Dynamic TDD: the Asynchronous Case and the Synchronous Case

Dynamic TDD: the Asynchronous Case and the Synchronous Case Ming Ding‡ , David L´ opez P´erez† , Guoqiang Mao∦‡⊓§♣ , Zihuai Lin¶ ‡

Data61, Australia {[email protected]} Nokia Bell Labs, Ireland {[email protected]} ∦ School of Computing and Communication, University of Technology Sydney, Australia ⊓ School of Electronic Information & Communications, Huazhong University of Science & Technology, Wuhan, China § School of Information and Communication Engineering, Beijing University of Posts and Telecommunications, Beijing, China ¶ The University of Sydney, Australia

arXiv:1611.02828v1 [cs.IT] 9 Nov 2016

†

Abstract—Small cell networks (SCNs) are envisioned to embrace dynamic time division duplexing (TDD) in order to tailor downlink (DL)/uplink (UL) subframe resources to quick variations and burstiness of DL/UL traffic. The study of dynamic TDD is particularly important because it serves as the predecessor of the full duplex transmission technology, which has been identified as one of the candidate technologies for the 5th-generation (5G) networks. Up to now, the existing work on dynamic TDD only considered an asynchronous network scenario. However, the current 4G network is a synchronous one and it is very likely that the future 5G networks will follow the same system design philosophy for easy implementation. In this paper, for the first time, we consider dynamic TDD in synchronous networks and present analytical results on the probabilities of inter-cell inter-link interference and the DL/UL time resource utilization. Based on our analytical results, the area spectral efficiency is further investigated to shed new light on the performance and the deployment of dynamic TDD in future synchronous networks.

I. I NTRODUCTION The orthogonal deployment of dense small cell networks (SCNs) with the existing macrocell networks implies that small cells and macrocells operate on different frequency spectrum. Due to its capacity gain and easy implementation, such deployment has been selected as the workhorse for capacity enhancement in the 4th-generation (4G) and 5thgeneration (5G) networks developed by the 3rd Generation Partnership Project (3GPP) [1]. It is also envisaged that dense SCNs will embrace time division duplexing (TDD), which does not require a pair of frequency carriers and offers the possibility of tailoring the amount of time radio resources to the downlink (DL)/uplink (UL) traffic conditions. In this line, seven TDD configurations, each associated with a specific DL/UL subframe number in a 10-milisecond TDD frame, are available for semi-static selection at the network side in the 4G Long Term Evolution (LTE) networks [2]. In order to allow a more dynamic and independent adaptation of TDD SCNs to the quick variation of DL/UL traffic demands, a new technology, referred to as dynamic TDD, has drawn much attention recently [3–7]. In dynamic TDD, the configuration of the TDD DL/UL subframe number in each cell or a cluster of cells can be dynamically changed

Fig. 1. An example of the LTE TDD configurations. (’D’ and ’U’ denote a DL subframe and an UL one, respectively.)

on a per-frame basis, i.e., once every 10 milliseconds [2]. Dynamic TDD can thus provide a tailored configuration of DL/UL subframe resources for each cell or a cluster of cells at the expense of allowing inter-cell inter-link interference, e.g., DL transmissions of a cell may interfere with UL ones of a neighboring cell and vice versa. The study of dynamic TDD is particularly important because it serves as the predecessor of the full duplex (FD) transmission technology [4, 8], which has been identified as one of the candidate 5G technologies. The signal-to-interference-plus-noise ratio (SINR) performance of dynamic TDD has been analyzed in [5], assuming deterministic positions of BSs and UEs, and in [6, 7], considering stochastic positions of BSs and UEs. However, most previous theoretical works only investigate dynamic TDD operating in an asynchronous network, and does not study dynamic TDD operating in a synchronous one. More specifically, in an asynchronous network, e.g., Wireless Fidelity (Wi-Fi), the TDD transmission frames are not aligned among cells, and thus the inter-cell inter-link interference is statistically uniform in the time domain and only depends on the DL/UL transmission probability. However, in a synchronous network, such as LTE, the TDD transmission frames from different cells are aligned to simplify the protocol design of radio networks. As a result, the inter-cell inter-link interference becomes a function of the LTE TDD configuration structure. Fig. 1 shows an example of such LTE TDD configuration structure. In Fig. 1, one TDD frame is composed of 10 subframes and the time length of each subframe is 1 millisecond [2]. As an example, we assume that BS 1 and BS 2 use the TDD configurations with 6 and 8 DL subframes, respectively. For this synchronous network with frame alignment, we can see that the first 6 and the last 2 subframes of BS 1 will not see any

UL-to-DL or DL-to-UL interference from BS 2. However, this is not the case for the 7-th and 8-th subframes of BS 1, which are UL subframes and collide with the DL subframes of BS 2 with a probability of 100 %. Hence, the average probability of the DL-to-UL interference for the UL in BS 1 is 50 %. In contrast, for an asynchronous network, each UL subframe of BS 1 will experience DL-to-UL interference from BS 2 with an 80 % probability, since BS 2 transmits DL subframes 80 % of the time. Thus, ignoring the frame alignment in synchronous networks can lead to a considerable over-estimation of intercell inter-link interference as shown by this example. Unfortunately, works that considered dynamic TDD in the synchronous case were based on simulations and lack of analytical expressions [3, 4]. In this paper, for the first time, we will present analytical results on dynamic TDD for the synchronous case. The main contributions of this paper are as follows: • We derive closed-form expressions for the probabilities of inter-cell inter-link interference, considering dynamic TDD in the synchronous case. Such probabilities are shown to vary with the BS and UE densities and are distinctively different from the existing results in [6, 7]. • We also derive closed-form expressions for the DL/UL time resource utilization (TRU), considering dynamic TDD in the synchronous case. Such results quantify the high efficiency of resource usage in dynamic TDD. • Based on the above analytical results, the area spectral efficiency (ASE) of dynamic TDD in the synchronous case is further investigated, with special attention paid to the UL part by considering full and partial interference cancellation technologies [4], so that the overwhelming DL-to-UL interference among BSs can be mitigated. II. N ETWORK S CENARIO

AND

W IRELESS S YSTEM M ODEL

In this section, we present the network scenario and the system model considered in the paper. A. Network Scenario We consider a cellular network with BSs deployed on a plane according to a homogeneous Poisson point process (HPPP) Φ with a density of λ BSs/km2 . Active UEs are also Poisson distributed in the considered network with a density of ρ UEs/km2 . Here, we only consider active UEs in the network because non-active UEs do not trigger data transmission, and thus they are ignored in our analysis. According to [1], a typical density of the active UEs is round ρ = 300 UEs/km2 . In practice, a BS will mute its transmission if there is no UE connected to it, which reduces inter-cell interference and energy consumption [9]. Since UEs are randomly and uniformly distributed in the network, we assume that the active ˜ [10], the density of BSs also follow an HPPP distribution Φ ˜ BSs/km2 . Note that 0 ≤ λ ˜ ≤ λ, and a which is denoted by λ ˜ larger ρ leads to a larger λ. For each active UE, the probabilities of requesting DL data and UL data are respectively denoted by pD and pU , with pD + pU = 1. Besides, we assume that each request is

large enough to be transmitted for at least one TDD frame, which consists of T subframes. In the sequel, the DL or UL subframe number per frame will be shortened as the DL or the UL subframe number, because subframes are generally meant within one frame. Moreover, we consider the UL-afterDL TDD configuration structure, which has been adopted in LTE [2]. Fig. 1 provided an example of such UL-after-DL TDD configuration structure with T = 10. B. System Model Following [11], we adopt a general and practical path loss model, in which the path loss ζ (r) associated with distance r is segmented into N pieces written as  Dir  ζ1 (r) , when 0 ≤ r ≤ d1   ζ2Dir (r) , when d1 < r ≤ d2 ζ Dir (r) = . , (1) .. ..   .    Dir ζN (r) , when r > dN −1

where the string variable Dir denotes the path loss direction and takes the value of ’B2U’, ’B2B’ and ’U2U’ for the BS-to-UE path loss, the BS-to-BS path loss and the UE-toUE path loss, respectively. Besides, each piece ζnDir (r) , n ∈ {1, 2, . . . , N } , is modeled as  Dir,L ζ Dir,L (r) = AnDir,L , LoS: PrDir,L (r) n αn n Dir r , ζn (r)= Dir,NL ζnDir,NL (r) = AnDir,NL , NLoS: 1 − PrDir,L (r) n α n r (2) Dir,L Dir,NL where ζn (r) and ζn (r) are the n-th piece path loss functions for the LoS transmission and the NLoS transmission, respectively, ADir,L and ADir,NL are the path losses n n at a reference distance r = 1 for the LoS and the NLoS cases, respectively, and αDir,L and αDir,NL are the path loss n n exponents for the LoS and the NLoS cases, respectively. In practice, ADir,L , ADir,NL , αDir,L and αDir,NL are constants n n n n obtainable from field tests [2]. Moreover, PrDir,L (r) is the n-th piece LoS probability n function for the event that there is a LoS path between a transmitter and a receiver separated by a distance r. In this paper, we assume a practical user association strategy, in which each UE is connected to the BS having the smallest path loss (i.e., with the largest ζ (r)) [11]. Moreover, we assume that each BS/UE is equipped with an isotropic antenna, and that the multi-path fading between a transmitter and a receiver is modeled as independent and identically distributed (i.i.d.) Rayleigh fading [11]. Based on this system model, we can define the coverage probability that the typical UE’s DL/UL SINR is above a designated threshold γ as h i pcov,Link (λ, γ) = Pr SINRLink > γ , (3) where the string variable Link denotes the link direction and takes the value of ’D’ and ’U’ for the DL and the UL, respectively. Moreover, the DL/UL SINR is calculated by SINRLink =

P Link ζbB2U (r) h o , D + I U + P Link Iagg agg N

(4)

where P Link is the transmission power, r is the distance from the typical UE to its serving BS denoted by bo , h is the Rayleigh channel gain modeled as an exponentially distributed random variable (RV) with a mean of one as mentioned above, PNLink is the additive white Gaussian noise (AWGN) D U power, and Iagg (Iagg ) is the DL (UL) cumulative interference, respectively. It is important to note that: Link • For the DL, P takes the value of the BS power, i.e., D P , which is usually a cell-specific constant to maintain a stable DL coverage [2]. Besides, PNLink should be the AWGN at the UE side, i.e., PND . Link • For the UL, P takes the value of the UE power, U i.e., P , which is usually subject to semi-static power control such as the fractional path loss compensation (FPC) scheme [2]. Besides, PNLink should be the AWGN at the BS side, i.e., PNU . • Due to the existence of inter-cell inter-link interference, D U Iagg and Iagg are probabilistic interference emitted from interfering BSs and interfering UEs, respectively. The set of such interfering BSs and that of such interfering UEs’ ˜ D and Φ ˜ U , respectively. It serving BSs are denoted by Φ is easy to show that ˜D ∩Φ ˜ U = ∅, because full duplex [8] is not allowed – Φ in dynamic TDD; and ˜D ∪ Φ ˜U = Φ ˜ \ bo , because only the active BSs in – Φ ˜ \ bo can schedule DL/UL transmissions that inject Φ effective interference into the network. According to [11], the SINR-dependent DL/UL area spectral efficiency (ASE) in bps/Hz/km2 can be defined by Z +∞ ˜ log2(1 + γ) fΓLink(λ, γ) dγ, (5) ASE Link(λ, γ0 )=κLink λ

For dynamic TDD in the asynchronous case, it can be assumed that qlD = pD and qlU = pU [7]. As discussed in Section I, – matching the DL/UL subframe splitting ratio with the DL/UL data request ratio achieves a balanced performance for both the DL and the UL, which leads to the DL/UL transmission probability converging to the DL/UL data request probability; and thus – the DL/UL transmission probability (qlD and qlU ) will not change with the subframe index l. • For dynamic TDD in the synchronous case, computing qlD and qlU is a non-trivial task, because they depend on the following factors: – the distribution of the UE number in an active BS, which will be shown to follow a truncated Negative Binomial distribution in Subsection III-A; – the distribution of the DL/UL data request numbers in an active BS, which will be shown to follow a Binomial distribution in Subsection III-B; – the dynamic TDD subframe splitting strategy, and the corresponding distribution of the DL/UL subframe number, which will be shown to follow an aggregated Binomial distribution in Subsection III-C; and – the prior information about the frame structure, such as the UL-after-DL structure adopted in LTE [2], which will lead to subframe-dependent results of qlD and qlU to be presented in Subsection III-D. Based on the derived qlD and qlU , we will then study the analytical results on the probabilities of inter-cell inter-link interference and the DL/UL time resource utilization (TRU) in Subsection III-E and Subsection III-F, respectively.

where κ is the DL/UL time resource utilization characterizing how much time resource is actually used for the DL/UL, γ0 is the minimum working SINR for the considered SCN, and fΓLink (λ, γ) is the probability density function (PDF) of SINRLink at a particular BS density λ. Based on the definition of pcov,Link (λ, γ) in (3), which is the complementary cumulative distribution function (CCDF) of the DL/UL SINR, fΓLink (λ, γ) can be computed by
∂ 1 − pcov,Link (λ, γ) Link . (6) fΓ (λ, γ) = ∂γ III. M AIN R ESULTS As explained in Section I, for dynamic TDD in the synchronous case, the probabilities of inter-cell inter-link interference vary across the TDD subframes because the probabilities of scheduling DL and UL transmissions are different for each subframe. To formulate this, for the l-th subframe (l ∈ {1, 2, . . . , T }), we respectively denote the probability of BS transmitting DL signals and that of UE transmitting UL signals by qlD and qlU , with qlD + qlU = 1. Regarding qlD and qlU , we have the following observations: • For static TDD with a fixed TDD subframe configuration across the SCN, qlD and qlU are either one or zero, because its TDD subframe designation is deterministic.

A. The Distribution of the UE Number in an Active BS

γ0

Link

•

Considering both active BSs and inactive BSs, the coverage area size X can be characterized by a Gamma distribution [10]. Thus, the PDF of X can be expressed by fX (x) = (qλ)q xq−1

exp(−qλx) , Γ(q)

(7)

where q is a distribution parameter and Γ(·) is the Gamma function [12]. Note that according to our very recent study [9], q should depend on PrB2U,L (r) shown in (2). n Then, we denote the UE number per BS by a random variable (RV) K, and the probability mass function (PMF) of K can be derived as fK (k) = Pr [K = k] Z +∞ (ρx)k (a) exp(−ρx)fX (x)dx = k! 0  k  q Γ(k + q) ρ qλ (b) = , (8) Γ(k + 1)Γ(q) ρ + qλ ρ + qλ where (a) is due to the HPPP distribution of UEs and (b) is obtained from (7). It can be seem from (8) that K followsa ρ . Negative Binomial distribution [12], i.e., K ∼ NB q, ρ+qλ

As discussed in Subsection II-A, we assume that a BS with K = 0 is not active, which will be ignored in our analysis due to its muted transmission. Hence, we focus on the active BSs and further study the distribution of the UE number in an active BS. For clarity, the UE number in an active BS is ˜ Considering (8) and the fact that denoted by a positive RV K. ˜ lies in K ˜ 6= 0, we can the only difference between K and K ˜ conclude that K should follow atruncated  Negative Binomial ˜ ∼ truncNB q, ρ . More specifically, distribution, i.e., K ρ+qλ  ˜ the PMF of K is denoted by fK˜ k˜ , k˜ ∈ {1, 2, . . . , +∞}, and it is given by     h i fK k˜ ˜ = k˜ = fK˜ k˜ = Pr K , (9) 1 − fK (0)

where the denominator (1 − fK (0)) represents the probability ˜ of a BS being active. Note that based on the definition of λ ˜ λ in Subsection II-A, we have (1 − fK (0)) = λ . B. The Distribution of the DL/UL Data Request Number in an Active BS ˜ in After obtaining the distribution of the UE number K an active BS, we need to further study the distribution of the DL/UL data request number in an active BS, so that a tailored TDD configuration can be determined in a dynamic TDD network. In other words, the DL/UL data request number in an active BS reflects the DL/UL traffic load in such BS, and with the assumption of dynamic TDD, a TDD configuration should be smartly selected to make the splitting of the DL and UL subframes match such DL/UL traffic load condition. For clarity, the DL and UL data request numbers in an active BS are denoted by RVs M D and M U , respectively. Since we ˜ and each assume that the UE number in an active BS is K UE generates one request of either DL data or UL data, it is apparent that ˜ M D + M U = K. (10) As discussed in Subsection II-A, for each UE in an active BS, the probability of it requesting DL data and UL data is pD and ˜ M D should follow ˜ = k, pU , respectively. Hence, for a given K   D ˜ pD . More a Binomial distribution [12], i.e., M ∼ Bi k,
specifically, the PMF of M D is denoted by fM D mD , mD ∈ ˜ and it can be expressed by {0, 1, . . . , k},
  fM D mD = Pr M D = mD   D ˜
k−m
mD k˜ = . (11) 1 − pD pD D m ˜ pU ). Considering (10), it is easy to show that M U ∼ Bi(k,

C. The Distribution of the DL/UL Subframe Number with Dynamic TDD After knowing the distribution of the DL data request number M D in an active BS, we are ready now to consider dynamic TDD and derive the distribution of the DL subframe ˜ the DL subframe ˜ = k, number in an active BS. For a given K

number in an active BS is denoted by N D . Here, we adopt a dynamic TDD algorithm to choose the DL subframe number, which matches the DL subframe ratio with the DL data request D ˜ the ratio [4]. In more detail,for certain  values of m and k, D ˜ DL subframe number n m , k is determined by  D    m T , (12) n mD , k˜ = round k˜ where round (x) is an operator that rounds an real value x D to its nearest integer. In (12), mk˜ can be deemed as the DL data request ratio, because (i) mD denotes the DL data request number with its distribution characterized in (11); (ii) k˜ represents the UE number, and thus the total number of D the DL and UL data requests; and (iii) as a result, mk˜ T yields a desirable DL subframe number that matches the DL subframe ratio with the DL data request ratio. However, due to the integer nature of the DL subframe number, we use the round operator to generate a valid DL subframe number that D is nearest to mk˜ T in (12). Based
on (12), the PMF of N D is denoted by fN D nD , nD ∈ {0, 1, . . . , T }, and it can be derived as 
 fN D nD = Pr N D = nD ˜   D   k
m (a) X D = I round T =n fM D mD , (13) ˜ k mD =0 where (12) is plugged into (a), and I {X} is an indicator function that outputs
one when X is true and zero otherwise. Besides, fM D mD is computed by (11). Due
to the existence of the indicator function in (13), fN D nD can be viewed as an aggregated PMF of a Binomial distribution, since N D is generated from M D according to a many-to-one mapping characterized by (12). Since the total subframe number in a frame is T and each subframe should be either a DL one or an UL one, it is apparent that N D + N U = T , and hence we have

(14) f N U nU = f N D T − nU .

D. The Probability of Performing a DL/UL Transmission on a Subframe with Dynamic TDD Considering the distribution of the DL/UL subframe number in an active BS and the UL-after-DL structure of the synchronous TDD configurations, we can now derive the probability of performing a DL/UL transmission on a subframe with dynamic TDD. ˜ the probabil˜ = k, Based on (13) and conditioned on K ity of performing a DL transmission on the l-th subframe (l ∈ {1, 2, . . . , T }) can be calculated as h i ˜ = k˜ ql,Dk˜ = Pr Yl = ’D’| K   (a) = Pr N D ≥ l = 1 − FN D (l − 1) , (15)

where Yl denotes the link direction for the transmission on the l-th subframe, which takes a string value of ’D’ and ’U’ for

the DL and the UL, respectively. Besides, step (a) of (15) is due to the LTE
TDD configuration structure shown in Fig. 1, and FN D nD is the cumulative mass function (CMF) of N D in an active BS, which is written as D

FN D n

D






= Pr N

D

≤n

D



=

n X

can be derived as PrD2U = Pr [ Z = ’D’| S = ’U’] T X = Pr [ ( Z = ’D’| L = l)| S = ’U’] l=1

fN D (i) .

(16)

i=0

Similarly, the probability of performing an UL transmission on the l-th subframe can be given by ql,Uk˜ = 1 − ql,Dk˜ = FN D (l − 1) .

(17)

l=1

T (b) X D Pr [ S = ’U’| L = l] Pr [L = l] = ql Pr [S = ’U’] l=1

Furthermore, the unconditional probabilities of performing a DL and UL transmissions on the l-th subframe, i.e., qlD and qlU , can be respectively derived by calculating the expected values of ql,Dk˜ and ql,Uk˜ over all the possible values of k˜ as    P D  q D = +∞ k˜ q f ˜ ˜ ˜ l K k=1 l,k   , P  q U = +∞ ql,Uk˜ fK˜ k˜ ˜ l k=1

× Pr [L = l |S = ’U’ ] T (a) X D = ql Pr [L = l |S = ’U’ ]

T (c) X D ql = l=1

(18)

With the knowledge on the probability of each subframe being a DL one or an UL one, we can conduct an interesting study on the probabilities of inter-cell inter-link interference for dynamic TDD in the synchronous case. For clarify, such probabilities are formally defined as follows: The probability of the DL-to-UL interference is denoted by PrD2U and defined as Pr [ Z = ’D’| S = ’U’], where Z and S denote the link directions for the interference and the signal, respectively. Note that the probability of the UL-to-UL interference is denoted by PrU2U and defined as Pr [ Z = ’U’| S = ’U’]. From the definition of PrD2U and PrU2U , we have PrD2U + PrU2U = 1. Similarly, the probability of the UL-to-DL interfer△ ence is defined by PrU2D = Pr [ Z = ’U’| S = ’D’]. Besides, the probability of the DL-to-DL interference △ is defined by PrD2D = Pr [ Z = ’D’| S = ’D’], with U2D D2D Pr + Pr = 1.

Our main results on PrD2U and PrU2D are summarized in Theorem 1. Theorem 1. PrD2U and PrU2D can be derived in closed-form expressions as PT  qlD qlU  PrD2U = Pl=1 T qjU j=1 PT , (19) U D q U2D l ql  Pr = Pl=1 T qD j=1

,

(20)

where (a) is obtained from

due to the independence of the events ( Z = ’D’| L = l) and (S = ’U’); (b) is valid because of the Bayes’ Theorem; and (c) comes from the calculation on the probability of the signal being an UL one, which can be written by

E. The Probabilities of Inter-Cell Inter-Link Interference

•

U j=1 qj

Pr [ ( Z = ’D’| L = l)| S = ’U’] = Pr [ Z = ’D’| L = l] = qlD ,

  where fK˜ k˜ is obtained from (9).

•

1 T

qlU T1 PT

j

where qlD and qlU are obtained from (18).

Proof: By examining the inter-cell inter-link interference for the l-th subframe (l ∈ {1, 2, . . . , T }) one by one, PrD2U

Pr [S = ’U’] =

T X

Pr [ S = ’U’| L = j] Pr [L = j]

j=1

=

T 1 X U q . T j=1 j

(21)

Similarly, it is easy to derive the results for PrU2D , which concludes our proof. As discussed at the beginning of Section III, for static TDD, we have PrD2U = PrU2D = 0 since all the TDD subframes are of the same sequence and well-aligned. For dynamic TDD in the asynchronous case, we have PrD2U = pD and PrU2D = pU [7], due to the random collision of the dynamic TDD subframes. On the other hand, as shown in Theorem 1, PrD2U and PrU2D for dynamic TDD in the synchronous case are much more complex, which are expected to have a major D U impact on the evaluation of Iagg and Iagg in (4). F. The DL/UL Time Resource Utilization From (5), the DL or UL time resource utilization (TRU) is denoted by κD or κU , and it can be deemed as the probability that the signal transmission is a DL one or an UL one. Hence, enlightened by (21), we have ( PT κD = T1 j=1 qjD . (22) P T κU = T1 j=1 qjU Note that the results in (22) can be applied to dynamic TDD in both the asynchronous and the synchronous cases, because the TRU characterizes the efficiency of resource usage in dynamic TDD, no matter what the synchronization assumption is.

1 0.9 0.8 0.7

PrD2U [Asynchronous dynamic TDD] PrU2D [Asynchronous dynamic TDD]

(Analytical) (Analytical)

PrD2U [Synchronous dynamic TDD]

(Simulation)

PrD2U [Synchronous dynamic TDD] PrU2D [Synchronous dynamic TDD]

(Analytical) (Simulation)

PrU2D [Synchronous dynamic TDD]

(Analytical)

Time resource utilization (TRU)

Probability of inter-cell inter-link interference

PrD2U & PrU2D [Synchronous static TDD] (Analytical)

0.6 0.5 0.4 0.3 0.2

1 0.9 0.8

(Simulation) (Analytical) (Simulation) (Analytical) (Simulation) (Analytical) (Simulation) (Analytical)

0.7 0.6 0.5 0.4 0.3 0.2

0.1

0.1

0 10-1

10

0

10

1

2

10

2

10 2

0 10-1

3

D

The probability of inter-cell inter-link interference.

For the trivial case of static TDD, it is straightforward to derive κD and κU as     D P N0  κD = 1 − +∞ D (0) f ˜ k˜ f M ˜ K T k=1    , (23) N0U ˜  κU = 1 − P+∞ f U (0) f k ˜ M ˜ K T k=1

where fM D (0) and fM U (0) are respectively the probabilities that the typical UE does not request any DL and UL data for ˜ = k˜ (see Subsection III-B). Besides, N D and N U a given K 0 0 are respectively the subframe numbers for the DL and the UL in static TDD. IV. S IMULATION

AND

D ISCUSSION

In this section, we present numerical results to validate the accuracy of our analysis. In our simulation, we adopt the following parameters recommended by the 3GPP [2]. In (2), N = 2 and for n ∈ {1, 2}, AB2U,L = 10−10.38 , AB2U,NL = n n −14.54 B2B,L −9.84 B2B,NL 10 , An = 10 , An = 10−16.94 , AU2U,L = n 10−9.85 , AU2U,NL = 10−17.58 , αB2U,L = 2.09, αB2U,NL = n n n B2B,NL U2U,L U2U,NL 3.75, αB2B,L = 2, α = 4, α = 2, α = 4. n n n n Besides, the LoS probability function for PrB2U,L (r) and PrB2B,L (r) is a two-piece exponential function defined as [2] ( 1−5 exp (−R1 /r) , 0 < r ≤ d1 PrB2U,L (r)=PrB2B,L (r)= , 5 exp (−r/R2 ) , r > d1 (24) 1 . In addition, a where R1 = 156 m, R2 = 30 m and d1 = lnR10 simple LoS probability function for PrU2U,L (r) is given by [2] ( 1, 0 < r ≤ 50 m U2U,L Pr (r)= . (25) 0, r > 50 m Besides, according to [2], the power values are set to: PND = −95 dBm, PNU = −91 dBm, P D = 24 dBm, and P U is determined for each UE based on the FPC scheme [2]. In addition, the UE density is set to ρ = 300 UEs/km2 , which leads to q = 4.05 in (7) [9]. Finally, we assume that γ = 1, pD = 32 and T = 10. Thus, for static TDD, we have N0D = 7 and N0U = 3 in (23), which achieves the best match with pD and pU , according to (12).

100

101

102

103

Base station density λ [BSs/km 2] (ρ = 300UEs/km2, pD = 2/3)

Base station density λ [BSs/km ] (ρ = 300UEs/km , p = 2/3)

Fig. 2.

DL TRU [Static TDD] DL TRU [Static TDD] UL TRU [Static TDD] UL TRU [Static TDD] DL TRU [Dynamic TDD] DL TRU [Dynamic TDD] UL TRU [Dynamic TDD] UL TRU [Dynamic TDD]

Fig. 3.

The time resource utilization.

A. Validation of the Results on the Probabilities of Inter-Cell Inter-Link Interference The analytical and simulation results of PrD2U and PrU2D are plotted in Fig. 2. From this figure, we can draw the following observations: • • •

•

The analytical and simulation results match well, which validates the accuracy of our analysis. For static TDD, PrD2U and PrU2D are zeros as discussed in Subsection III-E. For dynamic TDD in the asynchronous case, it is confirmed that PrD2U = pD and PrU2D = pU [7]. For dynamic TDD in the synchronous case, as the BS density λ increases, PrD2U and PrU2D gradually grow and converge to the results of dynamic TDD in the asynchronous case. This is because: – when λ increases, the UE number in each active BS decreases; and – hence, when λ is high enough to reach the limit of one UE per active BS, all the subframes will be used as either DL ones or UL ones, the probability of which solely depends on pD or pU .

B. Validation of the Results on the Time Resource Utilization The analytical and simulation results of κD and κU are plotted in Fig. 3. From this figure, we can see that: •

•

For static TDD, κD starts from 0.7 and decreases as λ increases. This is because N0D = 7 and T = 10, and thus static TDD maintains N0U = 3 UL subframes even if there is no UL data request in a BS, leading to a large time resource waste. Moreover, the sum of κD and κU is much less than one when λ is large, e.g., λ = 1000 BSs/km2 , showing the inefficiency of static TDD in dense SCNs. For dynamic TDD, κD starts from 0.7 and converges to pD = 32 as λ increases. This is because when λ is high enough to reach the limit of one UE per active BS, all the subframes will be used as DL ones with a probability of pD . Moreover, the sum of κD and κU always equals to one, thanks to the dynamic adaption of DL/UL subframes to DL/UL data requests.

1 0.9 0.8 0.7

0.6 0.55

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0.45

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Area spectral efficiency [bps/Hz/km2]

Probability of SINRU>γ

Synchronous static TDD Asynchronous dynamic TDD [No D2U IC] Asynchronous dynamic TDD [Partial D2U IC] Asynchronous dynamic TDD [Full D2U IC] Synchronous dynamic TDD [No D2U IC] Synchronous dynamic TDD [Partial D2U IC] Synchronous dynamic TDD [Full D2U IC]

900 800 700 600

Synchronous static TDD Synchronous dynamic TDD Synchronous dynamic TDD Synchronous dynamic TDD Synchronous static TDD Synchronous dynamic TDD Synchronous dynamic TDD Synchronous dynamic TDD

C. The Coverage Probability Performance Due to the page limitation, we only show the simulation results of the UL coverage probability in Fig. 4. Note that our analytical results on PrD2U and PrU2D are used for the D U simulation of Iagg and Iagg in (4). Also note that the UL performance is important because the UL SINR is vulnerable to the DL-to-UL interference [4]. To mitigate such interference, we also investigate the effectiveness of the full interference cancellation (IC) and the partial IC technologies [4], which remove all and the top three DL-to-UL interfering signals based on ζ B2B (r), respectively. From Fig. 4, we can see that: •

•

The difference between the UL coverage probability of asynchronous dynamic TDD and that of synchronous dynamic TDD is as large as 15 %, e.g., when λ = 50 BSs/km2 , pcov,U (50, 1) = 0.487 for the former case and pcov,U (50, 1) = 0.558 for the latter one. This shows the importance of studying synchronous dynamic TDD. Dynamic TDD without IC achieves very poor performance compared with static TDD due to the strong DLto-UL interference. However, with the use of full IC or merely partial IC, the UL coverage probability of dynamic TDD can be significantly improved.

D. The ASE Performance From Fig. 4, we should not conclude that dynamic TDD exhibits no significant performance gain compared with static TDD due to the detrimental DL-to-UL interference. Instead, we need to investigate the ASE performance, which includes the time resource utilization and is shown in Fig. 5. From this figure, we can see that dynamic TDD in the synchronous case can achieve a much larger ASE compared with static TDD, mainly due to the dynamic adaption of DL/UL subframes to DL/UL data requests. For example, when λ = 1000 BSs/km2 , the ASE of static TDD and that of dynamic TDD with partial IC are around 500 bps/Hz/km2 and 700 bps/Hz/km2 , respectively. However, if the DL-to-UL interference is not properly treated, the UL ASE of dynamic TDD will suffer from a performance loss compared with static TDD, especially for 5G dense SCNs [1], e.g., λ > 100 BSs/km2 .

[No D2U IC] [Partial D2U IC] [Full D2U IC]

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Base station density λ [BSs/km ]

The UL coverage probability.

[No D2U IC] [Partial D2U IC] [Full D2U IC]

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2

Fig. 4.

(DL + UL) (DL + UL) (DL + UL) (DL + UL) (UL part) (UL part) (UL part) (UL part)

Fig. 5.

The area spectral efficiency.

V. C ONCLUSION For the first time, we analytically studied dynamic TDD in synchronous networks. Our study demonstrated that the probabilities of inter-cell inter-link interference should vary with the BS and UE densities. Besides, we showed the importance of treating the DL-to-UL interference by means of full IC or partial IC, especially for 5G dense SCNs. R EFERENCES [1] D. López-Pérez, M. Ding, H. Claussen, and A. Jafari, “Towards 1 Gbps/UE in cellular systems: Understanding ultra-dense small cell deployments,” IEEE Communications Surveys Tutorials, vol. 17, no. 4, pp. 2078–2101, Jun. 2015. [2] 3GPP, “TR 36.828: Further enhancements to LTE Time Division Duplex (TDD) for Downlink-Uplink (DL-UL) interference management and traffic adaptation,” Jun. 2012. [3] M. Ding, D. López-Pérez, A. V. Vasilakos, and W. Chen, “Dynamic TDD transmissions in homogeneous small cell networks,” 2014 IEEE International Conference on Communications Workshops (ICC), pp. 616–621, Jun. 2014. [4] M. Ding, D. Lopez, R. Xue, A. Vasilakos, and W. Chen, “On dynamic time division duplex transmissions for small cell networks,” IEEE Transactions on Vehicular Technology, vol. PP, no. 99, pp. 1–1, 2016. [Online]. Available: http://ieeexplore.ieee.org/document/7386709/ [5] M. Ding, D. López-Pérez, A. V. Vasilakos, and W. Chen, “Analysis on the SINR performance of dynamic TDD in homogeneous small cell networks,” 2014 IEEE Global Communications Conference, pp. 1552– 1558, Dec. 2014. [6] B. Yu, L. Yang, H. Ishii, and S. Mukherjee, “Dynamic TDD support in macrocell-assisted small cell architecture,” IEEE Journal on Selected Areas in Communications, vol. 33, no. 6, pp. 1201–1213, Jun. 2015. [7] A. K. Gupta, M. N. Kulkarni, E. Visotsky, F. W. Vook, A. Ghosh, J. G. Andrews, and R. W. Heath, “Rate analysis and feasibility of dynamic TDD in 5G cellular systems,” 2016 IEEE International Conference on Communications (ICC), pp. 1–6, May 2016. [8] S. Goyal, C. Galiotto, N. Marchetti, and S. Panwar, “Throughput and coverage for a mixed full and half duplex small cell network,” 2016 IEEE International Conference on Communications (ICC), pp. 1–7, May 2016. [9] M. Ding, D. Lopez-Perez, G. Mao, and Z. Lin, “Performance impact of idle mode capability on dense small cell networks with LoS and NLoS transmissions,” arXiv:1609.07710 [cs.NI], Sep. 2016. [10] S. Lee and K. Huang, “Coverage and economy of cellular networks with many base stations,” IEEE Communications Letters, vol. 16, no. 7, pp. 1038–1040, Jul. 2012. [11] M. Ding, P. Wang, D. López-Pérez, G. Mao, and Z. Lin, “Performance impact of LoS and NLoS transmissions in dense cellular networks,” IEEE Transactions on Wireless Communications, vol. 15, no. 3, pp. 2365–2380, Mar. 2016. [12] I. Gradshteyn and I. Ryzhik, Table of Integrals, Series, and Products (7th Ed.). Academic Press, 2007.