CN109450495A - A kind of MIMO capacity second-rate optimization method based on precoding channel compensation - Google Patents
A kind of MIMO capacity second-rate optimization method based on precoding channel compensation Download PDFInfo
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Abstract
The present invention is suitable for communication field, provide a kind of MIMO capacity second-rate optimization method based on precoding channel compensation, the MIMO capacity second-rate optimization method is the following steps are included: step S1: judging whether to be more than or equal to 2 to the transmission rank of mimo system, in this way, then carry out next step, if not, being not processed or each antenna mean allocation power；Step S2: between whether the TB number for judging mimo system is same TB, if so, power adjustment between TB is then carried out, if not, carrying out power compensation in TB.Solve the excessively high technical problem of the mimo system bit error rate.
Description
Technical Field
The invention belongs to the field of communication, and particularly relates to a MIMO capacity suboptimal method based on precoding channel compensation.
Background
The wireless communication technology is continuously developed, limited wireless resources face the dilemma of big explosion of communication data, and how to transmit more information with less frequency resources becomes a great challenge in the development of the wireless communication technology.
The MIMO technology is that a plurality of antennas are used at a transmitting end and a receiving end, and signals are transmitted and received through the plurality of antennas at the transmitting end and the receiving end, so that the capacity and the spectrum utilization rate of a communication system are improved in multiples without increasing the bandwidth.
The channel capacity can be generally defined as the maximum transmission rate of the system under the condition of ensuring that the error rate is arbitrarily small. Reliable transmission of data in the channel is only possible at rates below the capacity of the channel.
For SISO systems, shannon's theorem has given the ultimate capacity of the channel:
C＝BLog2(1+S/N)
where C represents the channel capacity of the system, B represents the system bandwidth, and S/N represents the SNR signal-to-noise ratio in decibels (db).
For MIMO systems, shannon's theorem has also given the ultimate capacity of the channel:
wherein, PiFor the transmission power, lambda, allocated to the ith subchannel in an equivalent systemiIs the ith non-zero eigenvalue of the channel correlation matrix.
According to the shannon theorem, when the state of the channel is known at the transmitting end, the transmitting end can perform optimal power distribution on each sub-channel according to the characteristic value of the channel and the water injection principle, so that the MIMO system reaches the maximum channel capacity. The principle of power allocation is as follows: more power is distributed for the channel with good channel condition; for the channel with poor channel condition, less power is distributed, even no power is distributed, and the characteristics of the channel are fully utilized, so that the transmission power is fully utilized as a whole, and the system reaches the limit capacity.
In order to improve the system capacity, high-order modulation needs to be used for the MIMO sub-channel with high signal-to-noise ratio, and low-order modulation needs to be used for the MIMO sub-channel with low signal-to-noise ratio, so that the high capacity and low bit error rate performance of the system can be guaranteed. However, this not only increases the decoding difficulty at the receiving end, but also increases the complexity of system implementation. In the current LTE system implementation, in order to reduce the system complexity, different modulation schemes are not flexibly configured based on the channel gains of different antennas, which means that the system capacity is not fully utilized.
Disclosure of Invention
The invention aims to provide a precoding channel compensation-based MIMO capacity suboptimal method, aiming at solving the technical problem of overhigh error rate of an MIMO system.
The invention is realized in such a way that a MIMO capacity suboptimal method based on precoding channel compensation comprises the following steps:
step S1: judging whether the transmission rank of the MIMO system is more than or equal to 2, if so, carrying out the next step, and if not, not carrying out processing or averagely distributing power to each antenna;
step S2: and judging whether the TB number of the MIMO system is between the same TBs, if so, carrying out power allocation between the TBs, and if not, carrying out power compensation in the TBs.
The further technical scheme of the invention is as follows: the power allocated among TBs in step S2 is based on independent modulation among TBs, an antenna is used to transmit data of TB1 and data of TB2, and the total power among TBs is allocated by TB1 power and TB2 power through a water-filling principle, so that:
wherein, PiIs the transmission power allocated to the ith channel.
The further technical scheme of the invention is as follows: the transmission power of the ith channel is a channel matrix H formed by N antenna transmission and M antenna reception in the MIMO system, and the channel matrix H is obtained through SVD singular value decomposition:
H＝UΛVT
wherein V is an orthogonal array of N x N, U is an orthogonal array of M x M, and Λ is a diagonal array of M x N;
solving the transmission power P by the water injection principle of the channel matrix Hi：
The further technical scheme of the invention is as follows: the TB internal power compensation in step S2 is based on TB internal uniform modulation, when a signal x passes through a precoding matrix F, it is transmitted to the air through N antennas, the air propagation is equivalent to passing through a channel matrix H, and it is received by M antennas, and the N antennas are used to transmit data of TB1 and data of TB2, then the diagonal matrix Φ of the power allocation matrix for precoding channel compensation is:
wherein for TB1, takeFor TB2, take
Then, a precoding matrix F is obtained:
F＝PΦ＝VΠG1G2…GMΦ
wherein G is1G2…GMP is the rotation matrix, the right matrix is decomposed by GMD, and phi is the power allocation matrix.
The further technical scheme of the invention is as follows: the GMD decomposition right matrix is a channel matrix H formed by N antenna transmission and M antenna reception in the MIMO system, and the channel matrix H is obtained through SVD singular value decomposition:
H＝UΛVT
wherein V is an orthogonal array of N x N, U is an orthogonal array of M x M, and Λ is a diagonal array of M x N;
and performing GMD geometric mean decomposition on the lambda, wherein after decomposition, the channel matrix has the following form:
H＝QRPT
wherein Q and P are a column orthogonal matrix, R is an upper triangular matrix with equal diagonal elements, and the diagonal elements are equal to the geometric mean of the positive singular values of the channel matrix H:
right matrix P ═ V Π G of GMD decomposition1G2…GM
The matrix obtained after the displacement is still a diagonal matrix, the size of diagonal elements is unchanged, and the diagonal elements are arranged from the upper left corner to the lower right corner in a descending order. G1、G2、…、GMFor rotating the matrix, a geometric mean decomposition of the diagonal elements of the diagonal matrix is implemented.
Corresponding precoding matrix F phi VΠ G1G2…GMΦ。
The invention has the beneficial effects that: the error rate of the MIMO system is reduced, and the overall capacity is improved as much as possible.
Drawings
Fig. 1 is a flowchart of a MIMO capacity sub-optimization method based on precoding channel compensation according to an embodiment of the present invention;
fig. 2 is a diagram of a MIMO system model of a MIMO capacity suboptimization method based on precoding channel compensation according to an embodiment of the present invention;
fig. 3 is a diagram of an MIMO equivalent channel model of an MIMO capacity suboptimization method based on precoding channel compensation according to an embodiment of the present invention;
fig. 4 is a schematic diagram of precoding of a MIMO system based on a MIMO capacity suboptimization method for precoding channel compensation according to an embodiment of the present invention;
fig. 5 is a downlink physical channel PDSCH processing flow of the MIMO capacity suboptimization method based on precoding channel compensation according to the embodiment of the present invention;
fig. 6 is a system capacity simulation diagram of power water filling between TBs and precoding channel compensation within TB of a MIMO capacity suboptimization method based on precoding channel compensation according to an embodiment of the present invention.
Detailed Description
Reference numerals:
fig. 1 to 6 show a MIMO capacity suboptimization method based on precoding channel compensation provided by the present invention, which implements channel compensation on MIMO sub-channels with low signal-to-noise ratio through precoding, balances the gain difference between MIMO sub-channels, and improves the system capacity as much as possible without increasing too much system complexity.
Furthermore, for the MIMO system with the transmission rank greater than or equal to 2, because each TB adopts an independent modulation mode, that is, different TBs can adopt different modulation modes according to channel estimation, high-order modulation is used for the MIMO sub-channel with high signal-to-noise ratio, and low-order modulation is used for the MIMO sub-channel with low signal-to-noise ratio, therefore, for the scene of independent scheduling among TBs, a power water filling mode can be adopted, and the improvement of the whole capacity of the system can be conditionally realized through reasonable power distribution among TBs. In view of this, the present invention implements a power allocation method in two steps for a MIMO system with a transmission rank greater than or equal to 2:
and (3) power allocation among TBs: based on independent modulation among TBs, power is firstly distributed among different TBs according to a power water injection principle, more power is distributed to the TBs with good channel conditions, and a higher-order modulation mode is adopted to fully exert capacity potential of the TBs.
TB internal power compensation: based on the fact of uniform modulation in the TB, because each channel in the same TB adopts a uniform modulation mode and the power required by the channel with high signal-to-noise ratio is less, a precoding channel compensation mode is adopted in the same TB to inject more power into the channel with low signal-to-noise ratio, thereby achieving the gain balance among the channels in the same TB and improving the overall capacity in the same TB.
Based on the power distribution method, the error rate of the MIMO system can be reduced, and the whole capacity can be improved as much as possible.
Firstly, SVD (singular value decomposition) of a channel matrix is performed, as shown in FIG. 2, a MIMO (multiple input multiple output) system model is provided, and SVD is performed on the channel matrix H, assuming that the channel matrix H is an M x N matrix, N antennas transmit and M antennas receive.
Assuming that the noise on each antenna is independent of each other and obeys a mean of 0 and a variance ofThe noise n and the transmitted signal x are independent of each other. Thus, a flat fading channel MIMO system can be represented as follows:
y＝Hx+n
wherein,
the channel matrix H maps vectors in n-dimensional space to k (k)<In m) dimensional space, k rank (h). Selecting a channel correlation matrix HTH, constructing a set of orthogonal bases v:
{v1,v2,…,vn}
namely, the method comprises the following steps:
the channel matrix H maps the set of bases to:
{Hv1,Hv2,…,Hvn}
obviously, they are two by two orthogonal, i.e.
Wherein λjFor the channel correlation matrix HTH, j-th eigenvalue.
Now, the mapped orthogonal basis is unitized:
because of the fact that
Hvi·Hvi＝λivi·vi＝λi
So that there are
|Hvi|2＝λi≥0
So as to take the unit vector
Thus, can obtain
Hvi＝σiui，
When k is<When i is less than or equal to m, p is1，u2，…，ukCarry out an extension u(k+1)，…，umSo that u is1，u2，…，umFor a set of orthogonal bases in m-dimensional space, i.e. { u }1，u2，…，ukExtension of the orthogonal basis to { u }1，u2，…，um}RmOf spacesThe unit orthogonal basis.
Likewise, for v1，v2，…，vkCarry out an expansion v(k+1)，…，vn(these n-k vectors exist in the null space of H, i.e., the base of the solution space where Hx is 0), such that v1，v2，…，vnSelecting { v } in the null space of H for a set of orthogonal bases in n-dimensional space(k+1)，v(k+2)，…，vnMake Hvi＝0，i>k, and take σi＝0
Then can obtain
Then the singular value decomposition of the H matrix can be obtained:
H＝UΛVT
v is an orthogonal matrix of N x N, U is an orthogonal matrix of M x M, and Λ is a diagonal matrix of M x N.
So that there are
This results in an SVD singular value decomposition of the channel matrix H.
Second, water injection principle
From SVD singular value decomposition, we obtain that any one M × N channel matrix can be represented as:
H＝UΛVT
wherein U and V are unitary matrices of dimensions M and N, UUT＝ImAnd VVT＝InHere ImAnd InMxm and nxn dimensional unit arrays, respectively, Λ is a non-negative diagonal array of M x N dimensions:
wherein (lambda)1,λ2,…,λk) Is a channel correlation matrix HTA non-zero characteristic value of H, and k rank (H).
When the transmitting antenna N and the receiving antenna M are independent from each other, k is min (M, N), and the SVD decomposition of the above formula is brought into the formula
y＝Hx+n
The following can be obtained:
y＝UΛVTx+n
if orderThen:
accordingly, a MIMO channel may be equivalent to k independent parallel subchannels, each having a channel gain that is a non-zero singular value of the channel matrix H. Fig. 3 shows an equivalent MIMO channel model.
Since these subchannels are completely independent, the capacity of the MIMO system is equivalent to the superposition of the capacities of these parallel subchannels, which is obtained by the shannon capacity equation:
wherein, PiThe transmission power allocated to the ith subchannel in the equivalent system.
When the state information of the channel is known at the transmitting end, in order to enable the capacity of the MIMO system to reach the maximum value, the optimal power distribution scheme can be solved by using a Lagrange multiplier method.
First, a lagrangian function is constructed:
f(P1,P2,…Pk)＝C(P1,P2,…Pk)-ηΦ(P1,P2,…Pk)
wherein
Φ(P1,P2,…Pk)＝P1+P2+…+Pk-PT＝0
PTTo transmit the total power.
Φ(P1,P2,…Pk) Indicating that the sum of the transmitted powers of the antennas is equal to PTThe total power is transmitted.
When the capacity of the MIMO system reaches the maximum value, according to the Lagrange multiplier method, the following equation sets up:
representing the function f (P)1,P2,…Pi) To PiAnd (5) calculating partial derivatives.
Then there are:
solving this system of equations yields:
order toμ is a constant and the solution of the above system of equations can be expressed as:
considering the actual situation, the allocated power PiIt is impossible to have a negative value, and when the capacity reaches an extreme value, the corresponding power PiWhen it is negative, power P is takeniNo power is allocated, i.e. 0. The solution of the above system of equations is then rewritten as:
wherein a is+Represents max (a,0), and
it should be noted that when P appearsi<0, as PiAfter the special processing of 0, in order to solve the maximum capacity C and guarantee the constraint conditionIt holds that P is required to correspond toiRemoving and reapplying Lagrange multiplier method and simultaneous equations, solving optimal power distribution scheme, and processing the special cases (or P in algorithm) by subsequent algorithmsiAll satisfy the condition Pi>0) And will not be described in detail.
Solution of the above equation set { P1,P2,…PkThat is, the MIMO system capacity reaches the maximum value, and each independent parallel sub-channel is usedThe water power value.
According to the above formula, the principle of power distribution according to the water injection principle is as follows: when the channel condition is good, more power is allocated; when the channel state is deteriorated, that is, the attenuation is large, the power allocated to the channel is reduced, or even no power is allocated, thereby making full use of the transmission power as a whole.
The maximum capacity of the MIMO system is thus obtained:
precoding channel compensation method
Based on the above derivation, we know that power allocation is performed according to the water-filling principle, and the power allocation strategy adopted to achieve the maximum capacity of the MIMO system is to allocate more power when the channel condition is good. However, it is not necessary to allocate more power to achieve the maximum capacity of the channel, and in order to achieve the maximum capacity of the channel, the power allocation must be implemented in accordance with the corresponding modulation scheme. For example, when the channel condition is good, more power is allocated and a higher-order modulation scheme is adopted, so that the maximum capacity of the channel is reached.
Therefore, in order to increase the system capacity, it is necessary to use high-order modulation for the MIMO sub-channel with high signal-to-noise ratio, and use low-order modulation for the MIMO sub-channel with low signal-to-noise ratio, so as to ensure the high capacity and low error rate performance of the system. However, this not only increases the decoding difficulty at the receiving end, but also increases the complexity of system implementation. In the current LTE system implementation, in order to reduce the system complexity, the same TB does not flexibly configure different modulation schemes based on the channel gains of different antennas, which means that the system capacity is not fully utilized.
Based on the fact that the same modulation scheme is configured for the TB unified scheduling, we know that when the channel condition is good, even if more power is allocated, the channel capacity is not necessarily improved correspondingly, and too much power allocation is also a waste, and conversely, for a channel with poor channel condition, if more power can be allocated, the shortage of channel gain can be compensated, the channel capacity is improved, and the capacity of the MIMO system is improved as a whole.
Therefore, the basic idea is to perform precoding compensation on each antenna of the same TB based on channel gain, and after precoding compensation, the performance of each sub-channel tends to be consistent, thereby achieving the maximization of the capacity of the MIMO system under the condition of adopting the complexity limitation of a uniform modulation scheme.
To simplify the complexity of the problem, first consider a full rank channel matrix H of M × N, i.e., N antennas transmit and M antennas receive, where the rank of the channel matrix H is N.
From the SVD singular value decomposition, we get:
H＝UΛVT
wherein the matrix Λ is as follows:
σicorresponding to the channel gain, in general, σiIs not uniform, which means that the gains of the sub-channels are not uniform. The matrix R obtained after transformation is an upper triangular matrix with equal diagonal elements, and the form of the matrix R is as follows:
for this purpose, we need to perform GMD geometric mean decomposition on Λ, and after decomposition, the channel matrix has the following form:
H＝QRPT
q and P are a column orthogonal matrix, R is an upper triangular matrix with equal diagonal elements, and the diagonal elements of the upper triangular matrix are equal to the geometric mean value of the positive singular values of H:
wherein, the right matrix P of GMD decomposition is V pi G1G2…GM。
The matrix obtained after the displacement is still a diagonal matrix, the size of diagonal elements is unchanged, and the diagonal elements are arranged from the upper left corner to the lower right corner in a descending order. G1、G2、…、GMFor rotating the matrix, a geometric mean decomposition of the diagonal elements of the diagonal matrix is implemented.
Matrix permutation;
the matrix Λ may need to be permuted, and is described below with a matrix of rank 3, assuming that each singular value in the singular matrixArranging σ from large to small1>σ3>σ2The following transformation process is carried out:
the function of the permutation matrix pi here is to achieve a descending order of the singular values on the diagonal of the channel matrix from the upper left corner to the lower right corner.
GMD geometric mean decomposition algorithm;
the specific GMD geometric mean decomposition algorithm is described below with an Λ matrix with rank 2 as an example:
assuming the Λ matrix as:
and performing bilateral Givens transformation on the matrix Λ to form a geometric mean diagonal matrix.
The expression for the Givens matrix is as follows:
the Givens transformation procedure is as follows:
wherein
At this time, letCan obtain the product
Givens matrix at this timeFor an optimal codebook, a uniform channel decomposition is achieved.
For the lambda matrix with the rank larger than 2, the matrix can be realized through multiple Givens transformationsUniform channel decomposition, so that there is a GMD decomposed right matrix P ═ V Π G1G2…GM
Pre-coding channel compensation;
fig. 4 is a schematic diagram of MIMO system precoding.
After passing through a precoding matrix F, a signal x is transmitted to the air through N antennas, and the air propagation is equivalent to passing through a channel matrix H and then is received by M antennas.
It can be seen that the optimal precoding matrix F ═ P Φ ═ V Π G1G2…GMΦ, after precoding, the model of the flat fading channel MIMO system can be expressed as follows:
y＝HFx+n
＝UΛVTPΦx+n
＝QRx+n
the matrix Q is obtained by channel estimation.
If orderThen:
the original transmitted signal x can thus be solved.
After the pre-coding channel compensation allocation, the performance of each sub-channel tends to be consistent, thereby achieving the purpose of realizing the maximization of the capacity of the MIMO system under the condition of adopting the complexity limitation of a uniform modulation scheme.
It should be noted that, the precoding channel compensation algorithm adopted herein does not need to perform additional power water-filling for each channel, that is, each subchannel only needs to input an equal amount of average power.
Fourthly, power water injection is carried out between TB;
based on the above derivation, we know that power allocation is performed according to the water-filling principle, and in order to reach the maximum capacity of the MIMO system, the power allocation strategy adopted is to allocate more power when the channel condition is good; when the channel state is deteriorated, that is, the attenuation is large, the power allocated to the channel is reduced, or even no power is allocated, thereby making full use of the transmission power as a whole.
As shown in fig. 5, which is a downlink physical channel PDSCH processing flow, data sent from the MAC layer to the physical layer is organized in the form of Transport Blocks (TBs), and if the UE supports space division multiplexing, at most 2 TBs are sent in one TTI. After CRC check and code block segmentation, inserting CRC, channel coding and rate matching into each code block, the TB obtains a data code stream, after scrambling and modulation, a plurality of symbols are obtained, after Layer mapping, the symbols are mapped to one or more transmission layers (layers), and each Layer corresponds to an effective data stream.
For the number of transmission layers, namely, the number of transmission orders or the number of transmission ranks, of an MIMO system (Layer is greater than or equal to 2), because the TBs adopt independent HARQ scheduling, and different TBs may adopt different modulation modes based on channel quality, we can still perform power allocation among the TBs based on a water injection principle, thereby achieving the optimal power allocation of the MIMO system from the perspective of the TBs and improving the overall capacity of the system.
Considering a MIMO system with a transmission rank of 2, assuming that 1-k antennas at the transmitting end are used for transmitting data of TB1 and k + 1-n antennas are used for transmitting data of TB2, TB1 and TB2 may allocate total power among TBs based on a water-filling principle:
wherein
Within the same TB, precoding channel compensation can still be performed based on method (III), so that the precoding channel compensation can be obtained
The power distribution matrix based on the pre-coding channel compensation algorithm has a diagonal matrix phi as follows:
wherein for TB1, takeFor TB2, take
Then, a precoding matrix F is obtained:
F＝PΦ＝VΠG1G2…GMΦ
wherein G is1G2…GMP is the rotation matrix, the right matrix is decomposed by GMD, and phi is the power allocation matrix.
The method is the inter-TB power water injection, and the MIMO system achieves the optimal power configuration from the TB level after the inter-TB power water injection in the same pre-coding channel compensation method; after the pre-coding channel compensation in the TB, the performance of each sub-channel tends to be consistent, the algorithm considers the independence of HARQ scheduling between the TBs and the uniformity of a debugging mode in the TB, the implementation of the algorithm can achieve the purpose of realizing the maximization of the capacity of an MIMO system under the complexity limiting condition of independent scheduling between the TBs and the uniform modulation mode in the TB, and compared with the Shannon limit capacity, the method is an MIMO capacity suboptimal method under the specific complexity condition.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.
Claims (5)
1. A MIMO capacity suboptimal method based on precoding channel compensation is characterized in that the MIMO capacity suboptimal method comprises the following steps:
step S1: judging whether the transmission rank of the MIMO system is more than or equal to 2, if so, carrying out the next step, and if not, not carrying out processing or averagely distributing power to each antenna;
step S2: and judging whether the TB number of the MIMO system is between the same TBs, if so, carrying out power allocation between the TBs, and if not, carrying out power compensation in the TBs.
2. The method of claim 1, wherein the power allocation among TBs in step S2 is based on independent modulation among TBs, antennas are used to transmit data of TB1 and data of TB2, and total power among TBs is allocated by TB1 power and TB2 power through water-filling principle, so that:
wherein, PiIs the transmission power allocated to the ith channel.
3. The MIMO capacity sub-optimization method of claim 2, wherein the transmission power of the ith channel is a channel matrix H formed by N-antenna transmission and M-antenna reception in the MIMO system, and the channel matrix H is obtained by SVD singular value decomposition:
H＝UΛVT
wherein V is an orthogonal array of N x N, U is an orthogonal array of M x M, and Λ is a diagonal array of M x N;
solving the transmission power P by the water injection principle of the channel matrix Hi：
4. The MIMO capacity suboptimal method of claim 3, wherein the intra-TB power compensation in step S2 is based on intra-TB uniform modulation, when the signal x passes through the precoding matrix F and is transmitted to the air via N antennas, the air propagation is equivalent to going through a channel matrix H and then being received by M antennas, the N antennas are used for transmitting the data of TB1 and the data of TB2, and the diagonal matrix Φ of the power allocation matrix for precoding channel compensation is:
wherein for TB1, takeFor TB2, take
Then, a precoding matrix F is obtained:
F＝PΦ＝VΠG1G2…GMΦ
wherein G is1G2…GMP is the rotation matrix, the right matrix is decomposed by GMD, and phi is the power allocation matrix.
5. The MIMO capacity sub-optimization method of claim 4, wherein the GMD decomposition right matrix is a channel matrix H formed by N-antenna transmission and M-antenna reception in the MIMO system, and the channel matrix H is obtained by SVD singular value decomposition:
H＝UΛVT
wherein V is an orthogonal array of N x N, U is an orthogonal array of M x M, and Λ is a diagonal array of M x N;
and performing GMD geometric mean decomposition on the lambda, wherein after decomposition, the channel matrix has the following form:
H＝QRPT
wherein Q and P are a column orthogonal matrix, R is an upper triangular matrix with equal diagonal elements, and the diagonal elements are equal to the geometric mean of the positive singular values of the channel matrix H:
right matrix P ═ V Π G of GMD decomposition1G2…GM
The n is a permutation matrix, the n matrix can realize the permutation of the Λ matrix, and the matrix obtained after the permutation is still diagonalAnd (4) array, wherein the sizes of the diagonal elements are unchanged, but the diagonal elements are arranged from the upper left corner to the lower right corner in descending order. G1、G2、…、GMFor rotating the matrix, a geometric mean decomposition of the diagonal elements of the diagonal matrix is implemented.
Corresponding GMD precoding matrix F phi V pi G1G2…GMΦ。
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