Frequency-Domain Multipacket Detection: A High ... - CiteSeerX

Frequency-Domain Multipacket Detection: A High Throughput Technique for SC-FDE Systems R.Dinis(1) , P.Carvalho(2) , L.Bernardo(2) , R.Oliveira(2) , M.Serrazina(2) and P.Pinto(2) (1) ISR-IST, Tech. Univ. of Lisbon, Portugal (2) UNINOVA, FCT-UNL, Monte da Caparica, Portugal Abstract - Usually, packets involved in a collision are lost, requiring their retransmission. However, the signal associated to collisions has important information concerning the packets involved. In fact, with proper retransmissions we can efficiently resolve collisions. In this paper we propose a frequency-domain multipacket detection technique for SC-FDE schemes (SingleCarrier with Frequency-Domain Equalization) that allows an efficient packet separation in the presence of successive collisions. This technique allows high throughputs, since the total number of transmissions is equal to the number of packets involved in the collision, even when the channel remains fixed for the retransmissions. Since we consider SC-FDE schemes and the complexity is concentrated in the receiver, this technique particularly appealing for the uplink of broadband wireless systems. 1 I. I NTRODUCTION In wireless systems multiple users might try to access a given channel and the objective of MAC protocols (Medium Access Control) is to allow this in an efficient way. When different users are simultaneously accessing a given channel we have a collision, an event that is almost unavoidable in wireless systems. The simplest and more common approach to cope with collisions is to assume that all packets involved are lost. This means that we need to retransmit all packets involved in a collision, which leads to significant reduction in the system throughput. To reduce the chances of multiple collisions a given user transmits in the next available slot with a given probability. With this strategy, if two packets collide we need three time slots to complete the transmission (more if there are multiple collisions). However, the signal associated to a collision contain information on the packets involved, which can be used to improve the system performance [1]. In fact, if we do not discard collided packets and we use proper retransmissions we can efficiently resolve collisions. To overcome this problem, a TA (Tree Algorithm) was combined with a SIC scheme (Successive Interference Cancelation) [2]. Within this SICTA technique, we do not discard the signal associated to a collision. Instead, if the packets of users A and B collide 1 This work was partially supported by the FCT (Fundac ¸ a˜ o para a Ciˆencia e Tecnologia), under the pluriannual funding and project U-BOAT PTDC/EEATEL/67066/2006, and the C-MOBILE project IST-2005-27423.

then, once we receive with success the packet of one of those users we can subtract the corresponding signal from the signal with collision and recover the packet from the other user. With this strategy, if two packets collide we need two time slots to complete the transmission (unless there are multiple collisions). The major problem with this technique is that packet errors might lead to a deadlock problem [3]. Moreover, the required number of transmissions might be high if we have successive collisions. These techniques have the major limitation that we do not take full advantage of the information in the collision. The ideal situation would be to use the signals associated to multiple collisions to separate the packets involved. In this paper we propose a frequency-domain multipacket receiver that allows an efficient packet separation in the presence of successive collisions. We consider the use of SCFDE schemes (Single-Carrier with Frequency-Domain Equalization), generally accepted as one of the best candidates for the uplink of future broadband wireless systems [4], [5]. Our multipacket detector has relatively low complexity, even for severely time-dispersive channels, since it allows an FFT-based implementation (Fast Fourier Transform). To be effective, our technique requires uncorrelated channels for different retransmissions. For systems where this is not possible, we consider a modified version of our technique where the frequencydomain block to be transmitted has different shifts for different retransmissions. This paper is organized as follows. The system characterization is made in sec. II and our multipacket detection technique is described in sec. III. The MAC scheme is analyzed in sec. IV and a set of performance results is presented in sec. V. Finally, sec. VI is concerned with the conclusions of this paper. II. S YSTEM C HARACTERIZATION In this paper we consider the uplink transmission in wireless systems employing SC-FDE schemes. We have a slotted system and each user transmits a packet during a given time slot (for the sake of simplicity, it is assumed that the packets associated to each user have the same duration and correspond to an FFT block). Whenever more than one user targets a given time slot we have a collision. It is assumed that different packets arrive simultaneously, i.e., there is some time-advance mechanism able to compensate different propagation times (in practice only a coarse compensation is required, since some time mismatches can

be absorbed by the cyclic prefix that is added to each FFT block). We also have perfect synchronization between different local oscillators (once again, only a coarse synchronization is required, since residual frequency offsets can easily be estimated and compensated using a technique similar to the one proposed in [6]). The time-domain block associated to the pth user (i.e., the corresponding packet) is {an,p ; n = 0, 1, . . . , N − 1}, where an,p is selected from a given constellation and N is the FFT size. When we have the collision of NP packets we retransmit the packets involved NP − 1 times. The received signal associated to a given time-slot is sampled and the cyclic prefix is removed, leading to the time(r) domain block {yn ; n = 0, 1, . . . , N − 1}. If the cyclic prefix is longer than the overall channel impulse response (r) then the corresponding frequency-domain block is {Yk ; k = 0, 1, . . . , N − 1}, where (r) Yk

=

NP X

(r) Ak,p Hk,p

+

(r) Nk ,

(1)

p=1 (r)

with Nk denoting the channel noise and {Ak,p ; k = 0, 1, . . . , N − 1} is the DFT (Discrete Fourier Transform) (r) of {an,p ; n = 0, 1, . . . , N − 1}. Hk,p is the overall channel frequency response for the pth user and the rth transmission attempt.

{y }

{Y } (1) k

(1) n

{y }

DFT

(2) n

0

0

{a } n,1

Det. 1

0

{a }

{a } n ,1

Det. 1

n,2

Det. 2 Iter. 1

Det. 2

{a } n,2

Iter. 2

Fig. 1. Iterative receiver for detecting two packets involved in a collision (NP = 2).

where the average values Ak,p0 are obtained as follows. The block {Ak,p0 ; k = 0, 1, . . . , N − 1} is the DFT of the block {an,p ; n = 0, 1, . . . , N − 1}, where an,p denotes the average symbol values conditioned to the FDE output. For QPSK these average values are given by2 ! ! LIn,p LQ n,p an,p = tanh + j tanh , (3) 2 2 with

III. S OLVING M ULTIPLE C OLLISIONS A. Receiver Structure Let us assume that NP packets are involved in a collision and each user retransmits its packet NP − 1 times. Therefore, the receiver has NP versions of the signals associated to the NP packets. Since the interference levels between packets are very high when we have a collision, we need to jointly detect all packets involved. We can use the NP versions of each packet for multipacket separation (a similar concept was proposed for LST (Layered Space-Time) systems [7]). We consider an iterative joint equalizer and multipacket receiver where each iteration consists of NP detection stages, one for each packet (see fig. 1, where it is assumed that NP = 2). When detecting a given packet we remove the residual interference from the other packets, as well as the residual ISI (Inter-Symbol Interference) associated to the packet that is being detected. For a given iteration, the receiver structure for the detection of the pth packet is illustrated in fig. 2, where we have NP frequency-domain feedforward filters, each one associated to the signal of a given collision (i.e., one retransmission), and NP frequency-domain feedback filters, each one using the average values conditioned to the FDE output of a given packet. The kth frequency-domain sample associated with the pth packet is

{Y } (2) k

DFT

LIn,p =

2 Re{˜ an,p } σp2

(4)

LQ n,p =

2 Im{˜ an,p } σp2

(5)

and

denoting the LLRs (LogLikelihood Ratios) of the ”in-phase bit” and the ”quadrature bit”, associated to an,p , respectively, and {˜ an,p ; n = 0, 1, . . . , N − 1} = IDFT {A˜k,p ; k = 0, 1, . . . , N − 1}. The variance σ 2 is given by σp2 =

N −1 1 1 X E[|an,p − a ˜n,p |2 ] ≈ |ˆ an,p − a ˜n,p |2 , 2 2N n=0

(6)

where a ˆn,p = ±1±j are the hard-decisions associated to a ˜n,p . The optimum feedforward coefficients that minimize the ”signal-to-noise plus interference ratio”, for a given packet and a given iteration, can be written as (r)

Fk,p =

(r) F˘k,p

γp

,

(7)

with γp =

N −1 NP 1 XX (r) (r) F˘k,p Hk,p , N r=1

(8)

k=0

A˜k,p =

NP X r=1

(r)

(r)

Fk,p Yk

−

P X p0 =1

(p0 )

Bk,p Ak,p0 ,

(2)

2 Without loss of generality, we assume that |a 2 n,p | = 2, i.e., an,p = ±1 ± j.

{a } {a }

A

{Y }

…



Detect packet p

(1) k

{Y } ( NP ) k

B

different frequency band or a different antenna), unless the channel changes significantly between retransmissions For systems where this is not practical, we could assume that the frequency domain block associated to the rth retrans(r) mission of the pth packet, {Ak,p ; k = 0, 1, . . . , N − 1}, is an interleaved versions of {Ak,p ; k = 0, 1, . . . , N − 1}. (r) Since this is formally equivalent to assume that {Hk,p ; k = 0, 1, . . . , N − 1}, r = 2, . . . , P are interleaved versions of {Hk,p ; k = 0, 1, . . . , N − 1}, the channel correlations for each frequency can be very small. However, to avoid transmitting signals with very large envelope fluctuations, it is better to (r) assume that {Ak,p = Ak+ζr ,p ; k = 0, 1, . . . , N − 1}, i.e., it is a cyclic-shifted version of {Ak,p ; k = 0, 1, . . . , N − 1}, with shift ζr . This means that the corresponding time-domain block (r) is {an,p = an,p exp(j2πζr n/N ); n = 0, 1, . . . , N − 1}, with a suitable ζr . Therefore, this technique is formally equivalent (r) (r) to have Ak,p = Ak,p and Hk,p a cyclic-shifted version of (1) Hk,p , with shift −ζr . The larger ζr the smaller the correlation (r) (1) between Hk,p and Hk,p , provided that ζr < N/2 (since we consider cyclic shifts, ζr = N is equivalent to have ζr = 0). In this paper we assume that the different ζr are the odd multiples of N/2, N/4, N/8, etc., i.e.,

Previous estimates

n , NP

n ,1

{a } New estimate n, p

{F } {Y } (1) k, p

(1) k

X

{A~ }

{a }

Σ

{Y }

+

( NP ) k

{a } n, p

n, p

k, p

Σ

IDFT

Soft dec.

-

{B }

X

(1) k, p

{F }

{A }

( NP ) k, p

{a }

k ,1

n,1

X

DFT

. . .

Σ

{A }

{a } n , NP

k , NP

X

DFT

ζ2 = N/2 ζ3 = N/4 ζ4 = 3N/4 ζ5 = N/8 ζ6 = 3N/8 ζ7 = 5N/8 ζ8 = 7N/8...

{B } ( NP ) k, p

Fig. 2.

Block for detecting the pth packet (A) and detail (B).

(r) and F˘k,p obtained from the set of NP equations: (r)∗

(1 − ρ2p )Hk,p

NP X

0

0

(r ) (r ) F˘k,p F˘k,p

(r)

r 0 =1

+

X

(r)∗

(1 − ρ2p0 )Hk,p0

NP X

0

0

(r ) (r ) (r) F˘k,p Hk,p0 + αF˘k,p =

r 0 =1

p0 6=p

(r)∗

= Hk,p , r = 1, 2, . . . , NP ,

(9)

where the correlation coefficient ρp is given by ρp =

N −1 1 X (|Re{an,p }| + |Im{an,p }|). 2N n=0

(10)

The feedback coefficients are given by (p0 ) Bk,p

=

NP X

(r)

(r)

Fk,p Hk,p0 − δp,p0

(11)

r=1

(δp,p0 = 1 if p = p0 and 0 otherwise). B. Dealing with Fixed Channels for Retransmissions It should be pointed out that the correlation between channels associated to different retransmissions should be low (if not, the system of equations (9) might not have a solution or it can be ill conditioned). This means that different channels should be employed for each packet retransmission (e.g., a

This allows small correlation between different Hk,p , for each frequency (naturally, as we increase r we increase the correlations). Moreover, envelope fluctuations on the time(r) domain signal associated to {an,p ; n = 0, 1, . . . , N − 1} are not too different form the ones associated to {an,p ; n = 0, 1, . . . , N − 1}3 . As an alternative, we could have ζr = (r − 1)N/NP , r = 1, 2, . . . , NP . However, the envelope fluctuations of the transmitted signals could be larger. IV. M EDIUM ACCESS C ONTROL The detection technique presented above is adapted for the uplink channels of a broadband wireless system, using a network-assisted diversity multiple access (NDMA) MAC protocol [1]. Mobile terminals (MT) send data to a base station (BS), which is responsible for running most of the calculations and to handle transmission collisions. BS detects collisions and uses a broadcast control downlink channel to send a collision signal, requesting MT to resend the collided packets. BS forces MTs to send the packets k times when k MTs collide. The remaining section studies how the throughput is influenced by (r)

3 For QPSK constellations the constellation associated to {a n,p ; n = 0, 1, . . . , N − 1} is also a QPSK constellation for r = 2, 3 and 4.

the packet error rate (PER), and compares the results with the performance of a contention-free scenario, based on TDMA. A. Throughput Analysis The NDMA throughput analysis follows [1], considering a sequence of epochs. An epoch is an empty slot or a set of slots where MTs send the same packet due to a BS request. Denoting Pe as the probability of a user’s buffer being empty at the beginning of a epoch, the binomial expressions for the probability of the epoch length for J MT are:   J k Pbusy (k) = (1 − Pe ) PeJ−k , k = 1, 2, . . . , J (12) k and

 Pidle (k) =

PeJ ,

k=1

0, otherwise.

The probability of having a useful epoch is   J k Pusef ull (k) = (1 − Pe ) PeJ−k PD (k)k k

average length of useful epoch average length of busy or idle epoch

Using (12) and (15), we can write   PJ J k (1 − Pe ) PeJ−k PD (k)k k=1 k k RN DM A = J (1 − Pe ) + PeJ

Traditional MAC protocols loose packets involved in collisions. The best performance with traditional MAC protocols is achieved when collisions are avoided, with a TDMA (time division multiple access) approach. The TDMA’s throughput depends linearly with the total offered load, and with the probability of correct detection of a single sender: RT DM A = λJPD (1)

(13)

(14)

(21)

As SNR→ ∞, we expect PD → 1. On these conditions, 16 can be written as RN DM A =

where PD (k) is the frame’s correct detection probability (equal to 1 − P ER) when k MTs are transmitting. We assume that no detection errors occur in the determination of the number of senders colliding. Finally, the throughput can be defined as RN DM A =

D. Comparison with other MAC Protocols.

J (1 − Pe ) . J (1 − Pe ) + PeJ

(22)

[1] shows that 22 is equal to RT DM A when a Poisson source is used. Therefore, NDMA and TDMA throughputs are equal when no detection errors occur, and converge to one near saturation. However, due to the detection gain for multiple transmission, it will be shown that NDMA outperforms TDMA for low signal to noise ratio values. SICTA was excluded from this comparison because it has a limited performance, and because it is also penalized compared to NDMA by the consecutive reduction on the number of transmitting stations defined by the tree algorithm.

(15) V. P ERFORMANCE R ESULTS

In this section, we present a set of performance results concerning the proposed detection technique in the presence of multiple collisions. We consider the uplink transmission (16) where an SC-FDE modulation is employed. Each packet has N = 256 data symbols, corresponding to blocks with length after some simplifications. 4µs. The data symbols are selected form a QPSK constellaB. Queue Analysis. tion, with Gray mapping. The channel encoder is the wellIf the BS does no detection errors, then [1] busy and idle known rate-1/2 64-state convolutional code with generators 1 + D2 + D3 + D5 + D6 and 1 + D + D2 + D3 + D6 . We epochs have the distributions described by   can use the channel decoder outputs in the feedback loop, J −1 k−1 J−k Pbusy (k) = (1 − Pe ) Pe , 1 ≤ k ≤ J (17) as in conventional turbo detection schemes, or soft decisions k−1 based on the mupti-packet detector output. The radio channel associated to each packet is characterized by the power delay and  J−1 J−2 profile type C for HIPERLAN/2 (HIgh PERformance Local   Pe + (J − 1) (1 − Pe ) Pe , k = 1 Area Network) [9], with uncorrelated Rayleigh fading on J −1 Pidle (k) = k−1 J−k−1 (1 − Pe ) Pe , 1 ≤ k ≤ J − 1 the different paths and the signals associated to all users  k (18) have the same average power at the receiver (i.e., the base station), which corresponds to a scenario where an ”ideal Pe is the unique solution on [0, 1] of the equation average power control” is implemented. We consider perfect λPeJ + (1 − λJ)Pe − (1 − λJ) = 0. (19) synchronization and channel estimation conditions. The channel for each packet retransmission can be either uncorrelated C. Delay Analysis. (denoted UC (Uncorrelated Channels)) or shifted versions of From the property of M/G/1 queue with vacation, the the channel in the first attempt, as described in sec. III-B average system delay for a data packet can be expressed as (denoted SP). 2 2 We assume that the base station knows how many packets λhbusy λhidle + , (20) are involved in the collision, as well as the user that transmitted D = hbusy + 2(1 − λhbusy ) 2hidle each packet. This means that the information concerning user where hbusy , h2busy , hidle and h2idle are the first and second identification needs extra protection. After detecting a collision moments of the busy and idle epoch respectively. the base station informs the users how many retransmissions

0

10

1

(o): N =1 P (*): N =2 P (+): N =3 P (∆): N =4 P

0.9 ____

0.8

Throughput

PER

0.7

−1

10

____

: UC − − − : SP

: UC − − − : SP (o): Iter. 1 (*): Iter. 4

0.6 0.5 0.4 0.3 0.2 0.1

−2

10

−6

−4

−2

0 E /N (dB) b

Fig. 3.

2

4

6

0

0 −6

PER after 4 iterations, for NP = 1 (without collision), 2, 3 and 4. Fig. 4.

are required (and, eventually, the slots that will be used for those retransmissions, to avoid collisions by additional users). Fig. 3 shows the average PER after 4 iterations and different values of NP . Our performance results are expressed as function of Eb /N0 , where N0 is the one-sided power spectral density of the noise and Eb is the energy of the transmitted bits (i.e., the degradation due to the useless power spent on the cyclic prefix is not included). Since we consider a rate-1/2 code, the energy of the information bits is 3dB higher. Clearly our technique is able to cope with a large number of collisions, with improved performances as we increase the number of packets involved in the collisions (and, consequently, the number of retransmissions), even for the SP technique (with the same channel for each retransmission). Naturally, as we increase the number of retransmissions the shifted versions of the channel frequency response have higher correlation between them, leading performances that are worse than with uncorrelated channels for the retransmissions. This subsection compares the NDMA and TDMA throughput values for the scenario simulated previously. Throughput is calculated using (16) and (21) and the PER values measured by the detection technique simulations. We considered a normalized throughput, i.e., we do not include degradation due to the cyclic prefix that is added to each block, as well as other packet overheads. Fig. 4 shows RN DM A for a total offered load (λJ) equal to 0.9. Clearly, it is possible to have a throughput close to the system load), even when the SP technique is employed and/or we just have one iteration at the multipacket detector; for four iterations we can improve the performance by about 1dB. This results from the fact that our receiver can effectively cope with collisions. Figs. 5, 6 and 7 show how RN DM A and RT DM A depends on the offered load, for Eb /N0 values of 2dB, 4dB and 6dB, respectively. The offered load (λJ) varies from very light load (10 %) until the saturation value (100%), where all bandwidth is required to satisfy the offered load. Results show

−4

−2

0 2 Eb/N0 (dB)

4

6

8

Throughput as a function of Eb /N0 , when λJ = 0.9.

that NDMA clearly outperforms TDMA for the conditions tested, especially for loads above 60%. On these conditions, the detection gains are optimized because the probability of having collisions involving multiple nodes is higher. Although the throughput for high system load can be close to 100%, the corresponding packet delay grows fast when the load is above 90% (see fig. 8). The throughput with the SP approach (where the channel remains fixed for the retransmissions) is almost equals to the UC throughput for Eb /N0 values above 4dB; for Eb /N0 below 2dB it is only 10% lower, showing that NDMA combined with the proposed detection method can be used for real systems, without requiring uncorrelated channels. It should be pointed out that our throughput model considered does not take into account invalid detection of the number of senders on a collision, as well as other factors that can influence the results for very low Eb /N0 values. VI. C ONCLUSIONS In this paper we proposed a frequency-domain multipacket receiver for the uplink of broadband wireless systems employing SC-FDE schemes. Our technique allows efficient packet separation, even when the channel remains fixed for different retransmissions. Since the required number of transmissions is equal to the number of packets involved in the collision, we can have very high throughputs. It should be pointed out that the complexity is concentrated in the receiver, making this technique particularly appealing for the uplink of broadband wireless systems. Moreover, the achievable gain lead to high Eb throughputs even for low values of N , which implies an 0 overall improvement of the system efficiency. R EFERENCES [1] M. Tsatsanis, R. Zhang and S. Banerjee, “Network Assisted Diversity for Random Access Wireless Systems”, IEEE Trans. on signal Processing, Vol. 48, pp. 702–711, Mar. 2000.

1

1 __

0.9

0.7

0.7

0.6

0.6

0.5 0.4

0.5 0.4

0.3

0.3

0.2

0.2

0.1

0.1

0 0.1

0.2

0.3

Fig. 5.

0.4

: UC −−: SP .. : TDMA

0.8

Throughput

Throughput

0.8

__

0.9

: UC −−: SP .. : TDMA

0.5

λJ

0.6

0.7

0.8

0.9

0 0.1

1

0.2

Throughput when Eb /N0 = 2dB.

0.3

Fig. 7.

0.4

0.5

λJ

0.6

0.7

0.8

0.9

1

Throughput when Eb /N0 = 6dB.

9

1 __

0.9

: UC −−: SP .. : TDMA

0.8

8 7 Delay (packets)

Throughput

0.7 0.6 0.5 0.4

6 5 4

0.3

3

0.2

2

0.1 0 0.1

0.2

0.3

Fig. 6.

0.4

0.5

λJ

0.6

0.7

0.8

0.9

1

Throughput when Eb /N0 = 4dB.

[2] Y. Yu and G. Giannakis, “SICTA: A 0.693 Contention Tree Algorithm Using Successive Interference Cancellation”, IEEE INFOCOM’05, Miami, USA, Mar. 2005. [3] X. Wang, Y. Yu and G. Giannakis, “A Roboust High-Throughput Three Algorithm Using Successive Interference Cancellation”, IEEE GLOBECOM’05, St. Louis, USA, Dec. 2005. [4] A. Gusm˜ao, R. Dinis, J. Conceic¸a˜ o, and N. Esteves, “Comparison of Two Modulation Choices for Broadband Wireless Communications”, IEEE VTC’00(Spring), May 2000. [5] D.Falconer, S.Ariyavisitakul, A.Benyamin-Seeyar and B.Eidson, “Frequency Domain Equalization for Single-Carrier Broadband Wireless Systems”, IEEE Comm. Mag., Vol. 4, No. 4, pp. 58–66, Apr. 2002. [6] T. Ara´ujo and R. Dinis, “Iterative Equalization and Carrier Synchronization for Single-Carrier Transmission over Severe Time-Dispersive Channels”, IEEE GLOBECOM’04, Nov.–Dec. 2004.

1 0.2

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Fig. 8.

0.6 λJ

0.7

0.8

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1

Packet delay.

[7] R. Dinis, R. Kalbasi, D. Falconer and A. Banihashemi, “Iterative Layered Space-Time Receivers for Single-Carrier Transmission over Severe Time-Dispersive Channels”, IEEE Comm. Letters, 2004. [8] D. Bertsekas and R. Gallager, Data Networks, 2nd ed., PrenticeHall, 2001. [9] ETSI, “Channel models for HIPERLAN/2 in Different Indoor Scenarios”, ETSI EP BRAN 3ERI085B, pp. 1–8, March 1998.