Feasibility of self-backhauling in full-duplex radio access systems under QoS constraints

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Feasibility of Self-backhauling in Full-Duplex Radio Access Systems under QoS Constraints

Dani Korpi^∗, Taneli Riihonen^†, and Mikko Valkama^∗

∗Laboratory of Electronics and Communications Engineering, Tampere University of Technology, Finland

†Department of Signal Processing and Acoustics, Aalto University School of Electrical Engineering, Finland e-mail: dani.korpi@tut.fi

Abstract—This paper investigates the feasibility of a radio access system with a self-backhauling access node under full- duplex and half-duplex operation modes. In particular, after making certain simplifying assumptions, closed-form solutions for the feasibility conditions of such a radio access system are derived for both of the considered operation modes. Furthermore, the analysis incorporates given quality of service (QoS) constraints for the system, defined in terms of minimum data rates. The numerical results show that the full-duplex scheme outperforms the corresponding half-duplex scheme under most circumstances, both in terms of the highest achievable rates and the highest tolerable path losses, when given the same QoS target. However, this requires a certain amount of self-interference attenuation in the access node. Performing a similar feasibility analysis without any simplifications in the system model is an important future work item.

I. INTRODUCTION

Inbandfull-duplex communications is an emerging technology for improving the spectral efficiency of future wireless networks, such as those implementing the upcoming 5G standard [1], [2]. In particular, an inband full-duplex device utilizes the spectral and temporal resources very efficiently by performing transmission and reception simultaneously using the same center-frequency, resulting in a two-fold increase in spectral efficiency. Several research groups have already proven the viability of inband full-duplex communication with real-life demonstrator prototypes [3]–[5].

The next step in making inband full-duplex communication a practical concept is determining how to best take advantage of it on a larger scale. One such promising idea is to utilize it for self-backhauling [6]–[10] which means that the access node (AN) would serve the uplink (UL) and downlink (DL) user equipments (UEs) while also connecting wirelessly to the wired backbone network via a backhaul node (BN) using the same radio resources. Doing all of this in the full-duplex mode would result in a greatly improved spectral efficiency as all the transmissions could be done on the same time–frequency re- source. This would make the wireless self-backhauling entirely transparent from the frequency and time allocation perspective in the sense that no additional frequency bands or time slots are needed, while also removing the need for expensive fiber- optic cables to provide the backhaul access.

In this work, we consider self-backhauling full-duplex ANs that have also massive transmit and receive antenna arrays at their disposal. The beamforming gain provided by the large

arrays further enhances the efficiency of the system [8], and the large transmit antenna array also allows the AN to form nulls into its own receive antenna array, significantly reducing the problem of self-interference (SI) [11].

In order to evaluate the feasibility of such a system, we will analyze the boundary conditions under which certain quality of service (QoS) conditions can be fulfilled. The QoS constraints are defined in terms of minimum data rates for both DL and UL. These feasibility boundaries are then compared to those of a corresponding half-duplex solution, where the AN is not capable of full-duplex operation.

In summary, our contributions can be detailed as follows:

• We derive the boundary conditions for the feasibility of the considered self-backhauling radio access system, under both full-duplex and half-duplex operation modes.

In particular, closed-form expressions for the achievable data rate regions and the maximum tolerable path losses are obtained.

• The performance of full-duplex and half-duplex ANs is compared by numerically evaluating the derived boundary conditions.

To facilitate a closed-form analysis, the results herein are restricted to a simplified scenario with equal path losses between the AN and each UL/DL UE and no interference between the BN and the UEs.

II. GENERICSYSTEMMODEL

We consider a self-backhauling AN that is using the same frequency band for all the transmissions, including UL, DL and the backhaul link. Furthermore, the system is analyzed under two different duplexing schemes: one where the transmission and reception are done in the inband full-duplex mode, and one where the conventional time-division duplex, i.e., half- duplex, mode is utilized. The former is illustrated in Fig. 1(a) while the latter is depicted in Fig. 1(b). The benefit of the full- duplex scheme is the increased spectral efficiency, but it suffers from SI and inter-user interference (IUI) between the UL and DL users. The half-duplex scheme, on the other hand, does not suffer from any interference, but it must alternate between the different communication tasks, resulting in a decreased spectral efficiency. In addition, the AN is assumed to have large transmit and receive antenna arrays with Nt and Nr

antennas, respectively.

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Access node Backhaul node UE UE

UE

UE UE

UE Full-duplex

(a)

UE

UE UE

UE

UE UE

UE

Half-duplex time slot 1 Half-duplex time slot 2

(b)

Fig. 1: An illustration of (a) the full-duplex, and (b) the half-duplex self-backhauling scheme. Note that in the full-duplex scheme also the uplink and downlink UEs interfere with each other, but this has been omitted in the picture to ensure its clarity.

Utilizing the modeling of [11] (although all the following analytical results are novel), the signal-to-interference-plus- noise ratio (SINR) of the signals transmitted by the AN can be expressed as follows for this type of a system:

SINRt,k =Lk(Nt−Mt−Nr)pk

σ²_t,N +σ²_t,I_,k , (1) whereLk is the path loss of the kth signal stream,Mt Nt

is the total number of receivers, pk is the transmit power of the kth signal stream, and σ²_t,N +σ_t,I,k² is the variance of the noise-plus-interference term. Note that Mt represents the combined number of DL UEs and/or the transmitted backhaul signal streams. This SINR expression takes into account the effect of nulling the receive antennas at the AN, which is necessary in order to minimize the amount of SI in the full- duplex scheme. In the half-duplex scheme, this is unnecessary and thereby the number of receive antennas does not need to be subtracted in the numerator, as will be seen later.

By employing ZF beamforming in the AN receiver as well, the SINR of thejth spatial stream received by the AN can be expressed in a similar manner as follows:

SINR_r,j = L_j(N_r−M_r)p_j

σ_r²_,N +σ_r²_,I_,j , (2) whereLj is the path loss of thejth signal stream,MrNris the number of received signal streams,pj is the corresponding transmit power, andσ_r,N² +σ_r²_,I_,j is the variance of the noise- plus-interference term. Again, Mr represents the combined number of all the received signals, consisting of those transmitted by the UL UEs and/or the BN.

III. SYSTEMCHARACTERIZATION UNDERMINIMUMRATE

CONSTRAINTS

Let us next characterize the feasible operating regions of the proposed self-backhauling radio access system. In particular, equations (1) and (2), alongside with the variables defined in Table I, can be used to establish a relationship between the realized data rates and the different system parameters, giving

TABLE I: The most important variables used in the paper.

Variable Definition

Nt/Nr Number of transmit/receive antennas at the AN D/U Number of DL/UL UEs in the cell

M_t^BH /M_r^BH Number of backhaul signal streams transmitted/received by the AN

Ld /Lu Path loss between the AN and the DL/UL UEs LUD Path loss between the UL and the DL UEs LBH Path loss between the AN and the BN

α Total amount of SI suppression in the AN σ_n² Noise floor in all the receivers

Pd Total transmit power used for the DL signal streams Pu Transmit power of an individual UE

P_d^BH Total transmit power of the BN

P_u^BH Transmit power allocated for self-backhauling in the AN η Proportion of time spent in the DL time slot (half-duplex) ρ_d /ρu DL/UL rate requirement for an individual UE

the following expressions for the total DL and UL data rates of the full-duplex scheme:

R^FD_d =Dlog₂

1 + LdΛ^FD_t Pd

D(σ²_n+U LUDPu)

, (3)

R^FD_u =Ulog₂

1 + L_uΛ^FD_r P_u σ²_n+α(Pd+P_u^BH)

, (4)

where

Λ^FD_t = Nt −Nr−D−M_t^BH

, (5)

Λ^FD_r = Nr −U−M_r^BH

, (6)

and the rest of the variables are as listed in Table I. Due to the full-duplex operation, the DL data rate is decreased by the IUI, while the UL data rate is reduced by the residual SI. Note that in this work we consider a scenario where the path loss between the BN and the UEs is sufficiently high such that they do not interfere with each other. Analyzing a case where also the mutual interference between the BN and the UEs is considered is one of our future work items.

The assumption of having equal mean channel gain within the group of DL or UL UEs is common in related lit- erature [12]–[15], especially for numerical results therein,

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because it allows to draw generic observations about the performance of the considered communication protocols in a normalized setting without cluttering them with the charac- teristics of any specific example system geometry. This also means that the data rates achieved by the UEs in UL and DL are uniform, which further simplifies the analysis. Moreover, for similar reasons, it is also assumed that the UL and DL UEs are separated such that the path losses between them are the same for all the UE pairs. Conducting this analysis in the generalized case of different path losses must be omitted from this paper due to the page limit, but it is an important future work item for us.

Using a similar derivation and making the same assumptions as above, the corresponding total UL and DL data rates for the half-duplex scheme can then be written as follows:

R^HD_d =ηDlog₂

1 +L_dΛ^HD_t P_d Dσ²_n

, (7)

R^HD_u = (1−η)Ulog₂

1 +L_uΛ^HD_r P_u σ_n²

, (8)

where

Λ^HD_t = Nt−D−M_t^BH

, (9)

Λ^HD_r = Nr−U −M_r^BH

. (10)

Note that in the half-duplex scheme there is no need to use any degrees of freedom for nulling the SI in the receive antennas, resulting in a higher SINR. Furthermore, the UL and DL signals avoid SI and IUI, unlike in the full-duplex scheme.

However, the data rates are obviously decreased by having to separate transmission and reception in time, controlled by the duplexing parameterη.

The UL and DL data rates of both schemes are subject to a QoS constraint that is expressed as follows:

R^X_d

D ≥ρd, (11)

R^X_u

U ≥ρ_u, (12)

where X ∈ {FD,HD}. These requirements ensure a minimum data rate for each individual UE. Note that the used system model assumes an identical rate for each UE in the UL and DL, meaning that the rate of an individual UE can be simply obtained by dividing the corresponding sum rate by the total number of UEs. Expressing the rates as a base 2 exponential, (3) and (4) give rise to the following inequalities for the full-duplex scheme:

1 + L_dΛ^FD_t P_d D(σ_n²+U LUDPu)

≥2^ρ^d, (13)

1 + LuΛ^FD_r Pu

σ_n²+α(Pd +P_u^BH)

≥2^ρ^u. (14) For the half-duplex scheme, (11) and (12) result in the following corresponding inequalities:

1 +LdΛ^HD_t Pd

Dσ²_n ^η

≥2^ρ^d, (15)

1 + L_uΛ^HD_r P_u σ_n²

^(1−η)

≥2^ρ^u. (16) Furthermore, an important consideration for the analyzed system is to ensure the self-backhauling capacity of the AN.

Using again the variables of Table I, the total backhaul data rates for the full-duplex scheme are

R^FD_d,BH =M_r^BHlog₂

1 + L_BHΛ^FD_r P_d^BH M_r^BH[σ_n²+α(Pd+P_u^BH)]

, (17) R_u,BH^FD =M_t^BHlog₂

1 + L_BHΛ^FD_t P_u^BH M_t^BHσ_n²

. (18)

In this work, it is assumed that the BN is capable of perfect SI cancellation due to it being a large infrastructure node. The backhaul rates for the half-duplex scheme can be defined in a similar manner as above and they are given by

R^HD_d,BH = (1−η)M_r^BHlog₂

1 +L_BHΛ^HD_r P_d^BH M_r^BHσ_n²

, (19) R^HD_u,BH =ηM_t^BHlog₂

1 +LBHΛ^HD_t P_u^BH M_t^BHσ_n²

. (20)

Let us remark that now R^X_d,BH is the achievable backhaul rate from the BN to the AN while, conversely,R^X_u,BH is the corresponding rate from the AN to the BN.

Using (17)–(20), the backhaul rate requirements for the two schemes can then be written as follows:

R^X_d_,BH ≥R_d^X, (21) R^X_u,BH ≥R_u^X. (22) Satisfying these inequalities ensures that the AN has enough backhauling capacity to support all the UL and DL traffic.

A. Feasibility Analysis of the Full-Duplex Scheme

Let us then determine under which extreme conditions the full-duplex scheme can still fulfill the QoS constraints in (11) and (12), i.e., what are the boundary conditions for the feasibility of full-duplex self-backhauling, assuming that R^FD_d /D=ρd andR^FD_u /U =ρu. Starting from (13) and (14), we can then obtain the following conditions for the DL and UL transmit powers:

Pd = D σ_n²+U LUDPu

(2^ρ^d−1)

LdΛ^FD_t , (23) Pu= σ_n²+α Pd+P_u^BH

(2^ρ^u−1)

LuΛ^FD_r , (24) where P_u^BH is solved from (18) under the presumption that R^FD_u /U =ρ_u andR^FD_u,BH =R^FD_u . In order to investigate the feasibility of the system, upper bounds for the DL and UL transmit powers are defined asP_d^max andP_u^max, respectively.

This gives rise to two meaningful scenarios: (i) Pd =P_d^max and Pu is set according to (24) or (ii) Pu =P_u^max and Pd

is set according to (23). In other words, the system is either limited by the DL transmit power or by the UL transmit power.

Note that in general bothPd =P_d^max andPu =P_u^max cannot

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hold at the same time, since then the QoS requirements would not necessarily be fulfilled due to SI and IUI. This means that either the UL or the DL transmit power must be set according to (23) or (24).

Then, to obtain the boundary conditions for the considered system, let us first assume that Pu = P_u^max, and Pd is set according to (23). Substituting then (23) into (14) and assuming R^FD_u /U = ρu gives the following expression for the achievable DL data rate with respect to the UL data rate:

ρd =ρ^I_d_,max = log₂



1 +

L_uΛ^FD_r

2^ρu−1 −^σⁿ²^+αP_Pmax^u^BH u

αDσ²_n

LdΛ^FD_t P_u^max +^{αU DL}_L ^UD

dΛ^FD_t



. (25) In a similar manner, when assuming thatP_d =P_d^max, andP_u is set according to (24), and substituting (24) into (13) when R^FD_d /D=ρd, the following expression can be obtained:

ρd =ρ^II_d_,max

= log₂



1 +

LuL_dΛ^FD_r Λ^FD_t P_d^max U DLUD(2^ρu−1)

σ_n²+α(P_d^max+P_u^BH) +_{U L}^σ²ⁿ^L^u^Λ^FD^r

UD(2^ρu−1)



. (26) The achievable rate region can then simply be defined as follows:

ρd ≤min ρ^I_d,max, ρ^II_d,max

. (27)

It can also be easily shown that the limits for the maximum transmit powers are fulfilled under this rate region.

Another interesting aspect of the considered system is the amount of path loss that can be tolerated in the DL and in the UL. Utilizing (25), (26), and (27), the relationship between the DL and UL path losses can be defined as:

L^dB_d ≤min

L^I,dB_d,max, L^II,dB_d,max

, (28)

where

L^I,dB_d,max = 10 log₁₀





αDσ²_n

Λ^FD_t P_u^max +^{αU DL}_ΛFD^UD t

LuΛ^FD_r

(2^ρu−1)(2^ρd−1)−₍₂^σρⁿ²d^+αP−1)P^u^BH_u^max



 (29) and

L^II,dB_d,max = 10 log₁₀





L_uΛ^FD_r Λ^FD_t P_d^max U DL_UD(2^ρu−1)(2^ρd−1)

σ_n²+α(P_d^max +P_u^BH) +_{U L}^σ²ⁿ^L^u^Λ^FD^r

UD(2^ρu−1)



. (30) Note that (28)–(30) consider the path loss as positive decibels, and hence the path loss limit also becomes an upper bound.

An interesting special case of these boundary conditions is whenP_d^max, P_u^max → ∞. It can be easily seen from (25)–

(30) that the feasibility boundaries for the achievable rates and maximum path losses can then be written simply as follows:

ρd <log₂

1 + LuLdΛ^FD_r Λ^FD_t αU DLUD(2^ρ^u−1)

, (31)

TABLE II: The essential default system parameters.

Parameter Value

Number of transmit/receive antennas at the AN (Nt/Nr) 200/100

Number of DL/UL UEs (D/U) 10/10

Number of DL/UL backhaul streams (M_r^BH/M_t^BH) 12/6 DL/UL rate requirement (ρd/ρu) 10/4 bps/Hz

Receiver noise floor (σ²_n) -90 dBm Amount of SI suppression in the AN (α) 120 dB Path loss between the AN and the DL/UL UEs (Ld/Lu) 90/90 dB

Path loss between the DL and the UL UEs (LUD) 90 dB Path loss of the backhaul link (LBH) 80 dB Maximum DL/UL transmit power (P_d^max/P_u^max) 35/5 dBm

L^dB_d <10 log₂

1 +αU DLUD(2^ρ^u−1) (2^ρ^d−1) LuΛ^FD_r Λ^FD_t

. (32) These expressions can be used to determine the fundamental boundary conditions for the feasibility of the considered self- backhauling radio access system.

B. Feasibility Analysis of the Half-Duplex Scheme

For comparison, the similar feasibility conditions for the half-duplex scheme are also analyzed. In this case, the boundaries can be obtained in a more straightforward manner since the UL and DL transmit powers are not dependent on each other, as can be seen from (7)–(8). In particular, by combining (7) and (8) we get the following rate region for the half-duplex scheme:

ρd ≤

1−ρu

φ

log₂

1 + LdΛ^HD_t P_d^max σ_n²

, (33) where

φ= log₂

1 +LuΛ^HD_r P_u^max σ_n²

. (34) Similarly, the tolerable path loss region can be written as follows:

L^dB_d ≤10 log₁₀



 Dσ²_n

2^φ−ρ^φρ^d^u −1 Λ^HD_t P_d^max



. (35) Note that the half-duplex scheme does not have any fundamental feasibility limits when P_d^max, P_u^max → ∞, and hence it can operate under any conditions, as long as the transmit powers are set to a sufficiently high level.

IV. NUMERICALRESULTS

To obtain some intuitive insight into the feasible operation regions of the full-duplex and half-duplex schemes, the two systems are next evaluated numerically using the derived analytical rate and path loss regions. The default system parameters, used in the calculations unless otherwise mentioned, are shown in Table II.

The achievable rate regions for the two schemes are first shown in Fig. 2. There, the regions of the full-duplex scheme are plotted for different amounts of SI cancellation, as well as with and without upper limits for the DL and UL transmit

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ρ_u(bps/Hz)

0 5 10 15 20

ρd(bps/Hz)

0 5 10 15

20 _FD,_α= 130 dB, fundamental boundary

FD, α= 130 dB, P_d/P_ulimited to 35/5 dBm FD, α= 120 dB, fundamental boundary FD, α= 120 dB, P_d/P_ulimited to 35/5 dBm FD, α= 110 dB, fundamental boundary FD, α= 110 dB, P_d/P_ulimited to 35/5 dBm HD, P_d/P_ulimited to 35/5 dBm

Fig. 2: The feasible rate regions for the full-duplex and half-duplex schemes, shown for different amounts of SI cancellation and for cases with and without an upper limit for the usable UL and DL transmit powers.

L_u(dB)

60 80 100 120

L d(dB)

60 70 80 90 100 110 120

130 _{FD, ρ}

u= 2, fundamental boundary FD, ρ_u= 2, P_d/P_ulimited to 35/5 dBm HD, ρ_u= 2, P_d/P_ulimited to 35/5 dBm FD,ρ_u= 4, fundamental boundary FD,ρ_u= 4, P_d/P_ulimited to 35/5 dBm HD,ρ_u= 4, P_d/P_ulimited to 35/5 dBm FD, ρ_u= 6, fundamental boundary FD, ρ_u= 6, P_d/P_ulimited to 35/5 dBm HD, ρ_u= 6, P_d/P_ulimited to 35/5 dBm

Fig. 3: The highest tolerable path losses for the full-duplex and half- duplex schemes, shown for different UL data rate requirements and for cases with and without an upper limit for the usable UL and DL transmit powers.

powers. The rate region of the half-duplex scheme is only shown for limited transmit powers, since it does not have an upper limit with infinite powers, as discussed earlier. In the figure, the region below each curve represents the feasible values forρ_u andρ_d, while anything above the curve cannot be reached.

It can be observed from Fig. 2 that, with the lower amounts of SI cancellation, the fundamental boundary of the full-duplex scheme is in fact quite close to the rate region obtained with the finite transmit powers. However, when the amount of SI cancellation increases, other factors start to limit the achievable rates under finite transmit powers, and the gap between the practical and fundamental boundaries widens.

Another significant observation is that, under very low UL data rate requirements, the half-duplex scheme can provide a higher DL data rate than the full-duplex scheme. This indicates that such extreme cases are better suited for traditional half-duplex operation modes. Nevertheless, with reasonable amounts of SI cancellation and more practical UL data rate requirements, the full-duplex scheme can obtain a higher DL data rate than the half-duplex scheme.

Figure 2 also shows that the rate regions are non-convex in some of the cases, which means that the size of the region could be increased by alternating between two different values for ρ_u andρ_d. However, investigating this type of a hybrid solution further is left for future work.

Another point of view into the feasibility of full-duplex self- backhauling is the maximum tolerable path loss between the AN and the UEs. To this end, Fig. 3 shows the acceptable path loss region for the half-duplex and full-duplex schemes, again with and without upper limits for the usable DL and UL transmit powers. In particular, Fig. 3 shows the maximum tolerable path loss for both the DL and UL UEs with three different UL data rate requirements. In the case without any limits on the transmit powers, it can be observed that the relationship between the DL and UL path loss is linear in logarithmic scale, as is also evident from (32). However, imposing limits

for the UL and DL transmit powers results in an upper bound for both of the path losses, as can be expected. Furthermore, it can also be clearly observed that, with the same transmit power limits, the full-duplex scheme can tolerate higher path losses than the half-duplex scheme. This is especially clear with the higher UL data rate requirements, since then the full- duplex scheme can tolerate 10–20 dB higher path loss levels for both the DL and the UL links.

V. CONCLUSION

In this paper, we investigated the feasibility of wireless inband full-duplex self-backhauling in a radio access system.

In particular, the achievable rate regions were derived in closed-form for both limited and unlimited transmit powers, alongside with the highest tolerable path losses in the uplink and in the downlink. For comparison, the same boundaries were also derived for a reference half-duplex scheme. The numerical results showed that, with sufficient self-interference cancellation performance, the full-duplex scheme has a larger rate region than its half-duplex counterpart, while also tolerat- ing higher path losses. This indicates that inband full-duplex self-backhauling is a potential method for providing the backhauling capabilities in the next generation ultra dense wireless networks. Furthermore, since these results were obtained under certain simplifying assumptions regarding the radio access system, confirming the findings with a more comprehensive and realistic system model is an important future work item for us.

ACKNOWLEDGMENT

The research work leading to these results was funded by the Academy of Finland (under the project #304147 ”In-Band Full-Duplex Radio Technology: Realizing Next Generation Wireless Transmission”), Tekes (under the TAKE-5 project), Tampere University of Technology Graduate School, Nokia Foundation, Tuula and Yrj¨o Neuvo Research Fund, and Emil Aaltonen Foundation.

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