MULTIPLE IN MULTIPLE OUT NETWORK CODED AMPLIFY AND FORWARD RELAYING SCHEME FOR THREE NODE BIDIRECTIONAL COOPERATION

This application is a divisional of co-pending U.S. application Ser. No. 13/810,408, filed Jan. 15, 2013, which is a 371 of International Application PCT/US10/43655 filed Jul. 29, 2010 herein incorporated by reference.

The present invention is directed to a three node cooperation scheme to assist in bidirectional transmissions (communications) of the draft IEEE 802.11n standard.

In multicast and broadcast applications, data are transmitted from a server to multiple receivers over wired and/or wireless networks. A multicast system as used herein is a system in which a server transmits the same data to multiple receivers simultaneously, where the receivers form a subset of all the receivers up to and including all of the receivers. A broadcast system is a system in which a server transmits the same data to all of the receivers simultaneously. That is, a multicast system by definition can include a broadcast system.

Consider multicast (downlink) and multi-access (uplink) channels with one access point (AP) and several nodes. In the IEEE 802.11n draft standard, a reverse direction (RD) protocol is introduced for fast scheduling of bidirectional traffic flows within a transmission opportunity (TXOP). The reverse direction protocol permits (allows) the node, which has obtained the TXOP to grant reverse directional transmissions to another node while it is still in control of the TXOP. If the channel conditions between the nodes are inadequate (poor) then transmissions between the two nodes suffer. That suffering may be reduced data rate and/or throughput.

In the IEEE 802.11n draft standard, a reverse direction (RD) protocol has been proposed as in FIG. 1. The reverse direction protocol of the IEEE 802.11n draft standard only schedules bidirectional transmission between two nodes. Each node is both a source node and a destination node. There is no existing scheduling protocol for three-node bidirectional transmissions in IEEE 802.11 WLAN standards. FIG. 1 illustrates the conventional unidirectional cooperation using a half-duplex relay node (RN). FIG. 1a shows the first stage of communication, in which Node₁transmits (sends, communicate) data S₁to both Node₂and the RN. FIG. 1b shows stage 2 of communication, in which the RN transmits (communicates, sends) data S₁to Node₂. That is, the RN transmits (communicates, forwards, sends) data S₁as Ŝ₁to Node₂. Correspondingly (and not shown), in the third stage of communication, Node₂transmits (sends, communicate) data S₂to both Node₁and the RN. In the fourth stage of communication, the RN transmits (communicates, forwards, sends) data Ŝ₂to Node₁. That is, the RN transmits (communicates, forwards, sends) data S₂as Ŝ₂to Node₁. Thus, in the conventional approach, there are four stages (phases) to complete communications using the half-duplex RN to assist Node₁and Node₂.

Network-coded three-node bidirectional cooperation with three stages (i.e., the reception of signals from nodes (source and destination) at the RN are orthogonal (separate)) has been studied, using Decode-and-Forward, Soft Decode-and-Forward, and Amplify-and-Forward in a single-antenna system, and a case when L₁=L₂=1 and L_R=2 etc, respectively. Note that L_i, i=1,2,R represents the number of antennas at Node₁, Node₂and RN respectively. The present invention uses Amplify-and-Forward for the general MIMO case with an arbitrary number of antennas at the nodes. This has not been addressed in any publications known to the Applicants.

As used herein a node includes (but is not limited to) a station (STA), a mobile device, a mobile terminal, a dual mode smart phone, a computer, a laptop computer or any other equivalent device capable of operating under the IEEE 802.11n draft standard.

Consider multicast (downlink) and multi-access (uplink) channels with one access point (AP) and several nodes. In the IEEE 802.11n draft standard, a reverse direction (RD) protocol is introduced for fast scheduling of bidirectional traffic flows within a transmission opportunity (TXOP). The reverse direction protocol permits (allows) the node, which has obtained the TXOP to grant reverse directional transmissions to another node while it is still in control of the TXOP. However, when the channel state (channel conditions) between the two nodes is not sufficient for providing fast and reliable transmissions (communication) between them, cooperation through a third node, a half-duplex relay node (RN), may be involved to assist transmissions (communications). When the transmission between these two nodes involves cooperation through a third node, a half-duplex relay node (RN), the situation becomes more complicated, and wireless network coding can be utilized to further increase system throughput. Each node is both a source node and a destination node.

In the present invention, as shown in FIG. 2 and described more fully below, wireless network coding is introduced into the system and combined with bidirectional cooperation to increase system throughput. The present invention describes a network-coded amplify-and-forward (NCAF) relaying scheme in such a three-node bidirectional cooperation scenario.

In three-node bidirectional cooperation scheme of the present invention, two nodes, Node₁and Node₂, are both source and destination nodes, and the RN is a relay node, assisting the bidirectional transmission between Node₁and Node₂. The relay node (RN) sequentially receives signals from both Node₁and Node₂, combines the two signals with pre-coding matrices for both of them, and broadcasts the mixed signal to both nodes on orthogonal channels. Each of the nodes (source and destination) receives both the transmission (communication) of the desired signal from the other node, and the transmission (communication) of the mixed signal from the RN. Each node can jointly decode the data it desires based on the knowledge of the signal it sent out (transmitted, communicated). The process is shown in FIG. 3, which will be further described below. The present invention not only describes the above network-coded amplify-and-forward (NCAF) relaying scheme, but also solves the design problem of the pre-coding matrices at RN for the received signals from the nodes (source and destination), so as to maximize the instantaneous capacity of the bidirectional cooperation system, subject to a total power constraint at the RN, given channel state information (CSI) in two cases:

(1) Without CSI of direct links at the RN: Only CSI of the channels from the nodes (source and destination) to the RN, and the channels from the RN to the nodes (source and destination), are known at the RN. CSI of the channels between the two nodes (source and destination) is not known at the RN.

(2) With CSI of the direct links at the RN: CSI of the channels from the nodes (source and destination) to the RN, and the channels from RN to the nodes (source and destination), and the channels between the two nodes (source and destination) are known at the RN.

In the Network-Coded Amplify-and-Forward (NCAF) relaying scheme of the present invention, the RN no longer forwards the amplified received signals from one node to another as in conventional amplify-and-forward cooperation. Instead, the RN combines two received signals from two nodes by firstly multiplying them with pre-coding matrices. Then the RN broadcasts (multicasts) the combined signal, which contains the mixed data of the bidirectional traffic flow. Each end node receives the signal from the RN. The nodes can then jointly decode its desired signal based on the knowledge of the signal it has sent out (transmitted, communicated). There is still diversity in the cooperation.

The NCAF relaying scheme of the present invention, may prove to be essential to the future the IEEE 802.11 draft Very High Throughput (VHT) standard. The advantage of the NCAF relaying scheme of the present invention is that only simple processing, i.e., linear pre-coding, is needed at the relay node (RN). It is also compatible with conventional cooperation using an amplify-and-forward relaying scheme. The NCAF relaying scheme of the present invention also solves the problem when the RN is not able to decode the received data due to an insufficient number of antennas equipped at the RN and is always feasible for any multiple-antenna systems.

A method and apparatus are described including receiving a first signal including first data in a first time slot of a first channel, receiving a second signal including second data in a second time slot of a second channel, determining a first pre-coding matrix, determining a second pre-coding matrix, applying the first pre-coding matrix to the first data to produce pre-coded first data, applying the second pre-coding matrix to the second data to produce second pre-coded data, generating a third signal by combining the pre-coded first data and the pre-coded second data and transmitting the third signal on the first channel and on the second channel. Also described are a method and apparatus including transmitting a first signal, receiving a second signal and jointly decoding the second signal including a first training sequence by removing the first training sequence and removing the first signal.

FIG. 2 shows the operation of the Network-Coded Amplify-and-Forward relaying scheme for bidirectional cooperation of the present invention using a half-duplex relay node. FIG. 2a shows the first stage of communication, in which Node₁transmits (sends, communicates) data S₁to both Node₂and the RN. In the second stage of communication as shown in FIG. 2b, Node₂transmits (sends, communicate) data S₂to both Node₁and the RN. In the third stage of communication as shown in FIG. 2c, the RN combines (mixes) data Ŝ₁+Ŝ₂for transmission (communication) to both Node₁and Node₂. Data Ŝ₁+Ŝ₂is formed by applying pre-coding matrices to data S₁and data S₂. The combination of data Ŝ₁+Ŝ₂is f(S₁+S₂). The number of stages has thus been reduced from four stages to three stages. It should be noted that in addition to applying pre-coding matrices to the data, beamforming matrices may also be applied to the data.

A system model and some notation is introduced first. X_iis the signal transmitted from Node, (i=1,2,R, and Node_Rdenotes the RN). Q_iis the beamforming matrix at Node_i, and it is an identity matrix if beamforming is not used. H_ijis the channel matrix from Node_jto Node_i. Y_ijand N_ijare the received signal and noise from Node_jto Node_i, elements are assumed to be independent and identically distributed Gaussian with variance σ_n². W_iis the pre-coding matrix applied to Y_Riat RN. The total transmitted power is P_iat Node_i(i=1,2) and P_Rat the RN.

The RN receives Y_R1=H_R1Q₁X₁+N_R1from Node₁in the 1^sttime slot, and Y_R2=H_R2Q₂X₂+N_R2from Node₂in the 2^ndtime slot. Then the RN mixes the weighted received signals as its broadcast signal

X_R=W₁Y_R1+W₂Y_R2=W₁H_R1Q₁X₁+W₂H_R2Q₂X₂+W₁N_R1+W₂N_R2.

The reception and decoding at one node (source and destination) is used as an example. It goes without saying that demodulation is performed at the reception end. The processing at the other node (source and destination) is similar. Node₁receives Y₁₂=H₁₂Q₂X₂+N₁₂from Node₂in the 2^ndtime slot, and Y_1R=H_1RX_R+N_1Rfrom the RN in the 3^rdtime slot, i.e., Y_1R=H_1RW₁H_R1Q₁X₁+H_1RW₂H_R2Q₂X₂+H_1RW₁N_R1+H_1RW₂N_R2+N_1R. The matrix form is

[Y12Y1R]=[0N1H1RW1HR1]Q1X1+[H12H1RW2HR2]Q2X2+[IN10N1×NR0N1×NR0N10N1H1RW1H1RW2IN1][N12NR1NR2N1R],(1)

i.e., Y₁=D₁X₁+A₁X₂+B₁N₁, where Y₁=[Y₁₂Y_1R]^T∈C^2L1×1, 0_Ni×Nj∈C^Li×Lj is a zero matrix, and I_N∈C^N×Nis an identity matrix. Note that at Node₁, X₁is known, but X₂is unknown and to be detected. N₁=[N₁₂N_R1N_R2N_1R]^T∈C^2(L1+LR)×1is the noise vector at Node₁, and the matrices,

D1=[0N1H1RW1HR1]Q1,A1=[H12H1RW2HR2]Q2andB1=[IN10N1×NR0N1×NR0N10N1H1RW1H1RW2IN1]

are assumed known. Based on the knowledge of X₁, Node₁can obtain Z₁=Y₁−D₁X₁=A₁X₂+B₁N₁, where Z₁is the equivalent received signal, and A₁is the equivalent channel matrix for signal X₂. Then Node₁can jointly decode X₂.

Similarly, Z₂=A₂X₁+B₂N₂, where Z₂, A₂, B₂and N₂are defined by exchanging the subscripts “1” and “2”, and “N₁” and “N₂” in their counterparts.

The problem is to determine W₁and W₂, W_i∈C^LR×LR, i=1,2, to maximize the instantaneous capacity of the system, subject to the transmit power constraint at the RN. W₁and W₂are the pre-coding matrices. That is, determine W₁and W₂, to maximize

f=logdet(I2N1+P2N2σn2(A1A1H)(B1B1H)-1)+logdet(I2N2+P1N1σn2(A2A2H)(B2B2H)-1),subjecttoP1N1tr{W1HR1Q1Q1HHR1HW1H}+σn2tr{W1W1H}+P2N2tr{W2HR2Q2Q2HHR2HW2H}+σn2tr{W2W2H}=PR,(1)

where tr(X) represents the trace of the matrix X.
Letting Q_i, i=1,2 be a unitary matrix, the constraint can be simplified to

P1N1tr{W1HR1HR1HW1H}+σn2tr{W1W1H}+P2N2tr{W2HR2HR2HW2H}+σn2tr{W2W2H}=PR.(2)

In the first case, the CSI of the channels (links) from Node_ito the RN and the RN to Node_j, are assumed available at the RN. The CSI of the links (channels) between Node_iand Node_j, i,j=1,2 and i≠j is not available. In this scenario, it is necessary to maximize an upper bound of f instead of f itself due to the lack of information in it. That is, determine W₁and W₂, to maximize

f1=logdet(IN1+P2N2σn2H1RW2HR2HR2HW2HH1RH(IN1+H1RW1W1HH1RH+H1RW2W2HH1RH)-1)+logdet(IN2+P1N1σn2H2RW1HR1HR1HW1HH2RH(IN2+H2RW1W1HH2RH+H2RW2W2HH2RH)-1)subjecttoP1N1tr{W1HR1HR1HW1H}+σn2tr{W1W1H}+P2N2tr{W2HR2HR2HW2H}+σn2tr{W2W2H}=PR(3)

as shown in Equation (2).

In the second case, the CSI of channels from Node, to the RN, from the RN to Node_j, and from Node_ito Node_j, are assumed to be available to the RN, i,j≠1,2 and i≠j. In this scenario, the design problem is to maximize (1) subject to (2).

By the singular value decomposition (SVD) theorem, the channels (links) can be decomposed to H_R1=U_R1A_R^1/2V_R1^H, H_R2=U_R2A_R2^1/2V_R2^H, H_1R=U_1RA_1R^1/2V_1R^Hand H_2R=U_2RA_2R^1/2V_2R^{H, where U}_R1,U_R2,V_1R,V_2R∈C^LR×LR, V_R1,U_1R∈C^L1×L1, and V_R2,U_2R∈C^L2×L2 are unity matrices; A_ij^1/2∈C^Li×Lj, i, j=1,2,R, are singular value matrices. In particular, A_ij=A_ij^1/2(A_ij^1/2)^H=diag{λ_ij,k}∈C^Li×Li, i, j=1,2,R, where ()^Tand ()^Hrepresent the matrix transpose and conjugate transpose operations, respectively. Also define T=V_1R^H_RV_2R∈C^LR×LR and denote T=(t_ij), i, j=1, . . . , L_R.

When the CSI of direct links between Node₁and Node₂is not available, let W₁=V_2R{tilde over (W)}₁U_R1^Hand W₂=V_1R{tilde over (W)}₂U_R2^H, where {tilde over (W)}₁, {tilde over (W)}₂∈C^LR×LR are to be determined. There is no closed form solution. But {tilde over (W)}_land {tilde over (W)}₂can be solved iteratively using Newton's method.

Furthermore, the problem statement can be rewritten in the following form, where the notation will be explained after the approach is introduced.

Determine λ, to minimize f₂(λ)   (4)

subject to λ≧0,   (5)

Sλ=q.   (6)

The Lagrangian function is L(λ, μ)=f₂(λ) −μ^T(Sλ−q),   (7)

where μ, is the vector containing the Lagrangian multipliers. Using Newton's method, the following iterative approach is used to solve for λ:

Step 1: Initiate λ⁰∈(0,max_λ).

Step 2: In each iteration, solve

[∇2f2(λk)-ST-S0]vk=[STμk-∇f2(λk)Sλk-q]forvk=(vλkvμk).(8)

Step 3: Take as next iteration

(λk+1μk+1)=(λkμk)+(vλkvμk).(9)

Step 4: If sum(sign(λ^k+1))≠length(λ^k+1) or sum(sign(max_λ−λ^k+1))≠length(λ^k+1), go back to Step 1. Otherwise, go to Step 5.

Step 5: If ∥v_λ^k∥²<Threshold, stop. Otherwise, k=k+1, and go to Step 2.

In Step 4, given x=(x₁, . . . , x_M)^Tis a column vector or length M, length(x)=M and

sum(x)=∑i=1length(x)xi·sign(x)={1,ifx>00,ifx=0-1,ifx<0,andsign(x)=(sign(x1),…,sign(xM))T.

Condition α₁is defined as “when L_i≧L_R, or when both L_i<L_Rand L_i(L_i−1)≧L_Rare satisfied”, and condition β_iis defined as “when both L_i<L_Rand L_i(L_i−1)≦L_R−1 are satisfied”. Therefore, there are three cases of solution as follows:

General Case 1: When α₁and α₂exist, both {tilde over (W)}₁and {tilde over (W)}₂are identity matrices multiplied by constants, respectively, i.e., {tilde over (W)}₁=λ₁I_LR, {tilde over (W)}₂=λ₂I_LR, λ₁, λ₂≧0. The notation in the iterative approach is as follows:

λ=(λ1,λ2)T,max_λ=(PR/daσn2,PR/dbσn2)T,µ=μandvk=(vλ1k,vλ2k,vμk)T.S=(da,db),q=PR/σn2,whereca,i=P1L2σn2λR1,i+1,cb,i=P2L2σn2λR2,i+1,i=1,…,M,da=∑i=1Mca,i,

db=∑i=1Mcb,i,

and M=min, (L₁, L₂, L_R). The Hessian and gradient of f₂(λ) are expressed as following:

∇2f2(λk)=(∂2f2(λk)∂λ2∂2f2(λk)∂λ1∂λ2∂2f2(λk)∂λ1∂λ2∂2f2(λk)∂λ22)and∇f2(λk)=(∂f2(λk)∂λ1∂f2(λk)∂λ2),where∂f2(λ)∂λ1=∑i=1M(-m1,i+m2,i-ca,im3,i+m4,i),∂f2(λ)∂λ2=∑i=1M(-cb,im1,i+m2,i-m3,i+m4,i),∂2f2(λ)∂λ12=∑i=1M(m1,i2-m2,i2+ca,i2m3,i2-m4,i2),∂2f2(λ)∂λ1∂λ2=∑i=1M(cb,im1,i2-m2,i2+ca,im3,i2-m4,i2),∂2f2(λ)∂λ22=∑i=1M(cb,i2m1,i2-m2,i2+m3,i2-m4,i2),andm1,i=λ1R,i1+λ1λ1R,i+λ2cb,iλ1R,i,m2,i=λ1R,i1+λ1λ1R,i+λ2λ1R,i,m3,i=λ2R,i1+λ1ca,iλ2R,i+λ2λ2R,i,m4,i=λ2R,i1+λ1λ2R,i+λ2λ2R,i.

General Case 2: When α_land β₂exist, {tilde over (W)}₁is an identity matrix multiplied by a constant, i.e., {tilde over (W)}=λ₁I_LR, λ₁≧0; while {tilde over (W)}₂=A₂^1/2=diag{λ_2,1^1/2, . . . , λ_2,LR^1/2}, λ_2,i≧0, i=1, . . . , L_R, is a diagonal matrix. The notation in the iterative approach is as follows:

λ=(λ1,λ2,1,…,λ2,LR)T,max_λ=(PR/daσn2,PR/cb,1σn2,L,PR/cb,Mσn2,1LR-MT)T,µ=(μ1,L,μL2(L2-1)+1)T,vk=(vλk,vλ2,1k,L,vλ2,LRk,vμ1k,L,vμL2(L2-1)-1k)T,1N=(1,…,1N).S=[0L2(L2-1)×1S2dacb,1,L,cb,M,01×(LR-M)],q=(0L2(L2-1)×1PR/σn2),whereca,i=P1L1σn2λR1,i+1,cb,i=P2L2σn2λR2,i+1,i=1,L,M,da=∑i=1Mca,i,

and M=min(L₁, L₂, L_R).

And

S2=[Re{s2}Im{s2}]∈RL2(L2-1)×LR,

where Re{·} and Im{·} are the functions which take the real and imaginary parts of the variables, and s₂comes from the linear equations

∑k=1LRλ2,ktki*tkj=0,

1≦i<j≦L₂, i.e.,

s2=(t11*t12t21*t22LtLR-1*tLR,2t11*t13t21*t23LtLR-1*tLR,3MMOMt11*t1,L2t21*t2,L2LtLR-1*tLR,2t12*t13t22*t23LtLR,2*tLR,3MMOMt12*t1,L2t22*t2,L2LtLR,2*tLR,L2MMOMt1,L2-1*t1,L2t2,L2-1*t2,L2LtLR,L2-1*tLR,L2)∈CL2(L2-1)2×LR.∇2f2(λk)=(∂2f2(λk)∂λ12∂2f2(λk)∂λ1∂λ2,1L∂2f2(λk)∂λ1∂λ2,LR∂2f2(λk)∂λ1∂λ2,1∂2f2(λk)∂λ2,12L∂2f2(λk)∂λ2,1∂λ2,LRMMOM∂2f2(λk)∂λ1∂λ2,LR∂2f2(λk)∂λ2,1∂λ2,1L∂2f2(λk)∂λ2,LR2)and,where∂f2∂λ1=∑i=1M(-m1,i+m2,i-ca,im3,i+m4,i),∂f2(λ)∂λ2,j={-cb,jm1,j+m2,j+∑i=1Mtji2(-m3,i+m4,i),1≤j≤M∑i=1Mtji2(-m3,i+m4,i),M+1≤j≤LR,∂2f2(λ)∂λ12=∑i=1M(m1,i2-m2,i2+ca,i2m3,i2-m4,i2),∂2f2(λ)∂λ1∂λ2,j={cb,jm1,j2-m2,j2+∑i=1Mtji2(ca,im3,i2-m4,i2),1≤j≤M∑i=1Mtji2(ca,im3,i2-m4,i2),M+1≤j≤LR,∂2f2(λ)∂λ2,j2={cb,j2m1,j2-m2,j2+∑i=1Mtji2(m3,i2-m4,i2),1≤j≤M∑i=1Mtji4(m3,i2-m4,i2),M+1≤j≤LR,∂2f2(λ)∂λ2,j∂λ2,l=∑i=1Mtji2tli2(m3,i2-m4,i2),1≤j,l≤LR,j≠l,m1,i=λ1R,i1+λ1λ1R,i+λ2cb,iλ1R,i,m2,i=λ1R,i1+λ1λ1R,i+λ2λ1R,i,m3,i=λ2R,i1+λ1ca,iλ2R,i+∑k=1LRλ2,ktki2λ2R,i,m4,i=λ2R,i1+λ1λ2R,i+∑k=1LRλ2,ktki2λ2R,i.