × K) matrix with elements of ones. It can be known from (31) that, P is a doubly-regular matrixa. Based on this property, it can be shown  that the ASE of a circle Wyner model is equivalent to that of an isolate cell, in which the transmit power per user is increased to (1 + 2α2), owing to exploitation of the interference from its two adjacent cells. Therefore, the ASE of the OMUD with ideal BS cooperation can be readily obtained from that of the single-cell case with OMUD.
where u = 1 + 2α2.
As shown in , (32) is an increasing function of 1 / σ2. Thus, when replacing 1 / σ2 of the single-cell case by (1 + 2α2) / σ2 of the ideal cooperative multicell case, we are implied that the ASE of OMUD with ideal BS cooperation is higher than that of the OMUD for a corresponding isolate cell. The main reason behind is obvious, the OMUD with ideal BS cooperation is capable of exploiting intercell interference, and turning it into the useful signal, which provides diversity gain as well as power gain, and correspondingly increases the achievable spectral-efficiency. When considering the effect of the system load-factor β, is an increasing function of β. Then, we can deduce that (32) and (33) are decreasing functions of β, resulting in that the ASE of the OMUD for the single-cell setup and of the OMUD with ideal BS cooperation minishes, as the system load increases. More specifically, when β → ∞, we have . Explicitly, when applying it to (32) and (33), we can see that the ASE tends to zero, as β → ∞.
4.2 Optimum multiuser detection with ideal data exchange
From Sections 3.2 and 3.4, we can see that the spectral-efficiency of the OMUD with ideal data exchange, as shown in (10), shares the same form as that of the MMSE-SIC without BS cooperation shown in (21). The only difference between them is that a BS in the multicell systems employing the OMUD with ideal data exchange only conflicts interference from one adjacent cell, while a BS in the systems employing the MMSE-SIC without BS cooperation conflicts interference from its two adjacent cells. To obtain the ASE of (10) and (21), an intuitive approach is first to derive the asymptotic eigenvalue distribution of the matrices in the form of HH H Σ-1. Then, the formula (29) in Section 4.1 is employed to obtain the ASE. However, the difficulty of this approach is to derive the asymptotic eigenvalue distribution of HH H Σ-1. Fortunately, the ASE of the MMSE-SIC without BS cooperation can be analyzed by deriving its asymptotic SINR at each detection stage. Once the asymptotic SINR is obtained, the ASE can be evaluated with the aid of (30). Since (10) for the OMUD with ideal data exchange shares the same form of (21) for the MMSE-SIC without BS cooperation, the ASE of the OMUD with ideal data exchange can be directly obtained from the method adopted for deriving the ASE of the MMSE-SIC without BS cooperation, which will be detailed in Section 4.4.
It is worthy of noting that here the asymptotic SINR γ(x) in (34) as well as the ASE expression of (30) are introduced only for the purpose of ASE evaluation, owing to the above argument that the spectral-efficiency of the OMUD with ideal data exchange and that of the MMSE-SIC without BS cooperation share the same form. However, we should realize that, in the OMUD with ideal data exchange, all the intracell users have the same asymptotic SINR. By contrast, under the MMSE-SIC without BS cooperation, the intracell users detected at different stages have different asymptotic SINR values.
4.3 MMSE-MUD without BS cooperation
The ASE of the MMSE-MUD and MMSE-SIC in presence of intercell interference has been studied in  for the direct-sequence code-division multiple-access (DS-CDMA) systems over non-fading channels. It has been demonstrated that the elements of spreading sequences and the channel fading gains between transmit/receive antennas are equivalent for the purpose of asymptotic analysis . Hence, in this contribution, we adopt the approaches provided in  to derive the asymptotic SINR in both this section and Section 4.4.
which is a fixed-point equation with a unique positive solution (, Proposition 3.2) that can be readily found through iterations.
where γ is the solution to (37).
Notice from (35)–(38) that γ is independent of the uniform distributed variable x. This is because the SINR of all the users is the same, when the MMSE-MUD without BS cooperation is employed. Additionally, from (36), we can deduce that γ is a decreasing function of β, yielding that γ approaches zero as β → ∞. In other words, we can have the similar conclusion that the ASE of MMSE-MUD without BS cooperation reduces, and finally tends to zero, as the system load increases, as that stated in Section 4.1.
4.4 MMSE-SIC without BS cooperation
Note that, we have (39) because, at a given detection stage, the asymptotic SINR at different BSs is the same, owing to the symmetric characteristic of our multicell system model.
by the iteration approach. Note that, in the above equation, x is uniformly distributed in (0,1]. Finally, the ASE of the multicell systems employing the MMSE-SIC without BS cooperation can be evaluated from (30) upon substituting (40). From (39) we can find that, when x is given, γ(x) is a decreasing function with β. Hence, it tends to zero, as β → ∞. However, when comparing (39) with (36), we can learn that the decreasing rate of γ(x) in (39) is slower than that of γ(x) in (36) due to the fraction of (1 - x) seen in (39). From this we are implied that the corresponding ASE decreases slower than that of the MMSE-MUD, as the system load-factor β increases.
from which (34) can be obtained.
It is worthy of noting again that, when the OMUD-PIC with data exchange is employed, all the individual users in a cell achieve the same rate. By contrast, when the MMSE-SIC without BS cooperation is employed, different users in a cell may communicate with different rates.
4.5 MMSE-SIC with ideal data exchange
which is suitable for using iterative approach to obtain the unique positive solution γ(x), as mentioned in the previous sections.
Additionally, similar to the analysis in previous sections, for a given x, γ(x) is a decreasing function of β and tends to zero, as β → ∞. The difference here is the extra factor of (1 - x) with regard to intercell users, which is resulted from the intercell interference cancellation via data exchange among BSs. Consequently, the ASE decreasing rate of the MMSE-SIC with ideal data exchange is even lower than that of the MMSE-SIC without BS cooperation, as analyzed in Section 4.4.
So far, we have obtained the formulas for estimating the ASE of all the schemes considered in this contribution. We found that the ASE of all the schemes tends to zero, as β → ∞, but the decreasing rates may be different. In the next section, we try to gain some insights from the cases when β → 0, which corresponds to the situations of massive MIMO systems [15, 17].
5 Asymptotic spectral-efficiency when β → 0
which is the spectral-efficiency of a single-cell MIMO system, when β → 0.
In the context of the other schemes, namely, the MMSE-MUD and MMSE-SIC without BS cooperation, and the OMUD and MMSE-SIC with ideal data exchange, when β tends to zero, we can readily find from (36), (39), (41), and (42) that their asymptotic SINR is the same and is given by γ = 1 / σ2. Hence, when β tends to zero, their ASE can be expressed as (48).
From the above analysis, we are implied that, when a multicell system is lightly loaded, yielding β → 0, the schemes of MMSE-MUD and MMSE-SIC without BS cooperation, and the OMUD and MMSE-SIC with ideal data exchange achieve the same spectral-efficiency, which is equal to the single-cell bound. By contrast, as shown in (49), the spectral-efficiency attainable by the OMUD with ideal BS cooperation may be higher than the single-cell bound. Furthermore, higher intercell interference generates higher spectral-efficiency for the OMUD with ideal BS cooperation. Hence, in a lightly loaded multicell system, either no BS cooperation is necessary or ideal BS cooperation has to be implemented in order to achieve an improved spectral-efficiency. However, as discussed previously in Section 3.1, implementing ideal BS cooperation requires exchange of both CSI and observations among BSs, which demands extremely high complexity.
Therefore, at least for the near future cellular communications, massive MIMO [15, 17] might be one of reasonable candidates. In massive MIMO systems, the number of users supported per cell is supposed to be significantly lower than the number of antenna elements per BS, which may be on the order of hundreds. Hence, they are typical systems of lightly loaded. Therefore, in this type of massive MIMO systems, no BS cooperation is necessary, as ideal BS cooperation is seems impossible due to the extreme requirement of backhaul resources. Furthermore, as the analysis in [15, 17] shows, in massive MIMO systems, low-complexity single-user detection, such as matched-filter (MF) based detection, tends to optimum and no MUD is necessary. This also makes the system design easier.
In the following section, we provide a range of results to demonstrate and compare the capacity or spectral-efficiency achievable by the multicell systems, when the various MUD and/or BS cooperation schemes are considered.
6 Performance results
In this section, performance results, which were either obtained from simulation or evaluated from the formulas derived, will be provided, in order to compare the achievable spectral-efficiency of the multicell MIMO systems employing different MUD and BS cooperation schemes considered in Section 2. The spectral-efficiency is expressed in terms of bits/s/Hz/User, representing the number of bits per second per Hertz per user. As a benchmark, in these figures, the spectral-efficiency of a single isolate cell is also included. Specifically, in the not so large system, the impacts of the system load, which is explained by the number of users per cell, SNR and the intercell interference strength, which is reflected by the parameter α, are demonstrated. From the figures, we can obtain the implication about the consistency between the results obtained by simulation and asymptotic analysis. Furthermore, as a benchmark for comparison, the spectral-efficiency of the zero-forcing MUD without BS cooperation [20, 27], which is obtained by simulations, is also included in some figures. For the multicell systems, where every BS employs a large number of antennas or supports a large number of users, it is extremely hard to obtain results via simulation. In these case, we will only provide the results evaluated from the formulas derived by asymptotic analysis in Section 4. Additionally, the keys used in the figures are summarized for convenience as follows:
Ideal Cooperation: OMUD with ideal BS cooperation considered in Sections 3.1 and 4.1;
Single-Cell Bound: Spectral-efficiency of a single isolate cell;
OMUD-PIC-DE: OMUD-PIC supported by ideal data exchange considered in Sections 3.2 and 4.2;
MMSE-MUD: MMSE-MUD without BS cooperation considered in Sections 3.3 and 4.3;
MMSE-SIC: MMSE-SIC without BS cooperation considered Sections 3.4 and 4.4;
MMSE-SIC-DE: MMSE-SIC with ideal data exchange considered in Sections 3.5 and 4.5.
When comparing the two detection schemes with ideal data exchange, the spectral-efficiency of the OMUD-PIC-DE scheme is slightly higher than that of the MMSE-SIC-DE scheme, when the system load is low. However, as the system load increases, their spectral-efficiency has a cross and, after it, the MMSE-SIC-DE scheme is capable of achieving higher spectral-efficiency than the OMUD-PIC-DE scheme. The reason behind the above observation is that, when the number of user per cell is relatively low, intracell interference dominates the detection performance. As the OMUD provides more reliable detection than the MMSE-MUD, the OMUD-PIC-DE scheme yields higher spectral-efficiency than the MMSE-SIC-DE scheme. However, when the number of users per cell increases, intercell interference becomes domination of the achievable spectral-efficiency. According to our analysis in Section 3.2, the OMUD-PIC-DE scheme can only suppress the interference from one of the two adjacent cells. By contrast, as shown in Section 3.5, the MMSE-SIC-DE scheme is capable of suppressing the interference from both adjacent cells. Consequently, the MMSE-SIC-DE scheme outperforms the OMUD-PIC-DE scheme.
Finally, when comparing the MMSE-MUD, MMSE-SIC, and the ZF-MUD, all of which do not carry out BS cooperation, the spectral-efficiency achieved by the MMSE-SIC is always higher than that attainable by the MMSE-MUD or ZF-MUD, provided that the number of users per cell is more than one. Among the three, the ZF-MUD scheme is always the worst, whose achievable spectral-efficiency is zero when the system is overloaded. This implies that the ZF-MUD scheme is incapable of providing the reliable communication in an overloaded system.
As in Figures 3, 4, and 5, the results in Figures 6 and 7 illustrate that the asymptotic results in general agree well with the results obtained via simulation. This observation becomes more declared, when N = K = 8 (Figure 7) is considered. As shown in Figure 6 corresponding to N = K = 4, for both the MMSE-MUD and the MMSE-SIC-DE schemes, the asymptotic spectral-efficiency has certain difference from that obtained by simulation. However, when N = K = 8, as shown in Figure 7, this difference becomes smaller.
Second, from the results of Figure 8, we can find that, as β increases, the asymptotic spectral-efficiency of all the schemes considered decreases, but at different rates, as described in Section 4. Specially, the ASE of the OMUD with ideal BS cooperation gradually converges to the single-cell bound. Therefore, when a multicell system is heavily loaded, i.e., when the value of β is high, the maximum spectral-efficiency achievable is equivalent to that achieved by a system, whose cells are operated separately without intercell interference. Among the other schemes, as seen in Figure 8, as the value of β increases, the MMSE-SIC-DE stands out from the others and achieves the highest spectral-efficiency, which is even better than that of the OMUD-PIC-DE. Considering the fact that the MMSE-SIC has much lower complexity than the OMUD-PIC , the MMSE-SIC with data exchange assisted BS cooperation may constitute a promising MCP scheme that is suitable for implementation in practical multicell systems.
In this contribution, we have investigated the spectral-efficiency of uplink multicell MIMO systems by both simulation and asymptotic analysis, when different BS operational schemes and MUD schemes are invoked. The impacts of system load, SNR and intercell interference strength on the achievable spectral-efficiency have been studied and demonstrated. Our studies and performance results demonstrate that the asymptotic results usually agree well with the simulated results, provided that the number of users per cell or/and the number of receive antennas per BS are not too low. Generally, in multicell MIMO systems, employing BS cooperation supported by data or/and CSI exchange among different BSs is beneficial to improving their spectral-efficiency. Owing to its capability to exploit intercell interference, the scheme of OMUD with ideal BS cooperation outperforms all the other schemes, with regard to their achievable spectral-efficiency. However, implementing the OMUD with ideal BS cooperation demands extremely high complexity and backhaul resources, which are hard to provide in practice. The scheme of MMSE-SIC with data exchange only is capable of achieving significantly higher spectral-efficiency than the schemes without BS cooperation. As the MMSE-SIC is a low-complexity MUD and the BS cooperation only requires data exchange, the MMSE-SIC supported by data exchange among BSs may constitute a promising MCP scheme that is suitable for implementation in practical multicell systems.
Furthermore, our studies demonstrate that, in a lightly loaded multicell system, BS cooperation does not yield much improvement of spectral-efficiency. By contrast, in a heavily loaded multicell system, the maximum spectral-efficiency achieved by using OMUD with ideal BS cooperation converges to the spectral-efficiency achieved by a multicell system, where the invoked cells are operated separately without intercell interference. Additionally, in a heavily loaded multicell system, the MMSE-SIC with data exchange achieves a higher spectral-efficiency than the OMUD-PIC supported by data exchange.
aAn N × K matrix is asymptotic doubly-regular, if and are independent of i and j for all , when the ratio β = K / N converges to a constant.
This study was supported in part by the National Basic Research Program of China (973 Program, Grant No. 2010CB731803) and the National Natural Science Foundation of China (Grant Nos. 60921001 and 61071072). The financial support of the China Scholarship Council (CSC) is also greatly acknowledged.
- Wyner A: Shannon-theoretic approach to a Gaussian cellular multiple-access channel. IEEE Trans. Inf. Theory 1994, 40(6):1713-1727. 10.1109/18.340450MATHMathSciNetView ArticleGoogle Scholar
- Gesbert D, Hanly S, Huang H, Shitz SS, Simeone O, Yu W: Multi-cell MIMO cooperative networks: a new look at interference. IEEE J. Sel. Areas Commun 2010, 28(9):1380-1408.View ArticleGoogle Scholar
- Zaidel B, Shamai S, Verdú S: Multicell uplink spectral efficiency of coded DS-CDMA with random signatures. IEEE J. Sel. Areas Commun 2001, 19(8):1556-1569. 10.1109/49.942517View ArticleGoogle Scholar
- Somekh O, Zaidel B, Shamai S: Spectral efficiency of joint multiple cell-site processors for randomly spread DS-CDMA systems. IEEE Trans. Inf. Theory 2007, 53(7):2625-2637.MathSciNetView ArticleGoogle Scholar
- Somekh O, Zaidel B, Shamai S: Sum rate characterization of joint multiple cell-site processing. IEEE Trans. Inf. Theory 2007, 53(12):4473-4497.MATHMathSciNetView ArticleGoogle Scholar
- Grieger M, Marsch P, Fettweis G, Cioffi J: On the performance of compressed interference forwarding for uplink base station cooperation. In IEEE Global Telecommunications Conference, GLOBECOM. Honolulu, Hawaii, USA; 2009:1-6.Google Scholar
- Marsch P, Fettweis G: Uplink CoMP under a constrained backhaul and imperfect channel knowledge. IEEE Trans. Wirel. Commun 2011, 10(6):1730-1742.View ArticleGoogle Scholar
- Dai H, Poor H: Asymptotic spectral efficiency of multicell MIMO systems with frequency-flat fading. IEEE Trans. Signal Process 2003, 51(11):2976-2988. 10.1109/TSP.2003.818201View ArticleGoogle Scholar
- Lee J, Toumpakaris D, Yu W: Interference mitigation via joint detection. IEEE J. Sel. Areas Commun 2011, 29(6):1172-1184.View ArticleGoogle Scholar
- Tulino A, Verdú S, Lozano A: Capacity of antenna arrays with space, polarization and pattern diversity. In Proceedings. 2003 IEEE Information Theory Workshop (ITW’03). Paris, France; 2003:324-327.View ArticleGoogle Scholar
- Tulino A, Verdú S: Random Matrix Theory and Wireless Communications. Amsterdam, The Netherlands: Now Publisher; 2004.MATHGoogle Scholar
- Hachem W, Loubaton P, Najim J: Determinstic equivalents for certain functionals of large random matrices. Annals Appl. Probab 2007, 17(3):875-930. 10.1214/105051606000000925MATHMathSciNetView ArticleGoogle Scholar
- Speicher R: Combinatorial Theory of The Free Product With Amalgamation And Operator-valued Free Probability Theory. Providence, Rhode Island: American Mathematical Society; 1998.Google Scholar
- Nica RSA: Lectures on the combinatorics of free probability. Cambridge: Cambridge University Press; 2006.MATHView ArticleGoogle Scholar
- Marzetta T: Noncooperative cellular wireless with unlimited numbers of base station antennas. IEEE Trans. Wirel. Commun 2010, 9(11):3590-3600.View ArticleGoogle Scholar
- Hoydis J, ten Brink S, Debbah M: Massive MIMO: how many antennas do we need? In IEEE, The 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton). Monticello, Illinois, USA; 2011:545-550.View ArticleGoogle Scholar
- Rusek F, Persson D, Buon Kiong L, Larsson E, Marzetta T, Edfors O, Tufvesson F: Scaling up MIMO: opportunities and challenges with very large arrays. IEEE Signal Process. Mag 2013, 30(1):40-60.View ArticleGoogle Scholar
- Blum R: MIMO capacity with interference. IEEE J. Sel. Areas Commun 2003, 21(5):793-801. 10.1109/JSAC.2003.810345View ArticleGoogle Scholar
- Telatar E: Capacity of multi-antenna gaussian channels. Europ. Trans. Telecommun 1999, 10(6):585-595. 10.1002/ett.4460100604View ArticleGoogle Scholar
- Verdú S: Multiuser Detection. Cambridge: Cambridge University Press; 1998.MATHGoogle Scholar
- Yang L-L: Multicarrier Communications. Chichester: John Wiley; 2009.Google Scholar
- Shamai S, Verdú S: The impact of frequency-flat fading on the spectral efficiency of CDMA. IEEE Trans. Inf. Theory 2001, 47(4):1302-1327. 10.1109/18.923717MATHView ArticleGoogle Scholar
- Yang L-L: Receiver multiuser diversity aided multi-stage minimum mean-square error detection for heavily loaded DS-CDMA and SDMA systems. IEEE Trans. Commun 2010, 58(12):3397-3404.View ArticleGoogle Scholar
- Tse D, Viswanath P: Fundermentals of Wireless Communication. Cambridge: Cambridge University Press; 2005.View ArticleGoogle Scholar
- Tse D, Hanly S: Linear multiuser receivers: effective interference, effective bandwidth and user capacity. IEEE Trans. Inf. Theory 1999, 45(2):641-657. 10.1109/18.749008MATHMathSciNetView ArticleGoogle Scholar
- Adams R, Essex C: Calculus: a Complete Course. Canada: Prentice Hall; 2010.Google Scholar
- Elayoubi S-E, Chahed T, Hebuterne G: On the capacity of multi-cell UMTS. In IEEE Global Telecommunications Conference, GLOBECOM. San Francisco, USA; 2003:487-491.Google Scholar
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.