Fig.1 The multicell processing model with two cells and two users
Abstract：In the scenario of downlink multicell processing with finite backhaul capacity in the case of two base stations and two mobile users, by regarding the channel as a multiple access diamond channel with two destinations, an achievability scheme that sends correlated codewords through the multiple access channel with common data is proposed. By considering the superposition structure, fully correlated codewords can be supported by the proposed scheme, which can benefit the system throughput in the case of a relatively-large-capacity backhaul. First, an achievable region for the achievable theory is given and it is proved from the perspective of information theory. Then, in the Gaussian scenario, a simulation combining dirty-paper coding and power allocating is provided for the achievable region. Simulation results demonstrate that when the backhaul capacity is relatively large, the proposed scheme outperforms the existing achievability scheme without the superposition structure.
Keywords：multicell processing; finite backhaul capacity; superposition; dirty-paper coding; power allocating
In cellular networks, multicell processing is a promising technique that allows for the joint processing of different base stations’ (BSs’) signals for the downlink or uplink, which increases the throughput of cellular systems[1-2]. Traditionally, in the scenario of downlink multicell processing, the experiment has been carried out under the assumption that all the base stations in the network obtain the data for all users via unlimited capacity links between the BSs and the central processor (CP)[3]. In this case, the cellular network forms a distributed MIMO broadcast channel which can improve the system throughput greatly[4]. However, the BSs communicate with the CP via finite-capacity backhaul in many practical scenarios[5]. The limited capacity backhaul links may not always suffice for the transmitting of the data of all the users from the CP to all the BSs, and as a result, the limited capacity backhaul links may become a bottleneck of network throughput. Therefore, it is interesting to investigate how to make the best use of finite-capacity backhaul links.
Several achievability schemes have been proposed for downlink multicell processing with finite-capacity backhaul. Ref.[6] proposed a compressed dirty-paper coding (DPC) scheme, where signals are precoded and compressed in the CP and then transmitted to the BSs. Improvements on this scheme were made in Ref.[7] by considering multivariate compression to introduce correlation between the quantization noises. A data sharing scheme was proposed in Ref.[8], where the message for each user from the CP is split into two types, consisting of private data intended for a single BS and common data intended for all BSs. In Ref.[9], a hybrid strategy combining the compression and data-sharing strategies was proposed, where messages for some users are sent directly to the BSs using part of the backhaul capacity while messages for the remaining users are precoded and compressed before being transmitted to the BSs using the rest of the backhaul capacity. A reverse compute-and-forward (RCoF) scheme was proposed in Ref.[10], where the limited backhaul is used to transmit the linear combinations of the precoded messages over a finite field. The achievability scheme proposed in Ref.[11] combines Marton’s achievability for the broadcast channel[12]and the achievability of sending correlated codewords over a multiple access channel[13]. The CP transmits the index information of correlated codewords to BSs via the finite-capacity backhaul link. Numerical results show that this scheme outperforms schemes proposed in Refs.[7,10] in certain cases.
In this paper, aiming at studying the two-cell downlink multicell processing problem, enlightened by the achievability scheme in Refs.[14-15], an achievability scheme was proposed, which is similar to the achievability scheme in Ref.[11], except that superposition coding is introduced. Ref.[14] shows that the achievability scheme with superposition outperforms the achievability scheme without superposition when the backhaul capacity is relatively large, since the superposition scheme can fully support correlated codewords while the non-superposition scheme cannot. Technically, similar to Ref.[11], by treating the problem as a Gaussian multiple access diamond channel with two destinations, our scheme can be viewed as the extension of the achievability scheme in Ref.[14]. More specifically, an inner codebook containing parts of the messages decoded by both BSs is introduced, which serves as common data. Four outer codebooks are then generated, two of which correspond to the remaining part of the message and two that correspond to two BSs. The BSs send correlated codewords along with the common data into the multiple access channel with two destinations. Since the superiority of the achievability scheme in Ref.[11] over other existing schemes for certain cases lies in its exploiting the gain of correlation between the transmitted signals from the BSs, our achievability scheme outperforms that of Ref.[11] when the backhaul link capacity is relatively large, due to the fact that with the introduction of superposition coding, more correlation between the transmitted signals from two BSs are supported. This is demonstrated through numerical results.
The following channel model is considered, which is named the two-destination multiple access diamond channel[4]. The capacity link from the CP to BSkisCk,k=1,2. The channel between the two BSs and the two mobile users (MUs) is characterized byp(y1,y2x1,x2) with input alphabets (X1,X2) and output alphabets (Y1,Y2). The system model is depicted in Fig.1.
Fig.1 The multicell processing model with two cells and two users
LetW1andW2be two independent messages transmitted from the CP to MU1 and MU2, respectively. Assume thatWkis uniformly distributed on {1,2,…,Mk},k=1,2. An (M1,M2,n,εn) code consists of an encoding function at the CPfn:{1,2,…,M1}×{1,2,…,M2}→{1,2,…,2nC1}×{1,2,…,2nC2}, two encoding functions at the two BSs
:{1,2,…,2nCk}→
,k=1,2, and two decoding functions at the MUs
:
→{1,2,…,Mk},k=1,2. The average probability of error is defined as
Pr[
(
)≠w1or
(
)≠w2W1=w1,W2=w2]
Rate pair (R1,R2) is said to be achievable if there is a sequence of (2nR1,2nR2,n,εn) codes such thatεn→0 asn→∞. The capacity region of the two-destination multiple access diamond channel is the closure of the set of all rate pairs.
For the two-destination Gaussian multiple access diamond channel,X1=X2=Y1=Y2=Rand the channel between the two BSs and each MU is a Gaussian multiple access channel. Thus, the received signal at the MUs are
Y1=X1+aX2+Z1
(1)
Y2=bX1+X2+Z2
(2)
whereX1andX2are the input signals from BSs 1 and 2, respectively, andZ1,Z2are two independent zero-mean unit-variance Gaussian random variables. It is assumed that (Z1,Z2) is independent of (X1,X2).The encoding functions at the two BSs must satisfy the average power constraints. For any
that BSksends to the Gaussian multiple access channel, it satisfies
Theorem 1 is the main result of this paper, which provides an achievable region for the two-destination multiple access diamond channel. By introducing the superposition structure, an inner codebook of correlated codewords is generated and the message index of this codebook is transmitted to both BSs. As a result, it forms common data at the two BSs, and they can beamform the common data to both receivers.
Theorem1 Rate pair (R1,R2) is achievable for the two-destination multiple access diamond channelp(y1,y2x1,x2) with parametersC1,C2,Q10,Q20if it satisfies
R1≤I(U0,U1,U2;Y1)-I(U1,U2;V0U0)
(3)
R1≤I(U1,U2;Y1
U0)
(4)
R1≤ C1+I(U1;V0
V0)+
I(U1;V1
U1,U0)-
I(U1,U2;V0U0)-Q20
(5)
R1≤ C2+I(U2;V0
V0)+
I(U2;V2
U2,U0)-
I(U1,U2;V0U0)-Q20
(6)
R2≤ I(V0,V1,V2;Y2)-I(V1,V2;U0V0)
(7)
R2≤I(V1,V2;Y2
V0)
(8)
R2≤ C1+I(U1;V0V0)+
I(U1;V1
V1,U0)-
I(V1,V2;U0V0)-Q10
(9)
R2≤C2+I(U2;V0V0)+
I(U2;V2
V2,U0)-
I(V1,V2;U0V0)-Q10
(10)
R1+R2≤ I(U0,U1,U2;Y1)+I(V0,V1,V2;Y2)-
I(U1,U2;V0
V0)-
I(U1,U2;V1,V2U0,V0)-I(U0;V0)
(11)
R1+R2≤ I(U1,U2;Y1U0)+Q10+I(V0,V1,V2;Y2)-
I(U1,U2;V0V0)-
I(U1,U2;V1,V2U0,V0)
(12)
R1+R2≤ I(U0,U1,U2;Y1)+I(V1,V2;Y2V0)+Q20-
I(U1,U2;V0V0)-
I(U1,U2;V1,V2U0,V0)
(13)
R1+R2≤ I(U1,U2;Y1
V0)+
Q20-I(U1,U2;V0V0)-
I(U1,U2;V1,V2U0,V0)
(14)
R1+R2≤ C1+I(U1;V0V0)+
I(U1;V1U1,U0)+
I(V2;Y2
U0)-
I(V1,V2;U0
U0,V0)
(15)
R1+R2≤ C2+I(U2;V0V0)+
I(U2;V2U2,U0)+
I(V1;Y2
U0)-
I(V1,V2;U0U0,V0)
(16)
R1+R2≤ C1+I(U1;V0V0)+
I(U1;V1
U0)+
I(V2;U0
U0,V0)-
I(U1;U2
V0)-
I(U1,U2;V0V0)-
I(U1,U2;V1,V2U0,V0)-Q10-Q20
(17)
I(U1;V0U0)+I(V1;U0
U0,V0)≤
I(U1;Y1,U2
U0)
(18)
I(U2;V0U0)+I(V2;U0U0,V0)≤
I(U2;Y1,U1
U0)
(19)
for some distributionp(u0,u1,u2,v0,v1,v2)p(x1
u0,u2,v0,v2), and someQ10andQ20that satisfy (Q10+Q20)≤min{C1,C2} andQk0≥0,k=1,2.
A brief outline of the proof of Theorem 1 is as follows: The CP uses a codebook of the superposition structure, where (Q10+Q20) is the rate of the inner codebook. More specifically, fork=1,2, the CP splits messageMkinto three parts, i.e.,Mk0with rateQk0,Mk1with rate (Rk1-rk1) andMk2with rate (Rk2-rk2). The CP encodesM10andM20into the inner codebook of correlated codewords, and delivers the corresponding codeword index to both BSs. Then, the CP encodes the remaining parts of the two messages into four outer codebooks.
The CP encodesMk1andMk2into an outer codebook, which contains correlated codeword pairs,k=1,2. This codebook along with the inner codebook will be used by MUkin decodingMk0,Mk1,Mk2.
The CP encodesM1kandM2kinto another outer codebooks containing correlated codeword pairs,k=1,2. This codebook along with the inner codebook will be used by BSkto find the corresponding codeword
to be sent to the multiple access channel with two destinations,k=1,2.
The details of the proof of Theorem 1 are provided as follows. Based on a given distribution, the proof consists of four basic steps named codebook generation, encoding, decoding, and probability of error analysis.
A distributionp(u0,u1,u2,v0,v1,v2)p(x1
u0,u2,v0,v2) is fixed and the following proof will be based on this distribution.
The first part of the proof is codebook generation. Generate 2n(R10-r10)codebooksCU0(i0), each consisting of
sequences, in an i.i.d. fashion according top(u0), wherei0∈[1:2n(R10-r10)]. Index each codeword as
(i0,l0), wherel0∈[1:2nr10]. Similarly, generate 2n(R20-r20)codebooksCV0(j0), each consisting of
sequences, in an i.i.d. fashion according top(v0), wherej0∈[1:2n(R20-r20)]. Index each codeword as
(j0,m0), wherem0∈[1:2nr20]. Let
Qk0=Rk0-rk0 k=1,2
(20)
For each
(i0,l0) sequence wherei0∈[1:2nQ10],l0∈[1:2nr10], generate 2n(R1k-r1k)codebooksCUk|U0(i0,l0,ik) fork=1,2, each consisting of
sequences, in a conditional i.i.d. fashion according top(uk|u0), whereik∈[1:2n(R1k-r1k)]. Label these
sequences as(i0,l0,lk),lk∈[(ik-1)2nr1k:ik2nr1k]. Furthermore, for each (i0,l0,i1,i2), find all codeword pairs (
,
) that are jointly typical conditioned on(i0,l0) according top(u1,u2u0), where∈CU1|U0(i0,l0,i1) and∈CU2|U0(i0,l0,i2). The set of all codeword pairs found is denoted asCU1,U2|U0(i0,l0,i1,i2). According to Ref.[15],the number of such codeword pairs is lower bounded by 2n(r11+r12-I(U1;U2|U0)).
Similarly, for each(j0,m0) sequence wherej0∈[1:2nQ20],m0∈[1:2nr20], generates 2n(R2k-r2k)codebooksCVk|V0(j0,m0,jk) fork=1,2, each consisting of
sequences, in a conditional i.i.d. fashion according top(vkv0), wherejk∈[1:2n(R2k-r2k)]. Label these
sequences as(j0,m0,mk),mk∈[(jk-1)2nr2k:jk2nr2k]. Furthermore, for each (j0,m0,j1,j2), find all codeword pairs (
,
) that are jointly typical conditioned on(j0,m0) according top(v1,v2|v0), where∈CV1|V0(j0,m0,j1) and∈CV2|V0(j0,m0,j2). The set of all codeword pairs found is denoted asCV1,V2|V0(j0,m0,j1,j2). According to Ref.[15],the number of such codeword pairs is lower bounded by 2n(r21+r22-I(V1;V2|V0)).
For each pair (i0,j0), find a jointly typical sequence pair (,) according top(u0,v0), where∈CU0(i0) and∈CV0(j0). According to mutual covering lemma in Ref.[1], there exists such a jointly typical pair if
r10+r20≥I(U0;V0)
(21)
If there are such multiple codeword pairs, pick one pair randomly, and then label the codeword pair found as ((i0,
(i0,j0)),
(j0,
(i0,j0))). Consequently, 2n(Q10+Q20)such (,) pairs which form the inner codebookCU0V0are obtained.
For each (i0,j0,i1,i2,j1,j2), wherei0∈[1:2nQ10],j0∈[1:2nQ20],ik∈[1:2n(R1k-r1k)],jk∈[1:2n(R2k-r2k)],k=1,2, the following steps are performed:
Step1 Find all codeword pairs (
,
)∈CU1,U2U0(i0,
(i0,j0),i1,i2) that are jointly typical with(j0,
(i0,j0)) conditioned on(i0,(i0,j0)) according top(u1,u2,v0u0). The set of such codeword pairs is denoted asCU1,U2U0,V0(i0,j0,i1,i2). According to Ref.[15], the number of such codeword pairs is lower bounded by 2nr1, where
r1=r11+r12-I(U1;U2U0)-I(U1,U2;V0U0)
(22)
Note that it requiresr1>0.
Step2 Find all codeword pairs (,)∈CV1,V2V0(j0,(i0,j0),j1,j2) that are jointly typical with(i0,(i0,j0)) conditioned on(j0,(i0,j0)) according top(v1,v2,u0v0). The set of such codeword pairs is denoted asCV1,V2U0,V0(i0,j0,j1,j2). According to Ref.[15], the number of such codeword pairs is lower bounded by 2nr2, where
r2=r21+r22-I(V1;V2V0)-I(V1,V2;U0V0)
(23)
Note that it requiresr2>0.
Step3 Fork=1,2, find all codewords
∈CUkU0(i0,(i0,j0),ik) that are jointly typical with(j0,(i0,j0)) conditioned on(i0,(i0,j0)) according top(uk,v0u0). The set of such codewords is denoted asCUkU0,V0(i0,j0,ik). Similarly, find all codewords∈CVkV0(j0,(i0,j0),jk) that are jointly typical with(i0,(i0,j0)) conditioned on(j0,(i0,j0)) according top(vk,u0v0). The set of such codewords is denoted asCVkU0,V0(i0,j0,jk). Furthermore, find all codeword pairs (,) that are jointly typical conditioned on ((i0,(i0,j0)),(j0,(i0,j0))) according top(uk,vku0,v0), where∈CUkU0,V0(i0,j0,ik),∈CVkU0,V0(i0,j0,jk). Denote such codeword pairs found asCUk,VkU0,V0(i0,j0,ik,jk). According to [15], the number of codeword pairs inCUk,VkU0,V0(i0,j0,ik,jk) is upper bounded by 2n(rUVk+ε), where
rUVk= r1k-I(Uk;V0U0)+r2k-I(Vk;U0V0)-
I(Uk;VkU0,V0)
(24)
It also requiresrUVk≥0, fork=1,2.
Step4 Fork=1,2, for each codeword pair (,) inCUk,VkU0,V0(i0,j0,ik,jk), generate ansequence in a conditional i.i.d. fashion according to the distributionp(xkuk,vk,u0,v0).
Now, we describe the encoding procedure. At the central processor, messageWk(k=1,2) is split into (Wka,Wkb,Wkc), whereWka,WkbandWkcare uniformly distributed on {1,2,…,2nQk0}, {1,2,…,2n(Rk1-rk1)} and {1,2,…,2n(Rk2-rk2)}, respectively. When
(Wka,Wkb,Wkc)=(wka,wkb,wkc) k=1,2
the central processor inspectsCU1,U2U0,V0(w1a,w2a,w1b,w1c) andCV1,V2U0,V0(w1a,w2a,w2b,w2c) for a codeword quadruple (,,
,
) that are jointly typical conditioned on ((w1a,(w1a,w2a)),(w2a,(w1a,w2a))) according to the distributionp(u1,u2,v1,v2u0,v0). Let the found quadruple be denoted by (
,
,
,
). If no such quadruple can be found, the central processor sends 1 to both BSs 1 and 2.
Since joint typicality implies marginal typicality, (
,
) is in codebookCU1,V1U0,V0(w1a,w2a,w1b,w2b), and similarly, (
,
) is in codebookCU2,V2U0,V0(w1a,w2a,w1c,w2c). The central processor sends (w1a,w2a,w1b,w2b) and the row index of (,) inCU1,V1U0,V0(w1a,w2a,w1b,w2b) to BS 1. It also sends (w1a,w2a,w1c,w2c) and the row index of (,) inCU2,V2U0,V0(w1a,w2a,w1c,w2c) to BS 2. It requires that
(25)
so that each BS can receive its index with no error.
At the BS， upon receiving (w1a,w2a,w1b,w2b) and the row index of (,) inCU1,V1U0,V0(w1a,w2a,w1b,w2b), BS 1 identifies the (,) inCU1,V1U0,V0(w1a,w2a,w1b,w2b) and sends the corresponding
as its transmitted signal. Similarly, upon receiving (w1a,w2a,w1c,w2c) and the row index of (,) inCU2,V2U0,V0(w1a,w2a,w1c,w2c), BS 2 identifies (,) inCU2,V2U0,V0(w1a,w2a,w1c,w2c) and sends the corresponding
as its transmitted signal.
The third part of proof is decoding. Upon receiving
, if there is a unique codeword triple ((
,
),(,,
),(,,
)) where ((,,),(,,)) is inCU1,U2U0(,,
,
) for some (,), such that
,),(,,),(,,),) is jointly typical according top(u0,u1,u2,y1), then, the receiver of MU 1 declares that (W1a,W1b,W1c)=(,,) is sent; otherwise, it declares an error.
Receiver 2 performs a similar decoding scheme as Receiver 1 when receiving
,which will not be described in details for simplicity.
The probability of error analysis, which is the final part of the proof, will present relative error events and the analysis for them. Due to symmetry, the average probability of error is equivalent to the probability of error for an arbitrary message pair (w1,w2), where (w1,w2)∈{1,2,…,2nR1}×{1,2,…,2nR2}. Hence, without loss of generality, it is assumed that (W1,W2)=(
,
) is sent. ForW1=andW2=, denote (W1a,W1b,W1c)=(
,
,
) and (W2a,W2b,W2c)=(
,
,
), respectively.
First, consider the error eventE0, where no jointly typical quadruple (,,,) conditioned on ((,(,)),(,(,))) can be found inCU1,U2U0,V0(,,,) andCV1,V2U0,V0(,,,). By the mutual covering lemma[16], Pr[E0] approaches zero asn→∞ if
r1+r2≥I(U1,U2;V1,V2U0,V0)
(26)
Given thatE0does not occur, denote the jointly typical quadruplet found by CP as (,,,), which is short for ((
,
,
),(,,
),(
,
,
),(,,
)), then consider the following error events for MU1:
E10: ((,
),,,) is not jointly typical.
E11: There exists a∈CU1U0(,,i1), denoted as(,,l1). For somei1∈[1:2n(R11-r11)] such that ((,),(,,l1),,) is jointly typical, and(,),l1)≠, i.e.,l1≠
.
E12: There exists a∈CU2U0(,,i2), denoted as(,,l2). For somei2∈[1:2n(R12-r12)]such that ((,),,(,,l2),) is jointly typical, and(,,l2)≠, i.e.,l2≠
.
E13: There exists a (,)∈CU1,U2U0(,),i1,i2), denoted as ((,,l1),(,,l2)). For someik∈[1:2n(R1k-r1k)],k=1,2, such that ((,),(,,l1),(,,l2),) is jointly typical, and(,,l1)≠,(,,l2)≠, i.e.,l1≠,l2≠.
E14: There exists a ((i0,l0),(i0,l0,l1),(i0,l0,l2)), where (,)∈CU1,U2U0(i0,l0,i1,i2). For someik∈[1:2n(R1k-r1k)],k=1,2, such that ((i0,l0),(i0,l0,l1),(i0,l0,l2),) is jointly typical, and (i0,l0)≠(,).
At MU2, symmetric eventsE20,E21,E22,E23may occur and the description for them, which will not be presented here, is similar to the above description forE10,E11,E12,E13.
Thus, the probability of error Pr[E] may be upper bounded as
Due to the asymptotic equipartition property, for a sufficiently largen, it leads to Pr[
]≤ε. There is also
Pr[
] =
Pr[(
(
,
),
(,,l1),
,
)∈
2-n(I(U1,U2;Y1|U0)-ε)2n(R11+R12-I(U1;U2|U0)-ε)
Pr[
] =
Pr[(
(i0,l0),
(i0,l0,l1),
2-n(I(U0,U1,U2;Y1)-ε)2n(R10+R11+R12-I(U1;U2|U0)-ε)
Similar derivations follow Pr[E2k|
],k=1,2,3,4.
Thus, Pr[E]tends to zero asn→∞ if conditions (20) to (26) and the following set of constraints are satisfied:
R11≤I(U1;Y1,U2U0)R12≤I(U2;Y1,U1U0)R11+R12≤I(U1,U2;Y1
U0)R10+R11+R12≤I(U0,U1,U2;Y1)+I(U1;U2U0)R21≤I(V1;Y2,V2V0)R22≤I(V2;Y2,V1V0)R21+R22≤I(V1,V2;Y2
V0)R20+R21+R22≤I(V0,V1,V2;Y2)+I(V1;V2V0)
0≤rmk≤Rmk m=1,2,k=0,1,2
0≤Qk0≤Rk0 k=1,2
Rm=Qm0+Rm1-rm1+Rm2-rm2 m=1,2
Using the Fourier-Motzkin elimination, the achievable rates (3) to (19) in Theorem 1 are obtained.
Aiming at a better understanding of Theorem 1, a few remarks are presented:
1) WhenR1=Q10=0, by settingV0=V,V1=X1,V2=X2,Y2=Y,Q20=R0,U0=U1=U2=∅, the lower bound case in Ref.[3] is obtained.
2) By takingU0=V0=∅,Q10=Q20=0, the achievability scheme for the 2-destination multiple access diamond channel in Ref.[4] is obtained.
3) WhenC1andC2tend to infinity, by takingU1=U2=V1=V2=∅,U0=U,V0=V,Q10=R1andQ20=R2, which means that the full cooperation between BSs is achieved with the help of the superposition structure, Marton’s inner bound for the general broadcast channel[5]is obtained.
The achievable region provided by Theorem 1 is for discrete memoryless channels. In this section, by considering the Gaussian nature of the channel, the achievable rate region is computed. First, specify the distributionsp(u0,u1,u2,v0,v1,v2),p(x1
u0,u2,v0,v2). Combining the power allocation strategy[17-18]for superposition coding in Ref.[14] and the dirty-paper strategy in Ref.[11], the following distribution is then proposed for the evaluation of the mutual information terms in Theorem 1.
First, consider zero-mean unit-variance jointly Gaussian random variablesU0,V0with the correlation coefficientρ∈[-1,1]. Then, let
X1=U1+V1=
U0+
+
V0+
(27)
X2=U2+V2=
U0+
+
V0+
,
(28)
whereXkis the codeword with powerPkat BSk,k=1,2, (,
,,
) are Gaussian random variables independent of (U0,V0).A1,B1,A2andB2satisfy
(29)
whereP0kis the power allocated to (U0,V0) at BSk,k=1,2. Next, let
be a 2×1 Gaussian random vector with covariance matrixK
,k=1,2, where
with
A∈[0,P1-P01]
(30)
B∈[0,P2-P02]
(31)
α∈[-
,]
(32)
β∈[-
，]
(33)
Now, the dirty-paper coding is considered, where
is considered as the channel state, i.e., let
′=
and
′=
+A′, where
andand′ are independent. Furthermore, let
and
Based on the 4×4 covariance matrix of,,,and conditions (1), (2), (27) and (28), by computing the sum rates in Theorem 1 under constraints (29) to (33), the optimal sum rate can be obtained.
In the case ofa=b=0.9,P1=P2=1 andC1=C2=C, the achievable sum rate of the proposed superposition scheme is compared to the achievability scheme without the superposition structure in Ref.[4] and some other existing schemes in Fig.2.
The upper bound of min{2C,CMIMO} is denoted by the black dotted line, whereCMIMOis the capacity of the network when the backhaul capacity C is infinite. The red solid line denotes the sum rate of our superposition scheme and the green dashed line denotes the sum rate via the achievability scheme without the superposition structure[11]. The magenta dash-dot line denotes the sum rate of the RCoF scheme in Ref.[10] and the blue solid line with circle markers denotes the sum rate of the compressed DPC scheme considering the correlation between the quantization noises[7]. From Fig.2, it can be seen that in the medium backhaul capacity region, our proposed scheme outperforms the RCoF scheme and compressed DPC scheme. Furthermore, when backhaul capacity C is relatively large, our superposition scheme outperforms the scheme without the superposition structure.
Fig.2 The achievability sum rate vs. capacity of the backhaul link forP=1,a=b=0.9 andC1=C2=C
In this paper, the 2-BS-2-MU scenario of downlink multicell processing is studied. By viewing the problem as a multiple access diamond channel with two destinations, an achievability scheme exploiting the gain of correlation between the transmitted codewords is proposed, where superposition coding is introduced and it contributes to the superiority of the proposed scheme. The numerical simulation shows that the proposed scheme outperforms the existing achievability scheme without superposition coding when the capacities of backhaul link are relatively large. The inner codeword in this paper supports common data known at both BSs, and thus, enables more cooperation between the two BSs. As part of future work, a more involved superposition structure will be considered, where the inner codeword consists of not only the data decodable at both receivers as in the broadcast channel but also the common data sent to both BSs.
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References
摘要：在有限回程链路容量的下行链路多小区处理的场景中,针对2个基站2个用户的情况,通过将信道视为带有2个接收端的多址接入菱形信道,提出了一种可达性策略,将带有公共数据的相关码字传送到信道中．由于考虑了叠加编码的结构,该策略能够支持完全相关的码字,这使得在回程链路容量相对较大的情况下,系统吞吐量能够得到提升．首先给出了该可达性策略的可达域并从信息论的角度进行了证明．然后在高斯场景下,结合脏纸编码方法和功率分配方法,对可达域进行了仿真计算．仿真结果显示,当回程链路容量相对较大时,所提出的策略性能在某些情况下优于已知的未引入叠加编码的可达性策略.
关键词：多小区处理;有限回程链路容量;叠加编码;脏纸编码;功率分配
中图分类号：TN929
JournalofSoutheastUniversity(EnglishEdition) Vol．33，No．3，pp．260⁃265Sept．2017 ISSN1003—7985
DOI:10.3969/j.issn.1003-7985.2017.03.001
Foundationitems：The National Natural Science Foundation of China (No.61571123, 61521061), the Research Fund of National Mobile Communications Research Laboratory of Southeast University (No. 2017A03), Qing Lan Project.
Citation：Yi Xiao, Wu Mingzhan, Liu Nan. A superposition scheme for downlink multicell processing with finite backhaul capacity[J]．Journal of Southeast University (English Edition),2017,33(3):253-259．
DOI：10.3969/j.issn.1003-7985.2017.03.001.