Methods for multi-user MIMO wireless communication using approximation of zero-forcing beamforming matrix

This application claims the benefit of U.S. Provisional Application No. 62/056,489, filed on Sep. 27, 2014.

The field of invention is wireless communication, and more specifically relates to methods for signal detection and transmission in Multi-User (MU) Multiple-Input Multiple-Output (MIMO) wireless communication systems, and in particular to methods of inverse matrix approximation error calculation, of selecting the number of multiplexed User Equipment (UEs) in a MU-MIMO group, and of choosing the proper Modulation and Coding Scheme (MCS).

In a massive MIMO system [1], each Base Station (BS) is equipped with dozens to hundreds or thousands of antennas to serve tens or more UEs in the same time-frequency resource. Therefore, they can achieve significantly higher spatial multiplexing gains than conventional MU-MIMO systems, which is one of the most important advantages of massive MIMO systems, i.e., the potential capability to offer linear capacity growth without increasing power or bandwidth [1]-[3].

It has been shown that, in massive MIMO systems where the number of antennas M, e.g., M=128, is much larger than the number of antennas on served UEs K, e.g., K=16 [2],[3], Zero-Forcing (ZF) based precoding and detection methods, e.g., ZF, Regularized ZF (RZF), Linear Minimum Mean Square Error (LMMSE), can achieve performance very close to the channel capacity for the downlink and uplink respectively [2]. As a result, ZF has been considered as a promising practical precoding and detection method for massive MIMO systems [2]-[4]. Without loss of generality, hereafter it is assumed that each UE has only one antenna, thus the number of antennas on served UEs K equal to the number of served UEs.

In hardware implementation of ZF based detection or precoding methods, despite of the very large number of M, the main complexity is the inverse of a K×K matrix [2], [5], [6]. Unfortunately, for massive MIMO systems, although K is much smaller than M, it is still much larger than conventional MU-MIMO systems. As a result, in this case, the computation of the exact inversion of the K×K matrix could result in very high complexity [6], which may cause large processing delay so that the demand of the channel coherence time is not met. Hence, Neumann Series (NS) has been considered to compute an Approximate Inverse Matrix (AIM) in hardware implementation of massive MIMO systems [2], [5], [6].

For a specific resource element in a MU communication systems, e.g., a subcarrier in the frequency domain, the received baseband signal vector at the BS side is formulated as y=Hs+n+I int in the uplink transmission, where H is the wireless channel matrix between these K UEs and the BS, s is the transmitted signal vector, n is the hardware thermal noise and I int is the interference. With ZF based detection methods, the transmitted signals by the K UEs are estimated as ŝ=(Ĥ H Ĥ+αI K ) −1 Ĥ H y, where Ĥ is the measured channel matrix between these K UEs and the BS, I K is the identity matrix with order K, and α is a scaling factor satisfying α≥0. Let G=Ĥ H Ĥ+αI=D+E, where D is a diagonal matrix including the diagonal elements of G and E is a hollow matrix including the off-diagonal elements of G, then the NS of G −1 can be written as G −1 =Σ n=0 ∞ (I K −D −1 G) n D −1 . For the hardware implementation, the inverse matrix G −1 can be approximated as G −1 ≈Σ n=0 N-1 (I K −D −1 G) n D −1 , where N is the truncation order of NS. Similarly, to obtain the precoding matrix in the downlink also involves computing the inverse matrix. As a result, extra approximation errors are introduced into the estimated signals in the uplink or the transmitted signals in the downlink and they degrade the system performance. For hardware design, there is a trade-off between the truncation order N and the tolerable error, hence N needs to be large enough to ensure the system performance, e.g., the required spectrum efficiency, while the required computation resource is kept as low as possible to reduce the computation time and/or the hardware cost. Due to these reasons, the invention provided in this patent can be used to estimate the approximation error of NS and select the system parameters adaptively, e.g., the truncation order N, the MCS, and the number of multiplexed UEs K. As a result, the system robustness can be ensured with lower hardware cost.

This invention offers methods of estimating the inverse matrix approximation error and the flowchart of selecting related system parameters that can be implemented in massive MIMO systems to improve system performance.

It is an object of this invention to provide a method to calculate the Signal-to-Interference Ratio (SIR) caused by the approximation error of applying AIM in hardware implementation.

It is an object of this invention to provide methods to select the NS truncation order N and the number of multiplexed UEs K adaptively according to the SIR caused by AIM.

It is an object of this invention to provide methods to modify the Channel Quality Indicator (CQI) of each UE by incorporating the approximation error of AIM and select the proper MCS for each UE.

For ZF based detection in the uplink or precoding in the downlink, the SIR caused by the approximation error of AIM is calculated for the Resource Blocks (RBs) to be detected or precoded according to the number of antennas at the BS and the number of multiplexed UEs. With this SIR, the BS can select the proper value of truncation order of NS and the number of multiplexed UEs. Moreover, the BS can modify the CQI of each UE and select the proper MCS for each UE.

The aforementioned implementation of the invention as well as additional implementations would be more clearly understood as a result of the following detailed description of the various aspects of the invention when taken in conjunction with the drawings. Like reference numerals refer to corresponding parts throughout the several views of the drawings.

FIG. 1 illustrates a typical massive MU-MIMO communication system.

FIG. 2 illustrates the process of selecting MCS for each UE by incorporating the approximation error of AIM in the uplink.

FIG. 3 shows the flowchart for determining the number of served UEs K for a given M.

FIG. 1 presents a typical massive MU-MIMO communication system, where the BS 1 is equipped with a large number of antennas 2 to serve several UEs 3 in the same time-frequency resource. For such systems, NS can be employed to approximate the inverse matrix for ZF based detection methods in the uplink and precoding methods in the downlink. The SIR caused by approximation error of AIM with various numbers of transceiving antennas, multiplexed UEs, and truncation orders can be calculated by formulas (1)-(4) given below. Moreover, these values can be calculated off-line and stored in the memory of the BS in advance, e.g., in the form of a lookup table. For example, let M, K, and N denote the three aforementioned numbers respectively, where N≤4, then the SIR is calculated by the following formulas

⁢ S ⁢ ⁢ I ⁢ ⁢ R 1 ⁡ ( M , K ) = β 1 ( K - 1 ) ⁢ B 2 , M , N = 1 , ( 1 ) ⁢ S ⁢ ⁢ I ⁢ ⁢ R 2 ⁡ ( M , K ) = β 2 ( K - 1 ) ⁢ B 3 , M + 2 ⁢ ( K - 2 ) ⁢ ( K - 1 ) ⁢ B 2 , M 2 , ⁢ N = 2 , ( 2 ) S ⁢ ⁢ I ⁢ ⁢ R 3 ⁡ ( M , K ) = β 3 ( K - 2 ) ⁢ ( K - 1 ) ⁢ ( 5 ⁢ K - 8 ) ⁢ B 2 , M 3 + ( 2 ⁢ K - 3 ) ⁢ ( K - 1 ) ⁢ B 3 , M ⁢ B 2 , M ,

⁢ ⁢ N = 3 , ( 3 ) S ⁢ ⁢ I ⁢ ⁢ R 4 ⁡ ( M , K ) = β 4 ( 2 ⁢ K - 3 ) ⁢ ( K - 1 ) ⁢ B 3 , M 2 + ( 2 ⁢ K - 3 ) 2 ⁢ ( K - 1 ) 2 ⁢ B 4 , M ⁢ B 2 , M + ( K - 2 ) ⁢ ( K - 1 ) 2 ⁢ KB 2 , M 4 ,

⁢ ⁢ N = 4 , ( 4 )

where β 1 , β 2 , β 3 and β 4 are scaling factors which are determined by the parameters α, M, K and N, e.g., when α=0, then β 1 =β 2 =β 2 =β 4 =1.

For uplink data transmission, supposing that the number of receiving antennas is M and the number of UEs multiplexed on a specific RB is K, three methods to combat the approximation error of AIM are presented below.

Method-1

A minimal truncation order N min , N min ≤4, of NS is configured in the BS. When the BS detects the signals belonging to the K UEs on a specific RB, it first finds the maximal MCS of these K UEs, which is denoted by MCS max . Then, it compares the minimal required SINR for MCS max denoted by SINR MCS max and SIR N min (M,K). If SINR MCS max ≤SIR N min (M,K), the BS would adopt N min for NS on the current RB. Otherwise, the BS would find the minimal N, N≤4, so that SINR MCS max ≤SIR N (M,K). If the number of N that satisfies the condition cannot be found, the BS would choose N=8.

Method-2

When the BS selects the MCS for each UE multiplexed on a RB according to their CQIs, it modifies the CQI of each UE first by incorporating the approximation error of AIM. Then, it selects the MCS for each UE according to the modified CQI. For example, let CQI k denote the linear CQI value of the k th , k=1, . . . , K, UE before being modified, then the BS modifies it to CQI k New according to the following formula

C ⁢ ⁢ Q ⁢ ⁢ I k New = C ⁢ ⁢ Q ⁢ ⁢ I k × S ⁢ ⁢ I ⁢ ⁢ R N ⁡ ( M , K ) C ⁢ ⁢ Q ⁢ ⁢ I k + S ⁢ ⁢ I ⁢ ⁢ R N ⁡ ( M , K ) , k = 1 , … ⁢ , K , ( 5 )

where M and K denote the number of receiving antennas at the BS and the number of UEs multiplexed on a RB respectively. Finally, the BS selects the MCS for the k th UE according to CQI k New . This process is illustrated in FIG. 2 , which begins 4 when the BS schedules K UEs on a RB 5 . Then, when the BS selects the MCS for each UE multiplexed on this RB according to their estimated CQI, it modifies the CQI of each UE first by incorporating the approximation error of AIM 6 . After that, it selects the MCS according to the modified CQI 7 before the process ends 8 .

Method-3

A fixed value of truncation order N is configured for NS in the BS. For each allowable MCS in the uplink transmission, the maximal number of UEs multiplexed on a RB is calculated off-line and stored in the memory of the BS. For example, assuming L UL MCS levels in the uplink transmission of a wireless communication system, for the l th MCS, the minimal required SINR for the system specified Block Error Rate (BLER) is SINR l min , then the maximum number of multiplexed UE can be computed as

K l =arg max k (SIR N ( M,k )≥SINR l min ), l= 1, . . . ,L UL .  (6)

Hence, the l th , l=1, . . . , L UL , MCS level and its corresponding K l are stored in the memory of the BS. For each RB, the BS could determine the highest MCS level and the corresponding maximal number of multiplexed UE multiplexed according to their relation determined by (6).

For the downlink data transmission, supposing that the number of transmitting antenna is M and the number of UE multiplexed on the current RB is K, three methods to combat the approximation error are presented below.

Method-1

A minimal truncation order N min , N min ≤4, of NS is configured in the BS. When the BS computes the precoding matrix of these K UEs on a specific RB, it first finds the maximal MCS of these K UEs, which is denoted by MCS max . Then, it compares the minimal required SINR for MCS max denoted by SINR MCS max and SIR N min (M,K). If SINR MCS max ≤SIR N min (M,K), the BS would adopt N min for NS on the current RB. Otherwise, the BS would find the minimal N, N≤4, so that SINR MCS max ≤SIR N (M,K). If the number of N that satisfies the condition cannot be found, the BS would choose N=8.

Method-2

For example, let CQI k denote the linear CQI value of the k th UE before modified, then the BS modifies it to CQI k New according to the following formula

C ⁢ ⁢ Q ⁢ ⁢ I k New = C ⁢ ⁢ Q ⁢ ⁢ I k × S ⁢ ⁢ I ⁢ ⁢ R N ⁡ ( M , K ) C ⁢ ⁢ Q ⁢ ⁢ I k + S ⁢ ⁢ I ⁢ ⁢ R N ⁡ ( M , K ) , k = 1 , … ⁢ , K ( 7 )

where M and K denote the number of transmitting antennas at the BS and the number of UEs multiplexed on a RB respectively. Finally, the BS selects the MCS for the k th UE according to CQI k New .

Method-3

A fixed value of truncation order N is configured for NS in the BS. For each allowable MCS in the downlink transmission, the maximal number of UEs multiplexed on a RB is calculated off-line and stored in the memory of the BS. For example, assuming a total of L DL MCS levels in the downlink transmission of a wireless communication system, for the l th MCS, the minimal required SINR for the system specified BLER is SINR l min , then the maximum number of multiplexed UEs can be computed as

K l =arg max k (SIR N ( M,k )≥SINR l min ), l= 1, . . . ,L DL .  (8)

Hence, the l th , l=1, . . . , L DL MCS level and its corresponding K l are stored in a table. For each RB, the BS could determine the highest MCS level and the corresponding maximal number of multiplexed UE according to the relation determined by (8).

Another embodiment provides a method to estimate the probability of convergence of NS in calculating the AIM. Given the number of BS antennas M, this estimate can be used to determine the maximum number of served UEs K for the NS-based AIM to be a valid method in massive MIMO systems. One of such estimates is given as

M K > 5.83

which indicates that the NS-based AIM has very high convergence probability.

A tighter condition for G=Ĥ H Ĥ to be a Diagonally Dominant Matrix (DDM) in very high probability, resulting in a good NS-based AIM with a small number of N, is given as

M K > M ⁡ [ E ⁡ ( x ) + δ ⁡ ( x ) ] E ⁡ ( x ) + δ ⁡ ( x ) + 1 ( 9 )

where E(x)=(M−1)B(1.5, M−1) and δ(x)=√{square root over (E(x 2 )−E(x) 2 )} with E(x 2 )=(M−1)B(2, M−1). The function B(a,b) with a and b being complex-valued numbers is the beta function defined as

B ( a,b )=∫ 0 1 t a-1 (1 −t ) b-1 dt, {a}, {b}> 0.

This condition can be used to determine the maximum number of served UEs K given the number of BS antennas M for the NS-based AIM to achieve good performance and quick convergence, i.e., with small N, for ZF decoding or detection.

FIG. 3 shows the flowchart for determining the number of served UEs K, for a given M, to ensure high probability of convergence and/or quick convergence. The process begins 9 when the number of BS antennas M is selected or obtained 10 . Then, the number of served UEs S is found with a sufficiently large ratio of M/S to achieve high probability of convergence or high probability of DDM so that NS converges with a small N 11 . After that, the BS selects K≤S UEs to serve 12 before the process ends 13 .

Although the foregoing descriptions of the preferred embodiments of the present inventions have shown, described, or illustrated the fundamental novel features or principles of the inventions, it is understood that various omissions, substitutions, and changes in the form of the detail of the methods, elements or apparatuses as illustrated, as well as the uses thereof, may be made by those skilled in the art without departing from the spirit of the present inventions. Hence, the scope of the present inventions should not be limited to the foregoing descriptions. Rather, the principles of the inventions may be applied to a wide range of methods, systems, and apparatuses, to achieve the advantages described herein and to achieve other advantages or to satisfy other objectives as well.