4.1 Downlink Interference Control of LAA-LTE for Coexistence with Asym-
4.1.4 Effective Channel Model for LAA-WLAN Coexistence
4.1.4.3 Effective Channel Model from an eNB to an AP
LTE’s symbol and that of the considered Wi-Fi’s symbol, as shown in Fig. 30. We first perform a case study for the variableτ, and then derive the throughput treating it as a random variable.
For the frequency-domain CCA, an AP senses signals for the Wi-Fi’s OFDM symbol duration.
Thus, we derive the LAA-LTE’s signal received at an AP for the duration of one Wi-Fi’s OFDM symbol.
There are two cases depending on how a Wi-Fi’s OFDM symbol duration overlaps with multiple LAA-LTE’s OFDM symbols as follows:
• Case 1 (0≤τ < TtotalL −TtotalW ): a Wi-Fi’s symbol duration is overlapped with only one LAA-LTE’s symbol as in Fig. 30(a).
• Case 2 (−TtotalW ≤τ <0): two LAA-LTE’s symbols are overlapped with a Wi-Fi’s symbol duration as in Fig. 30(b).
4.1.4.3.1 Case 1 In Fig. 30(a), an AP obtains NCPW samples and NFFTW samples from xLm(t) for the CP duration and for the data duration, respectively. With the sample index n, the sampled points from xLm(t) are written as
sL[n] =xLm(t) t=n·TW
total/NtotalW +τ, n∈[0, NtotalW −1]
=
NFFTL −1
X
k=0
aLm,kb n·TtotalW
NtotalW +τ;fkL, TCPL , TdataL
!
, (55)
(a)0≤τ < TtotalL −TtotalW
(b) −TtotalW ≤τ <0
Figure 30: Received signal at an AP for eachτ case. The blue box means the cyclic prefix, and the white box is the data.
whereNtotalW =NCPW +NFFTW . The vector form of (55) is defined as sL,KeNB,AP×aL,
whereaL= [aLm,0, . . . , aLm,NL
FFT−1]T and sL= [sL[0], . . . ,
sL[NtotalL −1]]T, whereNtotalL =NCPL +NFFTL . The matrixKeNB,AP is defined as KeNB,AP
(n+1,k+1)=b n·TtotalW
NtotalW +τ;fkL, TCPL , TdataL
! ,
for n∈[0, NtotalW −1]andk∈[0, NFFTL −1].
4.1.4.3.2 Case 2 In Fig. 30(b), the(m−1)-th LAA-LTE’s symbol is overlapped for the index
0≤ nTtotalW
NtotalW <|τ| ⇐⇒n= 0, . . . ,
&
|τ|NtotalW TtotalW
'
−1,Nτ, while the m-th LAA-LTE’s symbol is overlapped for the sample index
|τ| ≤ n·TtotalW
NtotalW < TtotalW ⇐⇒n=Nτ+ 1, . . . , NtotalW .
Thus, the NtotalW samples of the LAA-LTE’s symbols are obtained as follows. For n ∈ [0, Nτ], sL[n]is derived as
sL[n] =xLm−1(t) t=n·TW
total/NtotalW +TtotalL −|τ|
=
NFFTL −1
X
k=0
aLm−1,kb nTtotalW
NtotalW +TtotalL −|τ|;fkL, TCPL , TdataL
!
. (56)
Forn∈[Nτ + 1, NtotalW −1], we have sL[n] =xLm(t)
t=n·TW
total/NtotalW −|τ|
=
NFFTL −1
X
k=0
aLm,kb n·TtotalW
NtotalW − |τ|;fkL, TCPL , TdataL
!
. (57)
In the vector form with (56) and (57), we have sL,KeNB,AP×aL=
Kτ
K1−τ
aL, (58) wheresL= [sL[0], . . . , sL[Nτ]sL[Nτ+1], . . . , sL[NtotalW −1]]TandaL= [aLm−1,0, . . . , aLm−1,NL
FFT−1aLm,0, . . . , aLm,NL
FFT−1]T. In (58),Kτ and K1−τ are defined as follows:
[Kτ](n+1,k+1)=b n·TtotalW
NtotalW +TtotalL −|τ|;fkL, TCPL , TdataL
!
for n∈[0, Nτ]and k∈[0, NFFTL ], and [K1−τ](n−N
τ,k+1)=b n·TtotalW
NtotalW − |τ|;fkL, TCPL , TdataL
!
for n∈[Nτ + 1, NFFTW ]and k∈[0, NFFTL ].
4.1.4.3.3 Frequency-Domain Effective Channel Matrix To take into account the effect of the channel impulses on the received signal, we denote the discrete-time-domain channel matrix from the eNB to the α-th AP as H˜eNB,APα ∈CNFFTW ×NtotalW , where
H˜eNB,APα
=
NCPW−Ntap+1
z }| {
0· · ·0 νNeNB,APtap α · · · ν1eNB,APα . .. . .. . ..
νNeNB,APα
tap · · · ν1eNB,APα
.
Then, the eNB’s signal received at the α-th AP is expressed by
rL= ˜HeNB,APα×sL= ˜HeNB,APαKeNB,AP×aL. (59)
By multiplying both sides of (59) withFW∈CNFFTW ×NFFTW , the FFT matrix of Wi-Fi, we obtain the frequency-domain received signal at the AP as
FW×rL=FWH˜eNB,APαKeNB,AP×aL.
As a result, in the frequency domain, the effective channel matrix from the eNB to theα-th AP can be defined as follows.
HeNB,APα =FWH˜eNB,APαKeNB,AP. (60) 4.1.4.3.4 Results of the Effective Channel Matrices Fig. 51 shows the channel model for the heterogeneous PHY link, i.e., the channel model from an eNB to AP and from an AP to UE, where the transmitter and receiver have different sets of PHY parameters. Specifically, Fig. 51 presents the square of the absolute value of each element of the derived effective channel matrices,HeNB,APα andHAPα,UE, averaged over the timing difference variablesτ1 and τ. Here, τ1 and τ are assumed to be uniformly distributed over [0,3.3 µs] and [−TtotalW , TtotalL −TtotalW ], respectively. The results show the interference from each LAA-LTE’s subcarrier (or each Wi-Fi’s subcarrier) to all the Wi-Fi’s subcarriers (or all the LAA-LTE’s subcarriers). For comparison, the channel model for the homogeneous PHY link, i.e., the channel model from an eNB to UE and from an AP to STA, is evaluated in Fig. 32, where the transmitter and receiver have the same PHY parameters. Specifically, Fig. 32 shows the square of the absolute value of each element of the derived effective channel matrices, HeNB,UE andHAPα,STA, which can be obtained by (49).
We consider Ntap= 16, where the long-term gain of each channel tap exponentially decreases, and where OFDM parameters of LAA-LTE and Wi-Fi are set in Table 8.
The left figures of Fig. 51(a), Fig. 51(b), Fig. 32(a), and Fig. 32(b) show the results for all the LAA-LTE’s and Wi-Fi’s subcarriers, while the right ones present the enlarged results for specific ranges. Note that the guard subcarriers part [66] of LAA-LTE is omitted from the figures.
In Fig. 51(a), the whole range result presents that an LAA-LTE’s subcarrier at transmission affects some Wi-Fi’s subcarriers around itself at reception. Specifically, from the right figure, an LAA-LTE’s subcarrier at transmission has the effect on one or two Wi-Fi’s subcarriers at reception. The LAA-LTE’s subcarriers at transmission, which are close to the center frequency of Wi-Fi, affect mostly a single Wi-Fi’s subcarrier at reception. As an LAA-LTE’s subcarrier at transmission moves away from the center frequency of Wi-Fi, however, the LAA-LTE’s subcarrier at transmission starts to interfere with two Wi-Fi’s subcarriers around itself at reception. On other other hand, as shown in Fig. 32(a), it is confirmed that an LAA-LTE’s subcarrier at transmission affects a single LAA-LTE’s subcarrier at reception with the same subcarrier index.
In Fig. 51(b), a similar tendency as in Fig. 51(a) is observed. In addition, the right figure of Fig. 51(b) presents that a Wi-Fi’s subcarrier at transmission interferes with several LAA-LTE’s subcarriers at reception, which is reasonable since the subcarrier spacing of Wi-Fi is larger than that of LAA-LTE. Specifically, a Wi-Fi’s subcarrier at transmission strongly affects around 21
(a) Averaged squared absolute values ofHeNB,APα
(b) Averaged squared absolute values ofHAPα,UE
Figure 31: Interference between LAA-LTE’s subcarriers and Wi-Fi’s subcarriers.
LAA-LTE’s subcarriers at reception. On the other hand, the right figure of Fig. 32(b) shows a Wi-Fi’s subcarrier at transmission affects a single Wi-Fi’s subcarrier at reception with the same subcarrier index.
From the simulation results, it has been confirmed that a single Wi-Fi’s subcarrier at trans- mission affects multiple LAA-LTE’s subcarriers at reception, whereas a single Wi-Fi’s subcar- rier (or a single LAA-LTE’s subcarrier) at transmission affects only its corresponding Wi-Fi’s subcarrier (or its corresponding LAA-LTE’s subcarrier) at reception. Therefore, the signal-to- interference-plus-noise ratio (SINR) for the homogeneous PHY link can be separately formulated
(a) Averaged squared absolute values ofHeNB,UE
(b) Averaged squared absolute values ofHAPα,STA
Figure 32: Interference between LAA-LTE’s subcarriers and between Wi-Fi’s subcarriers.
for each subcarrier, whereas the SINR of LAA-LTE (or Wi-Fi) per subcarrier for the heteroge- neous PHY link should be formulated by considering the interference from all the subcarriers of Wi-Fi (or LAA-LTE). In addition, since the packet structures of LAA-LTE and Wi-Fi are different from each other, a careful consideration of the symbol synchronization issue is also needed for the heterogeneous PHY link as done in Section 4.1.4.2 and 4.1.4.3.