Coordinated linear beamforming in downlink multi-cell wireless networks
View Patent ↗System and methods are disclosed for optimizing wireless communication for a plurality of mobile wireless devices. The system uses beamforming vectors or precoders having a structure optimal with respect to the weighted sum rate in a multi-cell orthogonal frequency division multiple access (OFDMA) downlink. A plurality of base stations communicate with the mobile devices and all base stations perform a distributed non-convex optimization exploiting the determined structure.
1. A method to optimize wireless communication for a plurality of mobile wireless devices, comprising:
a. determining a structure for downlink beamforming vectors optimizing a weighted sum-rate across multiple orthogonal resource slots in the time, frequency or code domain; and
b. distributing a non-convex optimization exploiting the determined structure over a plurality of base stations.
2. The method of claim 1 , wherein the non-convex optimization is responsive to one or more of: a set of channel estimates; user priorities; and maximum transmit power available at each base-station.
3. The method of claim 1 , wherein the non-convex optimization utilizes Karush-Kuhn-Tucker (KKT) equations.
4. The method of claim 1 , wherein the distributing over the base stations includes providing a small number of channel estimates at each base station and limited message passing among adjacent base stations.
5. The method of claim 1 , comprising obtaining channel estimates.
6. The method of claim 1 , comprising obtaining predicted channel estimates responsive to an average scheduling delay parameter.
7. The method of claim 1 , wherein the mobile wireless device comprises a multiple-input single-output (MISO) system wherein each user is equipped with a single receive antenna and receives a single data stream from its serving base station via space-division multiple-access (SDMA).
8. The method of claim 1 , comprising determining the optimal structure of the beamforming vectors optimizing the weighted sum-rate in a MISO system.
9. The method of claim 8 , comprising determining a leakage matrix.
10. The method of claim 9 , wherein determining a leakage matrix L m,k (n) comprises:
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where
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;
B m (n), B l (n), and B j (n) denote a set of users served by base stations m, l, and j, respectively, on slot n;
w m,k (n)εC P and w l,s (n)εC P denote the P-dimensional beam vector used by the base stations m and l, respectively, to serve users kεB m (n) and sεB m (n), respectively, on slot n;
P is the number of transmit antennas at each base station;
W={w m,k (n), kεB m (n), m=1, . . . , M, n=1, . . . N} indicates the collection of all beam vectors;
N is the total number of orthogonal resource slots;
M is the number of coordinated base stations;
α k (n)>0 is priority assigned by a scheduler to user k on slot n;
SINR m,k (n) and SINR j,u (n) denote the signal-to-interference-plus-noise ratio for users k and u, respectively, served by base stations m and j, respectively, on slot n and are given by the form of
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with G m,k (n)=h m,k (n)h m,k H (n)εC P×P and G l,u (n) and G j,k (n) have the same form as G m,k (n);
h m,k (n)εC P is a P-dimensional channel vector between base station m and user k and slot n (which includes small-scale fading, large scale fading and path attenuation) normalized by the standard deviation of the received noise.
11. The method of claim 10 , comprising determining
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where i m,k (n) stands for a scalar.
12. The method of claim 8 , comprising determining λ 1 , . . . , λ M and
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where {circumflex over (T)} m,k (n;λ m )={circumflex over (L)} m,k (n;λ m )+(λ m ln 2)I p , (•) † indicates the pseudo-inverse and x + =max{x,0}, {î m,k (n),{circumflex over (L)} m,k (n)} denotes most recent values of {i m,k (n),L m,k (n)}, λ 1 , . . . , λ M are non-negative Lagrangian multipliers associated to the transmit power constraints, α k (n)>0 is priority assigned by a scheduler to user k on slot n, P m,max is the maximum transmit power of base station m, L m,k (n) is a leakage matrix, h m,k (n)εC P is a P-dimensional channel vector between base station m and user k and slot n (which includes small-scale fading, large scale fading and path attenuation) normalized by the standard deviation of the received noise, P is the number of transmit antennas at each base station, B m (n) denotes a set of users served by base station m on slot n, and N is the total number of orthogonal resource slots, M is the number of coordinated base stations.
13. The method of claim 12 , comprising updating beam vectors as
w m,k ( n )={circumflex over (β)} m,k ( n;λ m ) {circumflex over (T)} m,k † ( n;λ m ) h m,k ( n ).
14. The method of claim 8 , comprising choosing an initial feasible set of beam vectors.
15. The method of claim 14 , wherein the initial feasible set is selected after splitting power across the available slots.
16. The method of claim 14 , comprising performing channel-matched beamforming to select the initial feasible set of beam vectors.
17. The method of claim 14 , comprising performing in-cell zero-forcing beamforming to select the initial feasible set of beam vectors.
18. The method of claim 14 , comprising performing maximum signal-to-leakage-plus-noise ratio (MSLNR) beamforming to select the initial feasible set of beam vectors.
19. The method of claim 1 , comprising providing an equivalent MISO system wherein each mobile user has multiple-receive antennas and performs rank-one receive beamforming before detection.
20. The method of claim 1 , wherein the mobile wireless device comprises a multiple-input multiple-output (MIMO) system and wherein each user is equipped with multiple receive antennas and receives multiple data streams from a serving base station via linear precoding.
21. The method of claim 20 , comprising determining a leakage matrix.
22. The method of claim 20 , comprising solving a following convex optimization problem at each base-station m, for a given {L m,k (n)} and {R m,k (n)}:
argmax
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where
L m,k (n) is a leakage matrix,
R m,k (n) is a covariance matrix of a co-channel interference plus noise seen by user kεB m (n) on slot n,
Q m,k (n)=W m,k (n)W m,k H (n)εC P×P is a covariance matrix to be optimized,
W m,k (n) indicates a precoding matrix used to serve user kεB m (n) on slot n by base station m;
N is the total number of orthogonal resource slots;
M is the number of coordinated base stations;
P is the number of transmit antennas at each base station;
B m (n) is a set of users served by base station m on slot n;
P m,max is the maximum transmit power of base station m, and
tr(•) denotes the trace operation
H m,k (n)εC N R ×P is a channel matrix between base station m and user k and slot n (which includes small-scale fading, large scale fading and path attenuation) normalized by the standard deviation of the received noise.
23. The method of claim 20 , comprising selecting an initial feasible set of positive semi-definite covariance matrices after splitting power across available slots.
24. The method of claim 23 , comprising performing Maximum Signal-to-Leakage-plus-Noise Ratio (MSLNR) precoding to select the initial feasible set of positive semi-definite covariance matrices.
25. The method of claim 1 , comprising determining an optimal structure of the linear precoders in a MIMO system.
26. The method of claim 21 , wherein determining a leakage matrix L m,k (n) comprises determining:
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,
where
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+
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k
and R j,u (n) has the same form as R m,k (n);
B m (n) is a set of users served by base station m on slot n;
N k is the number of receive antennas of user k,
W m,k (n)εC P×D m,k (n) and W j,u (n)εC P×D j,u (n) indicate precoding matrices used to serve users kεB m (n) and uεB j (n), respectively, on slot n by base stations m and j, respectively, and D m,k (n) and D j,u (n) denote the number of data streams delivered to users kεB m (n) and uεB j (n) on slot n by base stations m and j, respectively;
P is the number of transmit antennas at each base station;
Q={Q m,k (n)ε Q , kεB m (n), m=1, . . . , M, n=1, . . . N} indicates the collection of the positive-semidefinite covariance matrices;
N is the total number of orthogonal resource slots;
M is the number of coordinated base stations;
α k (n)>0 is priority assigned by a scheduler to user k on slot n;
H j,k (n)εC N k ×P is a channel matrix between base station j and user k and slot n (which includes small-scale fading, large scale fading and path attenuation) normalized by the standard deviation of the received noise.
27. A communication system, comprising:
a. a plurality of mobile devices that receive data made by linear precoding matrices having a predetermined structure for downlink precoding, the predetermined structure being optimal with respect to a weighted sum rate in a multi-cell orthogonal frequency division multiple access (OFDMA) downlink; and
b. a plurality of base stations communicating with the mobile devices, all base stations performing a distributed a non-convex optimization exploiting the predetermined structure.