Analysis of Channel Model for LAA-WLAN Coexistence with different OFDM Parameters between LAA and Wi-Fi
aa r X i v : . [ ee ss . SP ] A p r Analysis of Channel Model for LAA-WLANCoexistence with different OFDM Parametersbetween LAA and Wi-Fi
Harim Lee and Hyun Jong Yang,
Member, IEEE
Abstract
In this work, the channel model for the asynchronous Wi-Fi and LAA signals is investigated, alsotaking into consideration the impairment of the OFDM parameters between LAA and Wi-Fi. Even forthe same bandwidth, e.g., 20 MHz channel, OFDM parameters of LAA-LTE and Wi-Fi are different[1], [2]. In addition, the legacy Wi-Fi devices cannot receive or transmit synchronously with LAA-LTE.Thus, the orthogonality between the subcarriers is broken if LAA-LTE’s signals are received at Wi-Fi devices and vice versa. In order to facilitate an analysis of the throughput, we should derive thedistortion of LAA-LTE’s signals received at Wi-Fi devices and the distortion of Wi-Fi’s signals receivedat LAA-LTE devices due to the difference in OFDM parameters of LAA-LTE and Wi-Fi.
Index Terms
License assisted access LTE, channel model for LAA-WLAN Coexistence, impairment of the OFDMparameters between LAA and Wi-Fi
I. E
FFECTIVE C HANNEL M ODEL FOR
LAA-WLAN C
OEXISTENCE
According to each standard of LAA-LTE and Wi-Fi, both technologies adopt the orthogonalfrequency-division multiplexing (OFDM) for each physical-layer but with different numbersof subcarriers, different sampling periods, and different cyclic prefix (CP) and data durationeven in the same bandwidth. Hence, the orthogonality between the subcarriers is broken whenLAA-LTE’s signals are sampled at Wi-Fi devices and also vice versa. Moreover, since the
Harim Lee and Hyun Jong Yang are with the School of Electrical and Computer Engineering, Ulsan National Instituteof Science and Technology (UNIST), Ulsan, 44919, Korea (e-mail: { hrlee,hjyang } @unist.ac.kr). Hyun Jong Yang is thecorresponding author. Fig. 1. Definition of the function b ( t ; f, T , T ) with the cyclic prefix. TABLE IOFDM
PARAMETERS OF
LAA-LTE
AND W I -F I FOR A
20 MH
Z CHANNEL
LAA- Wi-Fi DescriptionLTE (Values for LAA-LTE and Wi-Fi) f L i f W i i -th subcarrier frequency △ f L △ f W Subcarrier spacing (15 kHz and 312.5kHz) T Ldata T Wdata
OFDM symbol duration (66.7 µ s and3.2 µ s) T LCP T WCP
Cyclic prefix duration (4.7 µ s and 0.8 µ s) T Ltotal T Wtotal
Total symbol duration (71.4 µ s and 4 µ s) N LFFT N WFFT
Number of subcarriers (2048 and 64) N LCP N WCP
Number of samples of CP (144 and16) transmission of LAA-LTE and Wi-Fi is initiated in an ad-hoc manner, frame and symbol synchis not guaranteed between LAA-LTE and Wi-Fi. As a result, we cannot derive per-subcarrierthroughput with the previous analysis framework. In this section, we derive an impact of thedifference in the physical-layer parameters on the effective channel.To begin, important OFDM parameters are denoted in Table I [2], [3].
We define the m -th transmit OFDM symbol of an eNB and an AP including CP as x L m ( t ) = N LFFT − X k =0 a L m,k b ( t ; f L k , T LCP , T
Ldata ) , ≤ t < T Ltotal , (1) x W m ( t ) = N WFFT − X k =0 a W m,k b ( t ; f W k , T WCP , T
Wdata ) , ≤ t < T Wtotal , (2)where a L m,k and a W m,k are the message symbols of the m -th subcarrier of LAA-LTE and Wi-Fi,respectively, and b ( · ) is defined as b ( t ; f, T , T ) = exp ( j πf ( t + T − T )) , ≤ t < T , exp ( j πf ( t − T )) , T ≤ t < T + T . (3)The definition of the function b ( · ) is illustrated in Fig. 1. The channel impulse response for the k -th path among N tap paths from the eNB to the α -th AP and from the α -th AP to the UE isdenoted as ν eNB , AP α k and ν AP α , UE k , respectively.Based on the notations, we firstly derive the received signals at an AP and UE, and then derivethe impact of the difference in the physical-layer parameters on the effective channel. A. Motivation of a New Derivation on the Effective Channels
To show the necessity of a new derivation on the effective channels, we start with discussinga transmission between homogeneous Wi-Fi nodes, i.e., the transmission from an AP to a STA.The vector of the message signals in the m -th OFDM symbol are denoted by a W m ∈ C N WFFT × , andthe IFFT and FFT matrices are defined by Q W ∈ C N WFFT × N WFFT and F W ∈ C N WFFT × N WFFT , respectively.In addition, ˜ H AP,STA ∈ C N WFFT × N WFFT is the time-domain circulant channel matrix from the AP tothe STA after the CP removal. Hence, the frequency-domain response is as F W ˜ H AP,STA Q W × a W m = H AP,STA × a W m (4)where H AP,STA = F W ˜ H AP,STA Q W . In general, the effective channel matrix H AP,STA is diagonalsince ˜ H AP,STA is circulant and F W = Q HW . Hence, each subcarrier has no effect on any othersubcarriers due to the orthogonality between the subcarriers in case of the transmission betweenhomogeneous nodes.In the scenario of LAA-WLAN coexistence, however, the subcarrier spacing of LAA-LTEand Wi-Fi is different as in Table I. Since △ f W is larger than △ f L , a Wi-Fi’s subcarrier can overlap with around ⌈ . / ⌉ = 21 LAA-LTE’s subcarriers. According to the overlap, we canintuitively recognize that a Wi-Fi’s subcarrier interferes multiple LAA-LTE’s subcarriers andvice versa. Therefore, the existing effective channel model between homogeneous nodes cannotbe used in the LAA-WLAN coexistence scenario.
B. Effective Channel Model from an AP to a UE
To derive the effective channel model from an AP to a UE, we derive a Wi-Fi’s signal receivedat the UE for the duration of one LAA-LTE’s OFDM symbol. We start with the followingnotations: In Fig. 2, τ is time difference from the starting point of the data part of x L m ( t ) to thatof the CP of x W p +1 ( t ) , where ≤ τ < T Wtotal ; τ is the duration from the starting point of the CPof x W p +1 ( t ) to that of the CP of x W p + M +1 ( t ) , where M is the number of Wi-Fi symbols completelyoverlapped with the data part of x L m ( t ) ; τ is the duration of the part of x W p + M +1 overlapped withthe data part of x L m ( t ) ; τ , CP , τ , CP , and τ , CP denote the duration of the part of x W p − ( t ) , x W p − ( t ) ,and x W p ( t ) overlapped with the CP of x L m ( t ) , respectively; τ , CP = T LCP − ( T Wtotal − τ ) − T Wtotal and τ , CP = T Wtotal − τ ; τ is T Wtotal when τ > . µs or T LCP − ( T Wtotal − τ ) when ≤ τ ≤ . µs .We first perform a case study for the variable τ , where τ , τ , τ , CP , τ , CP , and τ , CP arefunctions of τ , and then derive the throughput treating τ as a random variable. In addition, fornotational simplicity, the AP index is not considered if not essential based on the analogy of thesystem model for every AP.For clarifying possible cases, we denote by M ′ the number of Wi-Fi’s symbols within the CPof x L m ( t ) except for x W p as in Fig. 2. Then, we have M ′ = (cid:6) ( T LCP − ( T Wtotal − τ )) /T Wtotal (cid:7) . Basedon the definition of M ′ and the range of τ , and from Table I, we can obtain two possible cases, M ′ = 2 ( τ > . µs ) and M ′ = 1 ( ≤ τ ≤ . µs ). We shall derive the effective channel onlyfor the case of M ′ = 2 which is a more general case. The derivation for the case of M ′ = 1 can be readily obtained following the analogous derivation for the case of M ′ = 2 .
1) Samples for the CP Duration:
For M ′ = 2 , two symbols x W p − ( t ) and x W p − ( t ) are overlappedwithin the CP duration of the LAA-LTE’s symbol x L m ( t ) as in Fig. 2(a). For the time of [0 , τ , CP ) ,the sample index is obtained by ≤ nT LCP N LCP < τ , CP ⇔ ≤ n < (cid:24) N LCP τ , CP T LCP (cid:25) − , N τ , CP . (5) (a) M ′ = 2 ( τ > . µs )(b) M ′ = 1 ( ≤ τ ≤ . µs )Fig. 2. Received signal at an UE for each τ case. The blue box means the cyclic prefix and the white box is the data duration. Based on (5), the sampled points of x W p − ( t ) are s W m [ n ] = x W p − ( t ) (cid:12)(cid:12) t = n · T LCP /N LCP + T Wtotal − τ , CP (6) = N WFFT − X k =0 a W p − ,k b (cid:18) nT LCP N LCP + T Wtotal − τ , CP ; f W k , T WCP , T
Wdata (cid:19) . (7)For (7), the vector form is written as s W τ , CP , G , CP × a W p − , (8)where s W τ , CP = [ s W m [0] , . . . , s W m [ N τ , CP ]] T and a W p − = [ a W p − , , . . . , a W p − ,N WFFT − ] T . Here, the matrix G , CP is defined by [ G ] ( n +1 ,k +1) = b (cid:18) nT LCP N LCP + T Wtotal − τ , CP ; f W k , T WCP , T
Wdata (cid:19) , (9)for n ∈ [0 , N τ , CP ] and k ∈ [0 , N WFFT − , where [ X ] ( i,j ) denotes the ( i, j ) -th element of the matrix X . For the period τ , the sample index can be obtained as (cid:24) N LCP τ T LCP (cid:25) ≤ n < (cid:24) N LCP ( τ + τ ) T LCP (cid:25) − , N τ , CP , (10)and the sampled points of x W p − ( t ) are s W m [ n ] = x W p − ( t ) (cid:12)(cid:12) t = nT LCP /N LCP − τ , CP (11) = N WFFT − X k =0 a W p − ,k b (cid:18) nT LCP N LCP − τ , CP ; f W k , T WCP , T
Wdata (cid:19) , (12)where the time variable t for each Wi-Fi symbol is reset to 0 at the beginning of each Wi-Fisymbol for notational simplicity, as defined in (2) and shown in Fig. 2(a). Thus, the vector ofthe sampled points of x W p − ( t ) is derived as s W τ , CP , G , CP × a W p − , (13)where s W τ , CP = [ s W m [ N τ , CP + 1] , . . . , s W m [ N τ , CP ]] T and a W p − = [ a W p − , , . . . , a W p − ,N WFFT − ] T . Here, thematrix G is defined by [ G ] ( n +1 ,k +1) = b (cid:18) nT LCP N LCP − τ , CP ; f W k , T WCP , T
Wdata (cid:19) , (14)where n ∈ [ N τ , CP + 1 , N τ , CP ] and k ∈ [0 , N WFFT − . Finally, for the period τ , the sampleindex is calculated by N τ , CP + 1 ≤ n < (cid:24) N LCP ( τ + τ + τ ) T LCP (cid:25) − , N τ , CP , (15)and the vector of the sampled points from x W p ( t ) is derived as s W τ , CP , G , CP × a W p , (16)where s W τ , CP = [ s W m [ N τ , CP +1] , . . . , s W m [ N τ , CP ]] T and a W p = [ a W p, , . . . , a W p,N WFFT − ] T . The matrix G is defined by [ G ] ( n +1 ,k +1) = b (cid:18) nT LCP N LCP − τ , CP − τ , CP ; f W k , T WCP , T
Wdata (cid:19) , (17)for n ∈ [ N τ , CP + 1 , N LCP ] and k ∈ [0 , N WFFT − .
2) Samples for the Data Duration:
To ease notation, we reset the sample index for the data partdue to the difference in the sampling frequencies for the CP and data in LAA-LTE. Specifically, in Fig. 2(a), the p -th Wi-Fi’s symbol x W p is overlapped with the data part of the LAA-LTE’ssymbol, and the sample index is obtained as ≤ nT Ldata N LFFT < τ ⇐⇒ ≤ n < (cid:24) τ N LFFT T Ldata (cid:25) − , N . (18)For the duration [0 , τ ) , the sampled points of x W p ( t ) are written by s W m [ n ] = x W p ( t ) (cid:12)(cid:12) t = nT Ldata /N LFFT + T Wtotal − τ (19) = N WFFT − X k =0 a W p,k b (cid:18) nT Ldata N LFFT + T Wtotal − τ ; f W k , T WCP , T
Wdata (cid:19) , (20)and the vector form of the sampled points is derived as s W τ , G τ × a W p , (21)where a W p = [ a W p, , . . . , a W p,N WFFT − ] T and s W τ = [ s W m [0] , . . . ,s W m [ N ]] T . The matrix G τ is defined by [ G τ ] ( n +1 ,k +1) = b (cid:18) nT Ldata N LFFT + T Wtotal − τ ; f W k , T WCP , T
Wdata (cid:19) , (22)where n ∈ [0 , N ] and k ∈ [0 , N WFFT − .In the data part of the LAA-LTE’s symbol, there are M whole Wi-Fi’s symbols, where M = ⌊ ( T Ldata − τ ) /T Wtotal ⌋ . Hence, for the duration [ τ + T Wtotal ( q − , τ + T Wtotal q ) , q = 1 , . . . , M , thesample index n should satisfy N τ ,q ≤ n < N τ ,q , (23)where N τ ,q = (cid:24) N LFFT ( τ + T Wtotal ( q − T Ldata (cid:25) , (24) N τ ,q = (cid:24) N LFFT ( τ + T Wtotal q ) T Ldata (cid:25) − . (25) Since τ = M × T Wtotal , the time duration is [ τ , τ ) for all q . Hence, for the duration, the sampled points from x W p + q ( t ) are s W m [ n ] = x W p + q ( t ) (cid:12)(cid:12) t = nT Ldata /N LFFT − ( τ + T Wtotal ( q − (26) = N WFFT − X k =0 a W p + q,k b (cid:18) nT Ldata N LFFT − ( τ + T Wtotal ( q − f W k , T WCP , T
Wdata (cid:19) , (27)and the vector form of the sampled points is obtained as s W τ ,q , G τ ,q × a W p + q , (28)where s W τ ,q = [ s W m [ N τ ,q ] , . . . , s W m [ N τ ,q ]] T and a W p + q = [ a W p + q, , . . . , a W p + q,N WFFT − ] T . The matrix G τ ,q is defined by [ G τ ,q ] ( n − N τ ,q +1 ,k +1) = b (cid:18) nT Ldata N LFFT − ( τ + T Wtotal ( q − f W k , T WCP , T
Wdata (cid:19) , (29)where n ∈ [ N τ ,q , N τ ,q ] and k ∈ [0 , N WFFT − . Finally, for the duration [ τ + τ , T Ldata ) , the sampleindex n should satisfy (cid:24) N WFFT ( τ + τ ) T Ldata (cid:25) , N last ≤ n < N LFFT − , (30)and the sampled points of x W p + M +1 are s W m [ n ] = x W p + M +1 ( t ) (cid:12)(cid:12) t = nT Ldata /N LFFT − ( τ + τ ) (31) = N WFFT − X k =0 a W p + q,k b (cid:18) nT Ldata N LFFT − ( τ + τ ); f W k , T WCP , T
Wdata (cid:19) . (32)The vector form is derived as s W τ , G τ × a W p + M +1 , (33)where s W τ = [ s W m [ N last ] , . . . , s W m [ N LFFT − T and a W p + M +1 = [ a W p + M +1 , , . . . , a W p + M +1 ,N WFFT − ] T . Thematrix G τ is defined by [ G τ ] ( n − N last +1 ,k +1) = b (cid:18) nT Ldata N LFFT − ( τ + τ ); f W k , T WCP , T
Wdata (cid:19) , (34)where n ∈ [ N last , N LFFT − and k ∈ [0 , N WFFT − . s W = s W τ , CP s W τ , CP s W τ , CP s W τ s W τ , ... s W τ ,M s W τ = G , CP G , CP G , CP G τ G τ τ , . . . G τ τ ,M G τ τ | {z } , K AP , UE a W p − a W p − a W p a W p a W p +1 ... a W p + M a W p + M +1 | {z } , ˜ a W (35)
3) Frequency-Domain Effective Channel Matrix:
By combining the derived sampled pointsfor durations, the discrete-time Wi-Fi transmit vector for the overall duration of T LCP + T Ldata isderived as s W = K AP , UE × ˜ a W , (36)each element of which is constructed as (35).At this point, to consider the effect of the channel impulses on the received signal, we denotethe discrete-time-domain channel matrix from the α -th AP to the UE as ˜ H AP α , UE ∈ C N LFFT × N Ltotal ,which is defined by ˜ H AP α , UE = N LCP − N tap +1 z }| { · · · ν AP α , UE N tap · · · ν AP α , UE . . . . . . . . . ν AP α , UE N tap · · · ν AP α , UE . (37)Then, the received interference signal at the UE due to the AP’s signal is derived by r W = ˜ H AP α , UE × s W = ˜ H AP α , UE K AP,UE × ˜ a W . (38)By multiplying both sides of (38) with the FFT matrix of LAA-LTE F L ∈ C N LFFT × N LFFT , we canobtain the frequency-domain interference at the UE as F L × r L = F L ˜ H AP α , UE K AP,UE × ˜ a W . (39)As a result, the frequency-domain effective channel matrix from the α -th AP to the UE can be (a) ≤ τ < T Ltotal − T Wtotal (b) − T Wtotal ≤ τ < Fig. 3. Received signal at an AP for each τ case. The blue box means the cyclic prefix, and the white box is the data. defined as H AP α , UE = F L ˜ H AP α , UE K AP,UE . (40) C. Effective Channel Model from an eNB to an AP
To derive the eNB’s signal received at an AP, τ is defined as the time difference between thestarting point of an LAA-LTE’s symbol and that of the considered Wi-Fi’s symbol, as shownin Fig. 3. We first perform a case study for the variable τ , and then derive the throughputtreating it as a random variable. For the frequency-domain CCA, an AP senses signals for theWi-Fi’s OFDM symbol duration. Thus, we derive the LAA-LTE’s signal received at an AP forthe duration of one Wi-Fi’s OFDM symbol.There are two cases depending on how a Wi-Fi’s OFDM symbol duration overlaps withmultiple LAA-LTE’s OFDM symbols as follows: • Case 1 ( ≤ τ 1) Case 1: In Fig. 3(a), an AP obtains N WCP samples and N WFFT samples from x L m ( t ) for theCP duration and for the data duration, respectively. With the sample index n , the sampled pointsfrom x L m ( t ) are written as s L [ n ] = x L m ( t ) (cid:12)(cid:12) t = n · T Wtotal /N Wtotal + τ , n ∈ [0 , N Wtotal − (41) = N LFFT − X k =0 a L m,k b (cid:18) n · T Wtotal N Wtotal + τ ; f L k , T LCP , T Ldata (cid:19) , (42)where N Wtotal = N WCP + N WFFT . The vector form of (42) is defined as s L , K eNB,AP × a L , (43)where a L = [ a L m, , . . . , a L m,N LFFT − ] T and s L = [ s L [0] , . . . ,s L [ N Ltotal − T , where N Ltotal = N LCP + N LFFT . The matrix K eNB,AP is defined as [ K eNB,AP ] ( n +1 ,k +1) = b (cid:18) n · T Wtotal N Wtotal + τ ; f L k , T LCP , T Ldata (cid:19) , (44)for n ∈ [0 , N Wtotal − and k ∈ [0 , N LFFT − . 2) Case 2: In Fig. 3(b), the ( m − -th LAA-LTE’s symbol is overlapped for the index ≤ nT Wtotal N Wtotal < | τ | ⇐⇒ n = 0 , . . . , (cid:24) | τ | N Wtotal T Wtotal (cid:25) − , N τ , (45)while the m -th LAA-LTE’s symbol is overlapped for the sample index | τ | ≤ n · T Wtotal N Wtotal < T Wtotal ⇐⇒ n = N τ + 1 , . . . , N Wtotal . (46)Thus, the N Wtotal samples of the LAA-LTE’s symbols are obtained as follows. For n ∈ [0 , N τ ] , s L [ n ] is derived as s L [ n ] = x L m − ( t ) (cid:12)(cid:12) t = n · T Wtotal /N Wtotal + T Ltotal −| τ | (47) = N LFFT − X k =0 a L m − ,k b (cid:18) nT Wtotal N Wtotal + T Ltotal −| τ | ; f L k , T LCP , T Ldata (cid:19) . (48) For n ∈ [ N τ + 1 , N Wtotal − , we have s L [ n ] = x L m ( t ) (cid:12)(cid:12) t = n · T Wtotal /N Wtotal −| τ | (49) = N LFFT − X k =0 a L m,k b (cid:18) n · T Wtotal N Wtotal − | τ | ; f L k , T LCP , T Ldata (cid:19) . (50)In the vector form with (48) and (50), we have s L , K eNB,AP × a L = K τ K − τ a L , (51)where s L = [ s L [0] , . . . , s L [ N τ ] s L [ N τ + 1] , . . . , s L [ N Wtotal − T and a L = [ a L m − , , . . . , a L m − ,N LFFT − ,a L m, , . . . , a L m,N LFFT − ] T . In (51), K τ and K − τ are defined as follows: [ K τ ] ( n +1 ,k +1) = b (cid:18) n · T Wtotal N Wtotal + T Ltotal −| τ | ; f L k , T LCP , T Ldata (cid:19) (52)for n ∈ [0 , N τ ] and k ∈ [0 , N LFFT ] , and [ K − τ ] ( n − N τ ,k +1) = b (cid:18) n · T Wtotal N Wtotal − | τ | ; f L k , T LCP , T Ldata (cid:19) (53)for n ∈ [ N τ + 1 , N WFFT ] and k ∈ [0 , N LFFT ] . 3) Frequency-Domain Effective Channel Matrix: To take into account the effect of the channelimpulses on the received signal, we denote the discrete-time-domain channel matrix from theeNB to the α -th AP as ˜ H eNB , AP α ∈ C N WFFT × N Wtotal , where ˜ H eNB , AP α = N WCP − N tap +1 z }| { · · · ν eNB , AP α N tap · · · ν eNB , AP α . . . . . . . . . ν eNB , AP α N tap · · · ν eNB , AP α . (54)Then, the eNB’s signal received at the α -th AP is expressed by r L = ˜ H eNB , AP α × s L = ˜ H eNB , AP α K eNB , AP × a L . (55) By multiplying both sides of (55) with F W ∈ C N WFFT × N WFFT , the FFT matrix of Wi-Fi, we obtainthe frequency-domain received signal at the AP as F W × r L = F W ˜ H eNB , AP α K eNB,AP × a L . (56)As a result, in the frequency domain, the effective channel matrix from the eNB to the α -th APcan be defined as follows. H eNB , AP α = F W ˜ H eNB , AP α K eNB,AP . (57) 4) Results of the Effective Channel Matrices: Fig. 4 presents the square of the absolute valueof each element of the derived effective channel matrices, H eNB , AP α and H AP α , UE , averaged overthe timing difference variables τ and τ . Here, τ and τ are assumed to be uniformly distributedover [0 , . µs ] and [ − T Wtotal , T