Explicit power ramping during random access in LTE ...

Explicit power ramping during random access in LTE/LTE-A Jelena Miˇsi´c, Vojislav B. Miˇsi´c and M Zulfiker Ali Ryerson University, Toronto, ON, Canada M5B 2K3 Abstract—In this paper we model and evaluate power ramping as a mechanism for achieving explicit access priority among traffic classes in LTE/LTE-A, taking into account preamble SINR considerations, preamble collisions, capture effect, and Physical Downlink Control Channel (PDCCH) deficiency. The results show that explicit power ramping can provide reasonable performance differentiation among traffic classes but it still cannot overcome coupling among traffic classes which exists due to preamble collisions and insufficient PDCCH resources.

The paper is organized as follows: Section II describes the four step handshake and potential failure modes. Brief description of LTE/LTE-A random access procedure is presented in Section II. Analytical model of four-way handshake procedure with explicit power ramping is presented in Section III. Performance evaluation with and without power ramping is presented in Section IV. Finally, section V concludes the paper.

I. I NTRODUCTION Random access in Long Term Evolution/Long Term Evolution-Advanced (LTE/LTE-A) cells occurs in initial access by a terminal (User Equipment or UE), synchronization or handover. Random access is performed on the Physical Random Access Channel (PRACH) by four step handshake. Random access may be hindered by preamble collisions due to simultaneous UE access, outage condition at the eNodeB due to SINR violation and insufficient downlink resources on Physical Downlink Control Channel (PDCCH). The problem of efficient random access is important due to the rapidly increasing number of M2M (Machine-to-Machine Communications) terminals [10]. A number of solutions that can alleviate congestion during random access have been proposed, including access class barring, backoff and slotted access schemes [3], [5], [6], [8] and dynamic resource allocation schemes with optional prioritization [9], [13]. The standard also allows age-based power ramping where each preamble’s power is raised by a constant increment after every access failure. This is a lightweight technique which can be implemented at the physical layer with very low overhead [12], [2]. Age-based power ramping helps stations to complete four way handshake under low to moderate load but under moderate to high load it gradually increases the chance of outage condition at eNodeB by decreasing SINR [14]. However, in applications where success of the four-way handshake is critical, explicit user priorities assigned per traffic class may be more appropriate than the age-based ones. Therefore traffic classes need to be introduced for some applications like in healthcare and safety messages in VANET. In this paper we analyze priority differentiation during random access on PRACH implemented by assigning different preamble powers to traffic classes. We develop an analytical model that considers success failure of each step of four-way handshake, namely preamble collisions in first step including capture effect, outage condition in first and third steps, and PDCCH deficiency in two downlink steps. Our model uses realistic SINR characteristics on the PRACH. Capture effect refers to the situation when preambles collide but eNodeB decodes the request due to high SINR. Our analysis shows the extent of differentiation among classes using power increments and points to other coupling effects which affect it.

II. R ANDOM ACCESS UNDER EXPLICIT POWER RAMPING In case of a new call, handover, scheduling, tracking or synchronization request random access requires that the UE undergoes the four step handshake [4] on PRACH, which is one of the several physical channels used in LTE/LTE-A cells. PRACH is implemented as a number cf ∈ {1, 2, 3, 5, 10} of 1ms resource blocks within the basic LTE frame with duration of Tf = 10ms. In a typical LTE system with 5MHz bandwidth, the bandwidth dedicated to PRACH channel is W = 1.08 MHz. There are 16 patterns of allocating cf PRACH subframes due to inter-cell PRACH interference as well as multiplexing with Physical Uplink Scheduled Channel (PUSCH) and Physical Uplink Control Channel (PUCCH). The four-way handshake operates as follows. First, the UE randomly chooses a preamble from a set of N mutually orthogonal Zadoff-Chu (ZC) sequences [1], [4] and transmits it on PRACH. The set of N ZC preambles is partitioned into a subset of Nh preambles allocated to handoff calls for non-contention access, while the rest of Nn = N − Nh is allocated to new calls in contention-based access. For preamble format 0 (where PRACH occurs in a single subframe), a preamble with length of Nseq = 839 elements is transmitted within one preamble time of 800 µs, resulting in preamble element rate of R = 1.048M elements per second. This handshake step can fail due to preamble collisions as well as outage when eNodeB will not be able to decode request due to low SINR. eNodeB replies to correctly decoded preambles with a Random Access response (RAR) message which includes the decoded preamble; it is sent in time window of duration 1, 2, or 3ms, starting two time slots after PRACH. However, it is possible that two or more preambles collide without outage at the eNodeB and this situation will be denoted as capture. In this case EnodeB will send RAR message which will be received by collided stations. They will further transmit third handshake step message over PUSCH and if outage does not occur eNodeB will decode one of them, allocate resources for the call and reply in the fourth step. eNodeB sends RAR and contention resolution messages in the second and fourth step of the handshake, respectively, using PDCCH where 16 control channel elements (CCEs) are allocated in each 1 ms slot. Within each slot, eight CCEs are needed to convey between one and

three RAR messages, so the total number of CCEs available noise power density of Tx = 100.1x−log10 Nseq where Nseq is before the deadline to receive a RAR message is 80. In this preamble length. manner, at most NR = 15 RAR messages can be transmitted. The probability of violating SINR threshold (outage) per Calls that collide with outage will not receive a RAR in traffic class i can be written as the second step and will conduct a backoff procedure, using ,k2 ,...kΥ ,i (x) = a previously advertised backoff window Nw . We assume that ok1  Υ that backoff value chosen by the UE is uniformly distributed X W δ W η η i 0 s,1 > 10(log10 Nseq −0.1x) − kj δj − δi + within the range (0, Nw − 1). Correctly decoded calls receive P r  S R S 1 1 j=1 a RAR to which they respond with third step L2 /L3 message (2) in the same uplink resource. L2 /L3 message contains UE’s identity including C-RNTI and actual request; it is transmitted Inter-cell interference in the target cell follows a Gaussian over PUSCH. We assume that collision of L2/L3 messages will distribution with mean κ and variance equal to κ . Therefore m v prevent eNodeB from successfully decoding any message with sum of local and external interference for class i is Gaussian P a certain probability (which is, in fact, the probability of outage random variable with mean W η0 + Υ k δ − δ + κ i m,1 and j=1 j j S1 on PUSCH). variance equal to κv,1 . Then remaining capacity for class i and Finally, eNodeB sends a contention resolution message to SINR threshold equal to x also follows Gaussian distribution the UE whose L2 /L3 message was successfully decoded; the with mean of: message contains information about the resources allocated m(k1 , k2 , . . . kΥ , i, x) for the actual call. A missing message informs the UE that Υ a collision has occurred, in which case it will retry access after W δi (log10 Nseq −0.1x) W η0 X − 10 − = kj δj + δi − κm,1 random backoff. R S1 j=1 III. A NALYTICAL MODEL FOR EXPLICIT POWER RAMPING (3) Let us assume that there are Υ traffic classes, where traffic class 1 ≤ i ≤ Υ transmits with power ramping coefficient δi , so that the default received power at eNodeB is δi S1 . SINR for the preamble in a given PRACH slot is expressed as ratio of the energy of the entire preamble sequence and spectral density E of noise power Np0 [12], [4]. SINR violations lead to outage which is the cause of failure in steps 1 and 3 of the handshake. Let the request arrival rate of new traffic per class 1 ≤ i ≤ Υ be λi requests per PRACH slot; this can be translated to the λ c number of requests per second per class as λs,i = Ti ff . We assume that handoff calls arrive at the rate λh,i = kπ λi where kπ is in the range 0.10 . . 0.2, and that they use an exclusive set of Nh preambles to deploy a contention-free random access procedure [4], [12]. There are at most M re-transmission attempts in the case of missed preamble detection. In traffic class 1 ≤ i ≤ Υ there are kt,i new call requests and kh,i requests for handover calls, for a total of ki requests. We assume that numbers ki come from Poisson distribution and will be derived later. A. Outage on first handshake step

ok1 ,k2 ,...kΥ ,i (x) = erfc (r(k1 , k2 , . . . kM , i, x)) R ∞ − t2 where erfc(y) = √ 1 e 2 dt. y

(4)

(2π)

Further we need to relate probability of PRACH missed preamble detection and SINR. Missed preamble detection probability is defined as Pmpd (SINR) which is a function of E SINR = 10 log10 Np,i for a given PRACH bandwidth. Note 0 that a false alarm will not result in request re-transmission, therefore we will not consider it in this work. We have obtained analytical SINR characteristics Pmpd (x) by applying Thiele’s interpolation on points obtained by simulations in the range between 11dB-21dB, and shown in Fig. 17.12 from [12] as Pmpd (x) = 0.8 +

(x − 9) −5 +

x−11 −0.933+

−8.855+

x−13 x−15 x−17 −34.53+2.998x

−0.19+

Let us assume that a given request can be re-transmitted M E more times after a failed initial attempt. The ratio Np,i for a 0 request in i-th priority class is Nseq δi W Ep,i R = PΥ ηs,1 N0 k δ − δ + j j l j=1 S1 +

For clarity we can define the ratio of mean and standard deviation of remaining capacity for class i as r(k1 , . . . kΥ , i, x) = √ m(k1 , k2 , . . . kΥ , i, x)/ κv,1 , in which case (2) can be written as

η0 W S1

(1)

where ηs,1 is the power of external (out of cell) interference and η0 is spectral density of white noise. We assume that the ratio of external interference and received signal power ηs,1 S1 has Gaussian distribution on PRACH, and that its mean and variance are represented with κm,1 and κv,1 , respectively, where additional subscript 1 refers to the first handshake step. Outage condition occurs when variable part in expr. (1) exceeds the constant one. Before this can be written we need E to translate preamble SINR threshold from Np,i = xdB per 0 preamble element to the ratio of preamble element energy to

(5) and the probability that preamble will not be detected due to the PRACH outage can be formulated as Z 21 Ok1 ,...kΥ ,i= Pmpd (x) [ok1 ,...kΥ ,i (x + dx) − ok1 ,...kΥ ,i (x)] x=11 Z 21 d = Pmpd (x) ok1 ,...kΥ ,i (x)dx dx x=11 Z 21 2 1 −1 =√ Pmpd (x)e− 2 r(k1 ,...kΥ ,i,x) 2π x=11 d · r(k1 , . . . kΥ , i, x)dx (6) dx 0.1W δi ln(10) d where dx r(k1 , k2 , . . . kΥ , i, x) = − R10(0.1x−ln(N . seq )/ln(10)) For evaluation of outage probabilities in traffic class i in the first handshake step Po1,i and third handshake step Po3,i

respectively we will treat them as variables in derivation of total request arrival rates. Given initial request arrival rate λi we need to evaluate request arrival rates for class i = 1 . . Υ for all re-transmission attempts 0 ≤ j ≤ M as: λj,i = λi ,

j=0

λj,i = λi (Po1,i + Po3,i )j + (Po1,i + Po3,i )j−1 ·(1 − Po1,i )PP DCCH ) ,

j = 1 .. M

(7)

Similarly, handoff request rate for class i can be expressed as: λh,j,i = λh,i ,

j=0

λRAR =

λh,j,i = λh,i (Po1,i )j + λh,i (Po1,i )j−1 · (1 − Po1,i )PP DCCH

j = 1 .. M

λi,tot =

(8)

λj,i

λh,i,tot =

λh,j,i

(9)

Then, joint probability that ki requests per traffic classes i = 1 . . Υ will occur in the same PRACH slot becomes Υ Y (λi,tot + λh,i,tot )ki

ki !

i=1

e(−λi,tot −λh,i,tot )

(10)

Po1,i =

X k1 =0

kΥ,max

X

...

where Ps denotes scaling coefficient which models the fact that, for 1 < j preambles participating in a collision, only one RAR message is returned by the eNodeB. Assuming at most J preambles involved in a collision, it may be defined as PJ (λx )j

Pk1 ,...kΥ Ok1 ,...kΥ ,i

(11)

kΥ =0

Note that outage probability in first handshake step does not depend on transmission attempt as might be the case if priorities were based on the attempt iteration. B. Preamble collisions When preambles are transmitted with different traffic classes it is important to distinguish whether the preambles that collided belong to the same class (power level) or not. Consider a generic Poisson preamble traffic flow with intensity λx . Assuming that new call request chooses a preamble from the pool of Nn preambles using uniform distribution, the probability that two or more preambles will collide in same PRACH resource within this flow is (λx /Nn )e−λx /Nn (12) 1 − e−λx /Nn Then, the total probability that two or more UEs from any traffic class will collide is f (λx ) = 1 −

Υ X Pa = f ( λi,tot )

(13)

i=1

Probabilities that preamble transmitted by traffic class i UE will be involved in intra- and inter-class collision respectively are a Pa,i = f (λi,tot ) i Pa,i = Pa − f (λi,tot )

(14)

(16)

PΥ where λx = i=1 λi,tot /Nn and J = 5, which gives good result accuracy. Probability of PDCCH overload is, then, obtained as the probability of more than NR pending RAR replies to a single PRACH transmission competition: PP DCCH = 1 −

NR j X λ

RAR −λRAR

j=0

Then outage probability for class i may be calculated as k1,max

(15)

Ps = PJ

j=0

Pk1 ,...kΥ =

(λi,tot (Pa Ps + 1 − Pa ) + λh,i,tot )(1 − Po1,i )

j=2 j·j! (λx )j j=2 j!

j=0 M X

Υ X i=1

In order to get total arrival process, retransmission rates must be grouped by traffic class as M X

C. Causes of failure in first handshake step Failure in the first handshake step can be caused by outage at eNodeB, but also by the lack of resources at the PDCCH in the second step of the handshake, which occurs with the probability PP DCCH . Namely, RAR and contention resolution messages in the second and fourth step of the handshake, respectively, are sent on PDCCH which can accommodate up to NR messages upon every contention [7], [11]. Total arrival rate of successful candidates for RAR response is

j!

e

(17)

Note that collision of preambles without outage is not considered as a failure until final resolution is achieved in step four of the handshake. Probability of failed access attempt of class i in the first handshake step is Po1,i + (1 − Po1,i )PP DCCH .

(18)

D. Outage on third handshake step and capture effect For traffic class i, the probability of getting RAR after collision in the first handshake step is PL3,i = Pa (1 − Po1,i )(1 − PP DCCH )

(19)

Let PL3,i denote the probability of capture effect for call i. In third step uplink message L3 is sent. Arrival rate of L3 messages caused by capture effect over all traffic classes is uniformly divided over Nn preambles as PΥ λi,tot PL3,i λL,tot = i=1 (20) Nn Probability that j terminals send L3 message as a result of capture over same PUSCH resource is (λL,tot )j (21) j! It is reasonable to assume that spectral efficiency of uplink transmission in the third step is the same as for the first W 3 step, i.e., W R3 = R , but the SINR threshold on PUSCH resource must be significantly higher than on PRACH since it is observed over a single bit. Outage probability in the third step when j calls are present is   W3 1 W3 η 0 √ Ωj = erfc ( − − j − κm,3 )/ κv,3 (22) R3 T3 S3 Pξ (j) = e−λL,tot

where W3 , R3 , T3 denote bandwidth, data rate and detection threshold on the PUSCH resource block, and κm,3 and κv,3 are mean and standard deviation of Gaussian distribution. When this probability is averaged over the number of colliding terminals between 2 and J, the overall outage probability on the PUSCH resource block is PJ j=2 Pξ (j)Ωj (23) Pl = P J j=2 Pξ (j) Since λL,tot is small it is reasonable to assume that only a small number (J) UEs can collide at the third handshake step. Then, probability that L3 message will not get contention resolution response is PJ j−1 j=2 Pξ (j) j (1 − Pl ) (24) P f2/3 = Pl + PJ j=2 Pξ (j) Probabilities of failing and passing the third handshake step respectively are: Po3,i = Pa (1 − Po1,i )(1 − PP DCCH )P f2/3 Ps3,i = Pa (1 − Po1,i )(1 − PP DCCH )(1 − P f2/3 ) which leads to total success probability of four way handshake for traffic class i as: Pstot,i = (1 − Pa )(1 − Po1,i )(1 − PP DCCH ) + Ps3,i

(25)

Finally, regular and handover throughputs for traffic class i become: Θi = λi,tot Pstot,i Θh,i = λh,i,tot (1 − Po1,i )(1 − PP DCCH )

(26)

IV. P ERFORMANCE EVALUATION To evaluate the performance of random access with and without power ramping, we have solved the system of equations (4) to (25) above, using parameter values listed in Table I. We have assumed M = 2 re-transmission attempts and two traffic classes: one with default transmission power (i.e. δ2 = 0 dB) and the other with increased power coefficient δ1 set to 1, 2, and 3 dB, respectively. There was no difference in preamble power between successive re-transmission attempts for the same class. Cell preamble format was set to 0 and configuration index was set to 6 which means that 2 subframes are allocated for PRACH per LTE frame (cf = 2). New preamble arrival rates for two traffic classes are asymmetric, with λ1 = 0.5λ2 . Preamble arrival rate for traffic class 2 was varied between 200 and 1200 rps with additional λh,i = 0.1λi contributed by preambles transmitted handoff calls. For third handshake step, we assumed that W3 /R3 = 1 and T3 = 0.3, which corresponds to 10log Eb N = −5dB [4]. The maximum number of UEs colliding on PUSCH resource is limited to J = 5. The inter-cell interference between surrounding cells and PRACH in the target cell was modeled as a Gaussian random variable with mean κm,1 = κm,3 = 0.247 and standard deviation κv,1 = κv,3 = 0.078, while white noise density was η0 = 4 · 10−21 W/Hz. Outage probability and handshake success probability under default PDCCH resources (NR = 15) are shown in Figs. 1 and 3, respectively, as functions of new preamble arrival rate for second traffic class . Situation when PDCCH deficiency is

TABLE I PRACH PARAMETERS USED IN PERFORMANCE EVALUATION parameter Cell bandwidth PRACH bandwidth Preamble size Preamble format Total number of preambles in cell Number of preambles reserved for handoff Number of PRACH resources per frame Number of PDCCH resources for RAR Maximum number of re-transmissions Use of power ramping Power ramping coefficients

value 5 MHz W = 1.08MHz Nseq = 839 0 (800µs duration) N = 64 Nh = 10 cf = 2 15 / 30 M =2 explicit δ2 = 0, δ1 = 1, 2, 3dB

removed (NR = 30) is shown in Figs. 2 and 4. Results for higher priority traffic are denoted with solid lines, while those for low priority traffic are shown with diamond symbols. For reference, all diagrams also show the case without differentiation, i.e., when δ1 = δ2 = 0dB (dashed lines). Results indicate that increasing the transmission power helps higher priority class to a certain extent, with better performance obtained at higher transmission power increment. Outage probability for standard value of PDCCH resources NR = 15 shows that at λ2 = 1200 and λ1 = 600 rps, outage probability for high priority class decreases from no-priority line approximately by 0.03, 0.04 and 0.05 for each 1dB increment of δ1 . This corresponds to changes of 43%, 57% and 71% between increments of δ1 . At the same time outage probability for non-priority class increased by 0.015, 0.03 and 0.06, representing increase of 21%, 42% and 85%, respectively, for the same scenario. When the amount of PDCCH resources is doubled to NR = 30, outage probability for high priority traffic (at λ2 = 1200 rps) is smaller and decreases approximately by 36%, 54% and 69% per 1dB increment of δ1 while outage probability for low priority class increases by 27%, 54% and 109%, respectively. The difference between performance shown in Figs. 1 and 2 may be explained by observing two major sources of coupling between the traffic classes: namely, preamble collisions and missed deadlines by RAR messages caused by insufficient PDCCH resources. Traffic class with higher arrival rate will experience more collisions. However, requests from both classes which did not collide and those that experience capture effect are equally likely to suffer from the lack of PDDCH resources. Therefore, both coupling mechanisms tend to somehow decrease effect of priority differentiation. However, when PDCCH resource deficiency is eliminated with NR = 30, coupling exists mostly through preamble collisions, since all RAR responses will come on time and there will be no unnecessary repetition of preambles for which RAR replies missed the deadline. Therefore, the decline of outage probability for class 1 will be slightly smaller and increase of outage probability for class 2 will be larger due to different preamble arrival rates and collisions. Handshake success probability shows milder differentiation due to the impact of collisions in the first step, PDCCH deficiency and the capture effect in third handshake step. However, when NR = 15, at λ2 = 1200 rps success probability for traffic class 1 increases by 2.5% per δ1 = 1dB of power increment. Traffic class 2 experiences decline of 2%, 4% and 6% under the

classes 1 and 2: Prob. of H2H outage on PRACH 0.08

classes 1 and 2: Prob. of H2H outage on PRACH 0.07 0.06

0.06

0.05 0.04

0.04

0.03 0.02

0.02

0.01 0

0 200

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600 800 lambda2s

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(a) Outage probability for δ1 =1dB, NR = 15

(a) Outage probability for δ1 =1dB, NR = 30

classes 1 and 2: Prob. of H2H outage on PRACH 0.1

classes 1 and 2: Prob. of H2H outage on PRACH 0.08

0.08 0.06 0.06 0.04 0.04 0.02

0.02

0

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(b) Outage probability for δ1 =2dB, NR = 15

(b) Outage probability for δ1 =2dB, NR = 30

classes 1 and 2: Prob. of H2H outage on PRACH

classes 1 and 2: Prob. of H2H outage on PRACH

0.12

0.1

0.1

0.08

0.08 0.06 0.06 0.04

0.04

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0

0 200

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600 800 lambda2s

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(c) Outage probability for δ1 =3dB, NR = 15

(c) Outage probability for δ1 =3dB, NR = 30

Fig. 1. Outage probability in the first step of PRACH four way handshake when NR = 15

Fig. 2. Outage probability in the first step of PRACH four way handshake when NR = 30

same conditions. When NR = 30, coupling of traffic classes through downlink PDCCH queue is eliminated and handshake success probabilities are around 15% higher. We also notice that, at the same request arrival rate, success probability for high priority traffic increases by 2% per δ1 = 1dB step while its low priority counterpart decreases by approximately same amount. This is in agreement with the previous observation for outage probability.

extent. Further decoupling and differentiation should be done through partial or full separation of preamble pools among classes.

V. C ONCLUSION In this paper we have examined the performance of random access in LTE/LTE-A networks with explicit power ramping. Power ramping decreases outage probability of high priority traffic in the first handshake step and improves overall success probability of four way handshake. Performance results quantify the impact of priority differentiation by power ramping. We also demonstrate that increasing the amount of downlink PDCCH resources has a large impact on improvement of success probability, and that it decouples traffic classes to some

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Prob. of successfull handshake on random access

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(c) Success probability for δ1 = 3dB, NR = 30

Fig. 3. Success probability of four step handshake delay when NR = 15

Fig. 4. Success probability of four step handshake delay when NR = 30

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