Low Complexity Multiuser Detection Algorithm for Multi-Beam Satellite Systems

，

（College of Information and Communication Engineering，Harbin Engineering University，Harbin 150001，China）

Low Complexity Multiuser Detection Algorithm for Multi-Beam Satellite Systems

Yang Wang，Danfeng Zhao?and Xi Liao

（College of Information and Communication Engineering，Harbin Engineering University，Harbin 150001，China）

The minimum mean square error-successive interference cancellation（MMSE-SIC）multiuser detection algorithm has high complexity and long processing latency.A multiuser detection algorithm is proposed for multi-beam satellite systems in order to decrease the complexity and latency.The spot beams are grouped base on the distance between them in the proposed algorithm.Some groups are detected in parallel after a crucial group-wise interference cancellation.Furthermore，the multi-stage structure is introduced to improve the performance.Simulation results show that the proposed algorithm can achieve better performance with less complexity compared with the existing group detection algorithm.Moreover，the proposed algorithm using one stage can reduce the complexity over the fast MMSE-SIC and existing group detection algorithm by 9%and 20.9%.The processing latency is reduced significantly compared with the MMSE-SIC.

satellite communications；multi-beam satellites；multiuser detection；complexity

1 Introduction

The multi-beam satellite system is a promising scheme for next generation broadband satellite communications［1-2］.This multi-beam architecture allows for an enhancement of the spectral efficiency by reusing the available spectrum.The system can be regarded as a distributed MIMO system when full frequency reuse scheme is applied and the capacity can be improved further by multiuser detection techniques.

Refs.［3-6］investigated the channel capacity of multi-beam satellite systems with full frequency reuse and demonstrated the significant advantage over the conventional system with three or four color frequency reuse scheme.In Refs.［7-10］，they compared the throughputs when using the minimum mean square error（MMSE）and the minimum mean square errorsuccessive interference cancellation（MMSE-SIC）algorithm in multi-beam satellite systems.The MMSESIC algorithm can get a better performance. Furthermore，the BER performances of several multiuser detection algorithms in a multi-beam satellite system were evaluated in Ref.［11］and the best performance is achieved by the MMSE-SIC.However，the main drawbacks of the MMSE-SIC are its high complexity and long processing latency.A MMSE based group-wise SIC algorithm was proposed for the CDMA system in Ref.［12］to reduce the complexity and latency.Groups are detected successively and the latency is still long when the number of groups is large.

In this paper，a low-complexity MMSE group-wise IC（LC-MMSE-GIC）algorithm is proposed for the multi-beam satellite system.The multi-beam channel characteristic is exploited to reduce the computational complexity and processing latency in the proposed algorithm.The algorithm is distinct from the algorithm in Ref.［12］in two respects.Firstly，the grouping procedure is based on the distance between different beams in the proposed algorithm rather than grouping based on the received power level as in Ref.［12］. Secondly，contrary to the algorithm in Ref.［12］detecting groups successively，the proposed algorithm detects groups in parallel after a crucial group-wise interference cancellation，which results in lower complexity and latency.In addition，the algorithm in Ref.［12］is proposed for CDMA systems，which can not be applied to the TDMA multi-beam satellite system straightforwardly.

Notation：throughout the paper，denote the expectation and conjugate transpose of a matrix respectively.hkis thekth column of the matrixH．

2 System Model

We consider a multi-beam satellite system and focuson the return link of the system.More specifically，a cluster ofKspot beams is considered and all beams use the same frequency band.Fig.1 depicts a cluster of spot beams.User terminals with one antenna are uniformly distributed in the covered area.In TDMA multi-beam satellite systems we usually assume that a single user per beam is scheduled in each time slot［7-8］，which results in aK×Kdistributed MIMO system.The input-output relationship can be written as

wheresis the transmitted symbol vector andE｛ssH｝＝IK；nis a zero-mean complex Gaussian noise vector andis the received symbol vector；Hdenotes the channel matrix which is generated by a multiplicative model［3］.

Fig.1 Graphical description of satellite spot beams

In the multiplicative model［3］，the multi-beam satellite channel matrix is modeled as the product of a multi-beam antenna gain with a random fading matrix. The small scale fading and large scale shadowing are incorporated in the fading matrix.The resulting model reads as

whereBis the multi-beam antenna gain matrix；HRandXddenote the small scale fading and large scale shadowing matrices with elements that follow the Rician and log-normal distributions respectively.

The antenna gain of each user-beam pair inBdepends on the antenna beam pattern and user position. Therefore，the elementbijcan be represented as

whereθ3dBis the one-sided half-power beamwidth；θijis the angle between theith spot beam center and thejth user position as seen from the satellite；bmaxrepresents the maximum antenna gain；J1andJ3are the first kind Bessel functions of order one and three.

3 LC-MMSE-GIC Algorithm

The conventional MMSE-SIC multiuser detection algorithm is computationally intensive due to the matrix inversion［13］.In Ref.［14］，a fast MMSE-SIC algorithm is proposed.Although the complexity is significantly reduced by computing the MMSE filter matrix recursively，the processing latency is still long.

In multi-beam satellite systems，the inter-beam interference is low when the distance between two beams is large.This characteristic is exploited and a low-complexity，low-latency MMSE-GIC multiuser detection algorithm is proposed.

We divide all spot beams in a cluster into three groups based on the distance between them，which results in the following groups

where the elements are indices of spot beams which are indicated in Fig.1.Ni（i＝1，2，3）is defined as the number of spot beams in theith group.According to the grouping，the channel matrix and Eq.（1）can be written as

Subsequently，the symbols transmitted by users in group 1 and group 3 can be estimated in parallel based on the MMSE algorithm［7］，which gives

Demodulatingy1andy3，we get the estimated symbol vectors

At the beginning of the algorithm，can be obtained by demodulatingy2which is given by Eq.（4）.Q［G2］consists ofqi（i∈G2）．

Considering the effect of Δr1，Δr3and probable errors inthe performance may be limited.The multi-stage structure is introduced to improve the performance.In the second stage，are used to carry out the interference cancellation and signals ofgroup 2 are detected by Eq.（6）.

Then，the interference cancellation for signals of group1 and group 3 is operated in parallel.The detection in Eq.（3）is applied after the interference cancellation in Eq.（7）.The block diagram of the proposed algorithm with two stages is shown in Fig.2.

Fig.2 Block diagram of LC-MMSE-GIC with two stages

In order to getQ［G2］andQ2，the recursive method in Ref.［14］is used.Before the recursion，we apply elementary transformation to the channel matrix.This will allow us to obtainQ［G2］andQ2by only one recursion.The transformed channel matrix is represented as

Then，theQ2andQ［G2］can be given in Eqs.（10）and（11），whereconsists of the firstN2columns of

The proposed algorithm can be summarized in the following steps：

Step 1Calculate theQ2，Q11andQ33by the recursive method.Then，W［G2］，W11andW33can be obtained.Initializeto a zero vector.

Step 2Interference induced by group 1 and group 3 is mitigated using Eq.（5）.This step can be jumped in the first stage.

Step 3Detect the signal in group 2 by Eq.（4）in the first stage or Eq.（6）in the following stages.

Step 4Partition the symbol vectorrand remove the interference caused by users in group 2 using Eq.（7）.

Step 5After gettingandthe signals of users in group 1 and group 3 are detected in parallel using Eq.（3）.

Step 6Repeat Step 2 to Step 5 until the maximum iteration number is reached.

4 Complexity Evaluation

The complexity of the proposed algorithm is evaluated and compared with the fast MMSE-SIC in Ref.［14］and algorithm in Ref.［12］.According to the algorithm steps，we calculate the number of complex multiplications and additions in the proposed algorithm［15］.

In the first step，the MMSE filter matrices are calculated，which needs

multiplications and

additions.

Step 2 can be omitted and Step 4 can be simplified in the first stage.Therefore，Step 2 to Step 5 requiresmultiplicationsadditions in the first stage.

In the following stages，Step 2 to Step 5 are repeated.The number of multiplications and additions required at each stage is

Summing up the complexity，we get the total number of multiplications and additions which is listed in Table 1.MMSE-GIC denotes the algorithm inRef.［12］which is modified to fit the TDMA system andNsrepresents the number of stages.Assuming thatTpis the time of unit processing，and the latency of different algorithms is also given in Table 1.

Table 1 Complexity and latency of different algorithms

5 Simulation Results and Analysis

A multi-beam satellite system model is established according to the illustration in section 2.Seven spot beams in a cluster are considered and PSK modulations are employed.The complexity and BER performance of the proposed algorithm are evaluated and compared with the MMSE-SIC algorithms and the algorithm in Ref.［12］.

The numbers of operations and latency of different algorithms are listed in Table 2.The results indicate that the one-stage LC-MMSE-GIC has the lowest complexity and reduces the operation counts over the fast MMSE-SIC and MMSE-GIC by 9%and 20.9% respectively.The required operations in the two-stage LC-MMSE-GIC are also less than the MMSE-GIC，but increased by 10.5%compared to that in the fast MMSE-SIC.In addition，the latency of the grouping based algorithms is much less than the MMSE-SIC and the one-stage LC-MMSE-GIC has the lowest latency. Fig.3 depicts the complexity of different algorithms whenKincreases.The results show that the advantage of the LC-MMSE-GIC is more considerable whenKgets larger.

Table 2 Number of operations and latency

The performances of different algorithms are simulated，when the system employs BPSK and QPSK. The results are depicted in Figs.4 and 5.The performances of the conventional and fast MMSE-SIC algorithms are the same and are denoted by MMSE-SIC in the figures.The results in both figures show that the MMSE-SIC and MMSE-GIC algorithms achieve better performance than the one-stage LC-MMSE-GIC.The performance loss of one-stage LC-MMSE-GIC is about 0.2 dB and 0.4 dB at 10-4compared with the MMSEGIC and MMSE-SIC when BPSK is used.Besides，the two-stage LC-MMSE-GIC performs better than the MMSE-SIC and MMSE-GIC algorithms and the gain is about 0.2 dB and 0.4 dB at 10-4when BPSK is applied.

Fig.3 Computational complexity of different algorithms

Fig.4 BER performance of system with BPSK

Fig.5 BER performance of system with QPSK

6 Conclusions

In this work，a low-complexity，low-latency MMSE-GIC multiuser detection algorithm is proposed for multi-beam satellite systems.The complexity and latency of the algorithm are evaluated and compared with the fast MMSE-SIC and MMSE-GIC algorithms. The results are shown as follows：

1）Compared to the MMSE-GIC，the two-stage LC-MMSE-GIC can achieve better performance with a little less complexity.The performance gain is about 0.4 dB.

2）The one-stage LC-MMSE-GIC reduces the complexity over the fast MMSE-SIC by 9%while limiting the performance loss to 0.4 dB.The two-stage LC-MMSE-GIC can achieve a performance gain of 0.2 dB while the complexity is increased by 10.5% compared with the fast MMSE-SIC.

3）The LC-MMSE-GIC algorithm can decrease the processing latency significantly compared to the MMSESIC.

In addition，this algorithm can be extended to multi-beam satellite systems with a larger cluster.

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TN927.2

：

：1005-9113（2015）05-0105-05

10.11916／j.issn.1005-9113.2015.05.016

2014-04-29.

Sponsored by the China Postdoctoral Science Foundation（Grant No.2011M500640）.

?Corresponding author.E-mail：hongjianzyx＠126.com.