Preamble Design and System Acquisition in

Ultra Mobile Broadband Communication Systems

Michael Mao Wang, Sandeep Aedudodla, Aamod Khandekar, Ravi Palanki, and Avneesh Agrawal

Abstract The wide choices of deployment parameters in next generation wireless communication systems, such as flexible bandwidth allocation, synchronous/asynchronous modes, FDD/TDD, full/half duplex, and configurable cyclic prefix duration, etc., present significant challenges in preamble and system acquisition design. This paper addresses these challenges,

as well as the solutions provided by the 3GPP2 Ultra Mobile Broadband (UMB) standard. The proposed preamble design facilitates the maximal flexibility of the system configuration and yet has low overhead, low acquisition latency, and low complexity. Although the design is discussed under the UMB context, it also serves as a preamble design paradigm for an OFDMA communication system in general.

Keywords : Ultra Mobile Broadband (UMB), preamble, system

acquisition, orthogonal frequency-division multiplexing (OFDM).

I. INTRODUCTION

LEXIBLE configuration for variable deployment

requirements is one of the important and highly

desirable features for the next generation cellular

communication systems. For an OFDMA system, the

typical configuration parameters and modes can be

bandwidth allocation, synchronous/ asynchronous modes,

FDD/TDD, full/half duplex, and configurable cyclic prefix

duration, etc. However, the wide choice of deployment parameters and modes presents significant challenges in

acquisition system design. This paper addresses these

challenges and provides the design solution that has been

adopted by the 3GPP2 Ultra Mobile Broadband standard.

The Ultra Mobile Broadband (UMB) standard is a next

generation MIMO-OFDMA-based WWAN standard being

developed by the 3rd Generation Partnership Project 2

(3GPP2) [1]-[6], to enable ultra-high data-rate mobile

wireless connectivity. UMB can operate in a wide range of

deployments, thereby providing WWAN operators with a

lot of flexibility in optimizing their networks. For example, UMB can operate in a wide range of bandwidths (1.25 MHz

– 20 MHz); this flexibility enables an operator to customize

a UMB system for the spectrum available to the operator.

UMB has a unified design for full and half duplex FDD and

TDD and a scalable bandwidth from 1.25 to 20 MHz for

variable deployment spectrum needs. The system

bandwidths and their corresponding FFT sizes are listed in

Table 1.

Table 1 System bandwidth and the corresponding FFT size.

Bandwidth, MHz 1.25≤ 1.25-2.5 2.5-5 5-10 10-20

FFT size 128 256 512 1024 2048

The subcarrier spacing is fixed at 9.6 kHz corresponding

to an OFDM symbol duration of S 104 secT ≈ . The length

of the cyclic prefix of an OFDM symbol is variable,

CP CP S CP16 6.51 secT N T N= ≈ , where CP 1,2,3,4N = .

This allows the operator to choose a cyclic prefix length

that is best suited to the expected delay spreads in the

deployment.

At a UMB transmitter, the transmitted data are organized

as superframes. For a UMB access network, a superframe

consists of a preamble followed by PHY 25N = PHY

frames in the FDD mode or PHY 12N = PHY frames in

TDD mode. Both the preamble and the PHY frames consist

of S 8N = OFDM symbols. The preamble is used by an

access terminal for the purpose of system determination

and/or acquisition. The PHY frames are used for data traffic

transmission. In FDD half duplex mode, each PHY frame is

separated by a guard interval (g S3 4 78.13 secT T= = ),

whereas there is no separation in full duplex mode ( g 0T = ).

In TDD mode, a burst of { }BURST,F1,2N ∈ PHY frames are

transmitted continuously in time on the forward link and a

burst of { }BURST,R1N ∈ PHY frames are transmitted

continuously on the reverse link, resulting in a

BURST,F BURST,R:N N partitioning. In a typical 1:1 partitioning,

the 12 forward and the 12 reverse PHY frames are

interlaced and are separated by guard intervals, g,F S

3 4T T=

between a forward and a reverse PHY frame, and

g,R S5 32T T= between a reverse and a forward frame.

There is significantly more flexibility in UMB compared

to existing systems and emerging wireless technologies (e.g.,

3GPP(LTE), WiMAX and Wireless LANs, etc.). Flexible

parameters that can affect preamble structure are: (1)

Bandwidth allocation which corresponds to a PHY frame

FFT size of FFT 128 / 256 / 512 /1024 / 2048N = and the

number of guard tones; (2) FDD/TDD. FDD includes full

and half duplex and TDD includes choice of TDD

partitioning; (3) Cyclic prefix length (four possible values).

This allows the operator to choose a cyclic prefix length that

is best suited to the expected delay spreads in the

deployment; (4) Synchronous/ asynchronous modes. UMB systems can operate in synchronous mode, where different

sectors have access to a common timing reference such as

the Global Positioning System (GPS) and asynchronous

mode, where they do not. The flexibility in UMB system

configuration requires that the preamble be structured to

provide an efficient mechanism for system determination

and acquisition for an access terminal.

The widely variable bandwidths used in UMB wireless

systems, as well as the wide choice of deployment

parameters, present significant challenges in acquisition

F

978-1-4244-1722-3/08/$25.00 ©2008 IEEE. 1

system design. This paper describes these challenges, as

well as the solutions provided by the UMB standard.

II. PREAMBLE STRUCTURE

The UMB preamble consists of eight OFDM symbols. The first OFDM symbol is used to transmit the PBCCH

(Primary Broadcast Control Channel) while the next four

OFDM symbols are used to transmit the SBCCH

(Secondary Broadcast Control Channel) and the QPCH

(Quick Paging Channel) in alternate superframes.

The last three OFDM symbols carry acquisition pilots

TDM Pilots 1/2/3. TDM Pilots 2 and 3 are additionally

modulated by OSICH (Other Sector Interference Channel).

The ordering of the preamble OFDM symbols, i.e.,

placing PBCCH/SBCCH in front of the TDM Pilots, is to

provide sufficient AGC convergence time for the TDM

Pilots during initial acquisition. The structure of the superframe preamble is depicted in

Fig. 1

SBCCH /

QPCH

Fig. 1 Forward link superframe preamble structure.

The UMB preamble transmission is limited to the central

5MHz of the system bandwidth, even when the system

bandwidth of the deployment is 5MHz or more. That is

FFT,PRE FFTmin{ ,512}.N N= This has several advantages.

Firstly and most importantly, it significantly simplifies the

acquisition complexity since the PHY frame FFT size,

FFTN , may not be known a priori to the access terminal

during initial acquisition. Secondly, it prevents “energy

dilution” of time-domain signal taps. Since there are more

distinguishable channel taps for a given channel in wider

bandwidths, each such tap has lower energy when

compared to a channel tap in a narrowband signal. This

phenomenon, which we refer to as “energy dilution” can degrade the performance of any algorithm that attempts to

look for channel taps in the time-domain. Restricting the

TDM pilots to 5MHz mitigates the effect of energy dilution.

Thirdly, it lowers complexity by allowing for correlations

with shorter sequences (512 length sequences, as opposed

to 2048 length sequences in 20MHz). Finally, it helps in

faster initial acquisition, as an access terminal (AT) roaming

between deployments of at least 5MHz can always tune to

the central 5MHz and perform acquisition.

A. TDM Pilot 1

TDM Pilot 1 is used for initial coarse timing acquisition

whose waveform should be made as simple as possible (less

unknown parameters) to reduce the searching complexity.

TDM Pilot 1 is transmitted on the OFDM symbol with

index 5 in the preamble, spans the central subcarriers (at

most 480), and occupies every fourth subcarrier over this

span resulting in 4 copies of the same waveform in time

domain. The use of 4 replicas of the same waveform instead of just one is to reduce the waveform period such that the

access terminal’s frequency offset has less effect on the

correlation performed by the access terminal during the

search for the TDM Pilot 1 signal. TDM Pilot 1 uses a

frequency domain complex sequence (GCL sequence) that

carries preamble FFT size and cyclic prefix duration

information to modulate the subcarriers. The sequence is

( )0 1

4

1exp 2 ,

2 4 4k

G

k k k kP j u k

Nδ

δ δ+

+ − −= − ≤ < , (1)

where

{ }0 GUARD,LEFT FFTmax 16, , 2 240 ,k N N= −

{ }1 0 FFT GUARD,RIGHT FFTmin 4 , , 2 240 ,Pk k N N N N= + − +

and { }FFT16 max 0, / 2 256 .Nδ = + − It can be shown that

the corresponding time domain waveform of each period is

( )12

0

1exp 2 exp 2

2 2

GN

n

kG G

k kn n up j j u

N N

−

=

+−= − , (2)

which has a constant magnitude that helps improve peak to

average power ratio (PAPR). Low PAPR waveforms allow

for a higher power amplifier setting at the transmitter,

thereby extending coverage. It should be noted here that the

coverage requirements for acquisition are typically higher

than that for data traffic, since a mobile AT should be able

to acquire a sector before it is in the data coverage of a

sector, thereby allowing for seamless handoff to that sector

if required.

The relationship between the sequence parameters

, , G Pu N N , the cyclic prefix duration, and the preamble

FFT size is specified in Table 2. Information on cyclic

prefix (CP) duration and FFT size is necessary for detection

of acquisition information from TDM Pilot 2.

Note that TDM Plot 1 only gives possible timing (and CP duration) without identifying the sector.

Table 2 Relationship between TDM Pilot 1 sequence parameters

( ), , G P

u N N and cyclic prefix (CP) duration and FFT size.

Preamble FFT Size CP (μs)

128 256 512

( 8,23,23) (13,59,56) (17,127,120) 6.51

(12,23,23) (22,59,56) (39,127,120) 13.02

(14,23,23) (39,59,56) (110,127,120) 19.53

(22,23,23) (47,59,56) (112,127,120) 26.04

B. TDM Pilots 2 and 3

TDM Pilot 2 is a time domain Walsh sequence that carries

the sector’s unique PilotPhase (synchronous mode) or

PilotPN (asynchronous mode) that helps the access terminal

to distinguish multiple sectors in the deployment. PilotPN is

the 9-bit identifier of a sector. PilotPhase is defined as

2

(PilotPN+SF

I ) mod 512 where SF

I is the superframe index.

PilotPhase is used in the synchronous mode as the seed to

the scrambling sequence (PN sequence) such that each

sector not only has a unique scrambling sequence but also

changes from superframe to superframe enabling

processing gain across superframe. PilotPN, instead of

PilotPhase, is used for asynchronous mode, since two

sectors with different time bases could have the same

PilotPhase at the same time. The generator polynomial of

the PN sequence is given by

20 19 16 14( ) 1g D D D D D= + + + + . (3)

The Walsh sequence length equals to the preamble FFT size,

FFT,PREN , with index equals to the 9 bit PilotPhase/PilotPN

8 7 6 5 4 3 2 1 0p p p p p p p p p of value P between 0 and 511.

In the case that the preamble FFT size is less than 9 bits,

the LSBs of the 9 bits are used as the Walsh sequence index,

i.e., FFT,PREmodP N for

FFT,PRE512N < . The MSBs with

value FFT,PRE

P N are carried by a complex PN sequence

used to scramble the Walsh sequence with the 20-bit seed

given by 1 0

011010011010111011x x , where the last two

LSBs are reserved for the first two MSBs of the 9-bit

PilotPhase/PilotPN. Therefore, 1 0x =x =0 for

FFT,PRE512,N =

1 0 8x =0, x =p for

FFT,PRE256,N = and

1 8 0 7x =p , x =p for

FFT,PRE128N = . The resulting sequence

is transformed to frequency domain and used to modulate

all subcarriers except the guard subcarriers. Walsh

sequences with different indices possess different spectral

properties and the insertion of guard subcarriers may

destroy the Walsh code property depending on the Walsh

code’s spectral property. The use of complex scrambling of

Walsh sequence spreads the code energy evenly throughout the spectrum and, therefore, has less and the same effect on

all Walsh sequences regardless of the individual Walsh

code’s spectral property.

Like TDM Pilot 2, TDM Pilot 3 is also a time domain

Walsh sequence that carries 9-bit acquisition information.

The Walsh sequence length equals to the preamble FFT size,

FFT,PREN , with index equals to the 9 bit acquisition

information 8 7 6 5 4 3 2 1 0

a a a a a a a a a of value A between 0

and 511 which contains information on

synchronous/asynchronous mode (1 bit), four LSBs of

superframe index ( ( )4 SFLSB I if in asynchronous mode),

FDD/TDD mode (1 bit, if in synchronous mode), preamble

frequency reuse (1 bit, if in synchronous mode), full/half

duplex mode (1 bit if in synchronous/asynchronous FDD

mode), TDD partitioning (1 bit, if in synchronous and TDD mode), etc, which is necessary for decoding the PBCCH

packet.

Similarly, in the case that the preamble FFT size is less

than 9 bits, the LSBs of the 9 bits are used as the Walsh

sequence index, i.e., FFT,PREmodA N for

FFT,PRE512N < .

The MSBs with value FFT,PREA N are carried by a

complex PN sequence used to scramble the Walsh sequence

with the 20-bit seed given by

8 7 6 5 4 3 2 1 0 1 0011010011p p p p p p p p p x x , where

8 0p , , p are

the sector PilotPhase/PilotPN bits, the last two LSBs are

reserved for the first two MSBs of the 9-bit acquisition

information. Therefore, 1 0x =x =0 for

FFT,PRE512,N =

1 0 8x =0, x =a for

FFT,PRE256,N = and

1 8 0 7x =a , x =a for

FFT,PRE128N = .

The time sequence is converted to the frequency domain

and used to modulate the subcarriers if the subcarrier is not

a guard subcarrier.

For system FFT sizes of 128, 256 and 512, TDM Pilots 2

and 3 occupy all usable subcarriers. For system FFT sizes of 1024 and 2048, TDM Pilots 2 and 3 only occupies the

central 512 subcarriers.

Like TDM Pilot 1, TDM Pilots 2 and 3 have constant

magnitude in time domain. However, if the number of

usable subcarriers is less than the preamble FFT size, the

constant modulus property is distorted and the correlation

(cross/auto) properties of complex PN scrambled Walsh

sequences are also impaired as a result of the insertion of

guard subcarriers. Fig. 2 illustrates this effect.

Fig. 2 Change of cross/auto correlation CDF of the PN scrambled Walsh

sequence as a result of bandwidth reduction. The figure shows no

reduction, 25%, 50% and 75% reduction in bandwidth.

C. PBCCH and SBCCH

The Primary Broadcast Channel is carried on the first

OFDM symbol in the preamble. Each PBCCH packet is

CRC (12 bits) appended, encoded, channel-interleaved,

repeated, scrambled, with the seed containing the sector

PilotPhase/PilotPN, i.e., ( )128 64 1h P + + for synchronous

mode and ( )( )4 SF128 4LSB 1h P I+ + for asynchronous

mode, where h is a hash function, defined as

( )( )( )( )( )( )( )( )

32 32 20

32 32 20

( ) BR 2654435761 mod 2 mod 2 mod 2

BR 2654435761 2 mod 2 mod 2

h x x

x

=

⊕

where BR stands for the bit-reversal operation. The

scrambled data are QPSK modulated onto usable

subcarriers over one superframe but repeatedly transmitted over 16 superframes. The PBCCH packet contains the

44-bit system information including superframe index, and

deployment-wide static parameters like total number of

subcarriers, number of guard subcarriers (in units of 16),

etc., and is updated very 16 superframes. The static nature

of the PBCCH packet allows the transmission of the

PBCCH packet with low effective coding rate without high

3

overhead. This is done by updating the PBCCH packet

every 16 superframes and repeatedly transmitting the same

PBCCH packet over 16 consecutive superframes.

The ith PBCCH modulation symbol is mapped to the

subcarrier with index FFT FFT,PRE

2 2N N i− + if this

subcarrier is not a guard subcarrier where

FFT,PRE0 1i N≤ ≤ − . That is, the ith modulation symbol is

punctured if the subcarrier is a guard subcarrier. Note that

since the mapping of the modulation symbols to the

subcarriers is independent on the actual bandwidth of the

preamble or the number of guard subcarriers, the PBCCH

modulation symbols can thus be demapped without knowing the number of guard subcarriers which allows the

PBCCH packets to be decoded without the knowledge of

bandwidth.

The Secondary Broadcast Channel (SBCCH) is carried on

the OFDM symbols with indices 1 through 4 in the

superframe preamble in superframes with an odd value of

index. A SBCCH packet contains the channel information,

such as number of effective antennas, common pilot

channel hopping mode, number of sub-trees for SDMA, etc.

It is appended with CRC (12 bits), encoded,

channel-interleaved, repeated, scrambled, with the seed containing sector PilotPhase/PilotPN, QPSK modulated

onto usable subcarriers. The seed used for scrambling

equals to ( )16 72 ( ) 2 64 2h H S P+ + + for synchronous

mode and ( )( )16 7

4 SF2 ( ) 2 4LSB 2h H S P I+ + + for

asynchronous mode, where ( )H S is a 20-bit hash quantity

based on the 44-bit system information value S in PBCCH:

1. Initialize H with zero; Compute n and m such that

32m n− equals to the number of bits of S ; Set J to n

zeros followed by S ; And set 0i = .

2. While i m< , repeat Step 3.

3. ( )( )32 :32 31 ; 1,H H h J i i i i= ⊕ + = + where ( )32 :32 31J i i +

stands for bits 32i to 32 31i + of J .

The ith modulation symbol is mapped to

FFT FFT,PRE REUSE FFT,PRE FFT,PRE2 2 8 mod 8N N I N i N− + + of the

OFDM symbol with index FFT,PRE

8 1i N + .

The SBCCH packet is updated very superframe (except

the even frames).

OFDM symbols 1 through 4 in the preamble are used for carrying Quick Paging Channel (QPCH) on superframes

with even index. Placing the QPCH in preamble is justified

by the need by the mobile reading the paging message when

waking up in a new sector.

III. SYSTEM ACQUISITION

We now describe the signal and channel models to facilitate

an analysis of the acquisition scheme.

A. System Model

Transmitted Signal: TDM Pilot 1 and TDM Pilot 2

The transmitted GCL sequence in the OFDM symbol

corresponding to TDM Pilot 1 in the superframe preamble, is

given by (1). To simplify the analysis, we assume

GUARD,LEFT GUARD,RIGHT0N N= = . Then, for convenience we

write

4 , 0 1k k PG P k Nδ+= ≤ ≤ − (4)

and use FFTN in place of FFT,PREN . The complex

modulation symbols for the TDM Pilot 1 OFDM symbol are given by:

TDM1, 4 , 0 1

0, otherwise

k P

i

P G i k k NX

δ= + ≤ ≤ −= (5)

where 1 /TDM FFT PP N N= is a constant. Following the IFFT

operation, the time-domain TDM Pilot 1 OFDM symbol can be expressed as:

FFT 1

FFT0

1

TDM1 ( 4 ) FFT0

, 0 1

, 0 1P

N

n i nii

N

k n kk

x X v n N

P G v n Nδ

−

=

−

+=

= ≤ ≤ −

= ≤ ≤ −

(6)

where the complex exponentials are given by:

FFT2 /

FFT

FFT

1, , 0,1, , 1j kn N

nkv e k n N

N

π= = − (7)

Due to the GCL sequence occupying every 4th subcarrier, the TDM Pilot 1 OFDM symbol appears in time-domain as a periodic waveform with four periods. The transmitted signal for the TDM Pilot 2 symbol consists of a time-domain Walsh sequence given by:

FFTTDM2 FFT, , 0 1pn N ny P W n N= ≤ ≤ − (8)

where FFT ,

pN n

W denotes the Walsh sequence of length

FFTN with index FFT mod p N , where p is the

superframe’s sequence number.

Channel Model

The impulse response of the SISO fading channel is given by the stochastic tapped delay line model [9]:

TAP 1

0

( ) ( ) ( ) ( )N

i i

i

h t t t n tα δ τ−

=

= − + (9)

where ( )i tα is the tap gain assumed to be a complex

Gaussian random variable with zero mean and variance 2iσ and the corresponding tap delay is denoted by iτ . It is

assumed that the tap delays iτ change very slowly and are

assumed to be constants [9]. Also, it is assumed that the tap

gains ( )i itα α= are constant over M OFDM symbol

durations i.e. a block-fading channel and that the iα s are

independent. The noise process ( )n t is assumed to be

complex Gaussian with zero mean and variance 0N .

The goal of the system acquisition is to acquire the system parameters, necessary to access the system, from the preamble. The acquisition procedure is depicted in Fig. 3.

B. TDM Pilot 1 Detection

The UMB system acquisition starts from searching for TDM Pilot 1. At a given carrier frequency, the access terminal looks for TDM Pilot 1 signal for each of the 12 hypotheses given in Table 2 over the duration of at least one superframe until one candidate is detected.

We assume a single antenna at the receiver to simplify the

analysis. The chip-rate sampled received signal

corresponding to the TDM1 OFDM symbol, after removal of

the cyclic prefix is given by [9]:

4

Fig. 3 Flowchart of system acquisition procedure.

TAP

FFT

FFT

12 /

( )mod FFT

0

, 0 1S

i

Nj n fT N

n i n n N n

i

r e x n Nπ α η

−Δ

−=

= + ≤ ≤ − (10)

where CHIPi in Tτ = , with CHIPT being the chip duration and

FFT CHIPST N T= being the OFDM symbol duration. Also,

nη are samples of zero-mean complex Gaussian noise with

variance 0N . In (10), we assume that the duration of the

channel’s impulse response is less than the cyclic prefix

duration CPT . Also, we assume in (10) that the frequency

offset between the transmitter and receiver oscillators is

fΔ . We assume that the noise component in the received

signal is dominated by the interference from other sectors.

We see that the signal part of (10) represents a circular

convolution of the transmitted signal and the channel’s

impulse response, which is corrupted by the frequency offset

fΔ , which causes inter-carrier-interference (ICI). Assuming

a rectangular window for the OFDM symbol, the ICI can be

modeled as in [9]. Hence the FFT operation on the received

samples results in the samples denoted by kY , (i.e.

FFTn kr Y←⎯⎯→ ), which are given by:

FFT 1 1

FFT

0 0

( ) , 0 1FFTN N

k k k j j j k n nk

j nj k

Y H X H X A f f v k Nη− −

∗

= =≠

= + + Δ + ≤ ≤ − (11)

where the frequency-domain channel coefficients are given

by:

TAP 1

FFT

0

, 0 1i

N

k i n k

i

H v k Nα−

∗

== ≤ ≤ − (12)

and

FFT( ) sinc , 0 1j

j

f fA f j N

f

−= ≤ ≤ −

Δ (13)

In (13), jf j f= Δ with 1 uf TΔ = denoting the subcarrier

spacing. The second term on the right-side of (11) represents

the ICI caused due to the frequency offset fΔ . Now the FFT

coefficients of the received OFDM symbol that correspond to the GCL sequence are given by

FFT

FFT

1

4 4 4 4 4 4 4

0

1

(4 )

01

TDM1 4 TDM1 4 4 4

0

1

(4 )

0

( )

,

( )

, 0 1

P

P

N

k k k j j j k

jj k

N

n n k

nN

k k j j j k

jj k

N

n n k P

n

Y H X H X A f f

v

P H G P H G A f f

v k N

δ δ δ δ δ δ δ

δ

δ δ δ δ

δ

η

η

−

+ + + + + + +=≠

−∗

+=

−

+ + + +=≠

−∗

+=

=

= + +Δ

+

= + + Δ

+= ≤ ≤ −

(14)

The received samples corresponding to the GCL sequence

are multiplied by the stored GCL sequence ,k stG and the

product sequence is given by:

*4 , , 0 1k k k st Pq Y G k Nδ+′ = ≤ ≤ − (15)

This product sequence is zero-padded to create a 128IN =length sequence given by:

( ) / 2

0, 0 ( ) / 2

, ( ) / 2 ( ) / 2

0, ( ) / 2

I P

I P

k k N N I P I P

I P I

k N N

q q N N k N N

N N k N

− −

≤ < −′= − ≤ < +

+ ≤ ≤

(16)

An IN -point IFFT is performed on kq to obtain the

sequence nQ which can be expressed as:

12 /

0

1, 0 1

I

I

Nj kn N

n k I

kI

Q q e n NN

π−

=

= ≤ ≤ − (17)

Using (15), we can express (16) as:

12 ( ) / 2

0

, 0 1P

I P I

Nj n N N N

n k kn I

k

Q e q u n Nπ

−−

=

′= ≤ ≤ − (18)

where the complex exponentials:

2 /1, , 0,1, , 1Ij kn N

kn I

I

u e k n NN

π= = − (19)

The absolute values of the IFFT outputs are computed to

obtain 2| |n nS Q= which are then compared to a threshold

GCLγ to determine the strong paths. The probability

distribution of nS can be obtained as follows. We denote

the tap-gain vector by TAP0 1 1[ ]Nα α α −= . The IFFT

outputs nQ from (17) can also be expressed as:

FFT

1

( )

02

1*

( ) 4 ,

02

1*

TDM1 4 ,

0

1 1*

( ) TDM1 4 , 4 4

0 02

1 1* *

(4 ) ,

0 0

( )

P

I P

P

I P

P

P P

I P

P

N

n I N N k knn

k

N

I N N k k st knn

k

N

k k k st kn

k

N N

I N N j j k st j k knn

k jj k

N N

m m k k st kn

k m

Q N u q u

N u Y G u

P H GG u

N u P H GG A f f u

v G u

δ

δ

δ δ δ

δη

−

−=

−

− +=

−

+=

− −

− + + += =

≠

− −

+= =

′=

=

= + +Δ

+

(20)

5

where 0 1In N≤ ≤ − . From the above, we see that,

conditioned on , nQ is complex Gaussian distributed

with the mean (assuming perfect timing sync)

*

4 ,1

1*| ( ) TDM1

4 , 4 4020

( )

P

P

n I P

k k k st knN

N

Q I N Nn j j k st j k knk

jj k

H G G u

N u PH G G A f f u

δ

δ δ δμ

+−

−−

+ + +==≠

= + + Δ

(21)

where 0 1In N≤ ≤ − and noise variance which can be

shown to be: 2

| 0 /nQ P IN N Nσ = (22)

Hence the conditional probability density function of 2| |n nS Q= is non-central chi-squared with two degrees of

freedom, given by [10]:

2

| |

| 02 2 2

| | |

| | 2 | |1( ) exp ,n n

n

n n n

Q Q

S

Q Q Q

x xf x I

μ μσ σ σ

+= − (23)

where 0 1In N≤ ≤ − and 0 ( )I is the zeroth-order Bessel

function of the first kind. For each n, such that

0 1,In N≤ ≤ − the conditional threshold-crossing

probabilities given the threshold, GCLγ , are therefore given

by:

| GCL ,

| GCL ,

Pr( | ) for correct GCL, i.e. { } { }

Pr( | ) for empty channel or incorrect GCL, i.e. { } { }

n

n

D n k st k

F n k st k

P S G G

P S G G

γ

γ

= > =

= > ≠

The conditional probability of threshold-crossing for n can

be expressed as:

| GCL

| | GCL 1

| |

| | 2 21 ( ) ,n

n n

n n

Q

D S

Q Q

P F Qμ γ

γσ σ

= − = (24)

where 1( , )Q a b denotes the generalized Marcum

Q-function which can be computed as shown in [10]. In the

event of an empty channel, we note that nQ is a complex

Gaussian random variable with zero-mean and variance

equal to 0 /P IN N N , which results in nS being central

chi-squared distributed with two-degrees of freedom. Populating every 4th subcarrier with the GCL sequence in

TDM Pilot 1 results in the time-domain OFDM symbol containing four periods, each period containing

FFT 4N samples. Having these four periods is useful for

estimating the frequency offset fΔ [11]. Once the TDM1

processor determines a time-offset n for which nS crosses

the threshold, it estimates the frequency offset from the time-domain samples as

FFT

3/ 4

1

( ) ( )1 1ˆ2 3

n kN n

u k

r rf

T kπ+

=

Θ − ΘΔ = (25)

where ( )zΘ denotes the phase of complex number z .

The frequency offset correction then involves applying the

phase ramp FFTˆ2 /uj n fT N

eπ− Δ to the time-domain samples.

Upon the detection of TDM Pilot 1, the access terminal gains the knowledge of the TDM Pilot 1 boundary, the cyclic prefix duration and the preamble FFT size.

C. TDM Pilot 2 Detection

With the knowledge of the TDM Pilot 1 boundary, cyclic prefix (therefore, the TDM Pilot 2 boundary), and the

preamble FFT size, TDM Pilot 2 can be located and sampled at the bandwidth based on the preamble FFT size. The sampled data are first transformed to frequency domain via FFT with the obtained preamble FFT size. As with the TDM Pilot 1, the frequency domain data are spectrum-shaped. The resulting data are then transformed back to time domain sequence, descrambled, and a fast Hadamard transform (FHT) is used on the descrambled data to detect the Walsh sequence for the PilotPhase/PilotPN. For a preamble FFT size of less than 512, multiple PN descrambling sequences need to be tested to retrieve the MSB(s) of the PilotPhase/PilotPN.

In detail, the paths crossing the threshold obtained from TDM1 processing over one superframe are passed on for TDM2 processing, which involves performing the FHT and comparing the resulting sector energies to a threshold. The full analysis for TDM2 is similar to that of TDM1 and is thus not included here. However, the calculation of the threshold that is used during TDM2 processing is presented. The FHT threshold is chosen by design to maintain a false alarm

probability within a desirable level F,desiredP . A false alarm

event is defined as a threshold-crossing occurring in an empty channel, i.e. noise-only scenario. A false alarm event

would incur a penalty time of FAT . This penalty is attributed

to unnecessary attempts at decoding system information following a false alarm event. When only noise is present, the received signal corresponding to the TDM2 OFDM symbol can be expressed as:

FFT, 0 1n nr n Nη= ≤ ≤ − (26)

where nη are samples of zero-mean complex Gaussian noise

with variance 0N .

The FHT effectively performs correlations with each of the Walsh sequences and the output of the FHT

corresponding to the Walsh code with index p can be

expressed as:

FFT

FFT

1*

, FFT

0

, 0 1N

p

p n N n

n

FHT W p Nη−

=

= ≤ ≤ − (27)

which can be shown to be a zero-mean Gaussian random

variable with variance FFT 0N N . In a single-antenna

scenario, the decision statistic is given by the strength of the

FHT output: 2| |pFHT , which is central chi-squared

distributed with two-degrees of freedom. Given the FHT

threshold FHTγ , the false alarm probability can therefore be

expressed as [10]:

GCLF

0 FFT

expPN N

γ= − (28)

Hence to achieve a probability of false alarm F F,desiredP P≤ ,

the FHT threshold should be chosen that

FHT 0 FFT F,desiredlog( )N N Pγ = − (29)

The average time taken for acquisition given a non-empty

channel can be shown to be approximately ACQ SF DT T P= .

Upon the detection of TDM Pilot 2, the access terminal obtains the PilotPhase/PilotPN of the sector.

D. TDM Pilot 3 Detection

TDM Pilot 3 is next sampled at the corresponding

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bandwidth, spectrum-shaped and descrambled using the PilotPhase/PilotPN detected from TDM Pilot 2. Like the processing of TDM Pilot 2, the FHT is then applied to the descrambled data to detect the acquisition information. Multiple descrambling sequences may be tested for detecting the MSB(s) of the acquisition information if the preamble FFT size is less than 512.

Upon the detection of TDM Pilot 3, the acquisition information including synchronous/asynchronous mode, 4

LSBs of the superframe index ( ( )4 SFLSB I if asynchronous

mode), full/half duplex modes (if FDD mode), FDD/TDD mode (if synchronous), TDD partitioning (if TDD mode), preamble frequency reuse (if synchronous), etc, is available to the access terminal.

Fig. 4 shows the detection performance of TDM Pilots 1,2, and 3.

E. PBCCH Decoding

After the detection of the TDM Pilot 3, the access terminal is ready to decode the PBCCH packet. With the knowledge of the cyclic prefix length, FDD/TDD mode, the full/half duplex mode (if in FDD mode) and the partitioning (if in TDD mode), the access terminal is able to locate the PBCCH OFDM symbol in the following superframe

preamble at ( )( )S CP w g S PHY1T T T T N N+ + + + for FDD and

( ) ( )g,F g,R PHY BURST,R BURST,F BURST,RT T N N N N+ + in addition

for TDD, where w S 32 3.26T T= = μsec is the windowing

guard interval, samples at the bandwidth determined by the

preamble FFT size FFT,PREN and performs FFT with the

preamble FFT size FFT,PREN . With the information of

Preamble Frequency reuse, the frequency domain data are spectrum-shaped, demapped, demodulated, descrambled

with the seed, ( )128 64 1h P + + if synchronous or

( )( )4 SF128 4LSB 1h P I+ + if asynchronous, de-interleaved,

LLR calculated and decoded. Like in TDM Pilot 1,2, and 3 detection, the conservative spectrum-shaping may result in loss of SINR up to 3 dB. However, PBCCH is coded with very low code rate. Loss of 3 dB does not prevent PBCCH from successfully decoded.

Fig. 4 TDM Pilots 1, 2, 3 detection performance (95 percentile, joint false

alarm probability=0.001, 1 receive antenna, 5MHz bandwidth).

A failure to decode is most likely due to insufficient SINR. Therefore, if the decoding is not successful, the access terminal determines if the PBCCH carries the last transmission of the 16 transmissions by checking if the PilotPhase mod 16 equals to 15 (synchronous mode) or if the four LSBs of the superframe Index (asynchronous mode) equals to 15. If the current received PBCCH is not the last of the 16 transmissions, the LLR from the successive transmission of the PBCCH are combined with the LLR stored in the LLR buffer and another decoding attempt is made. Otherwise, the buffer is cleared and LLR data are not combined. This procedure is repeated until a successful decoding. The maximum number of transmissions the access terminal can combine is 16 since the PBCCH packet is updated very 16 superframes. Fig. 5 illustrates the incremental redundancy decoding process.

Fig. 5 Illustration of the incremental redundancy decoding of a PBCCH

packet.

Fig. 6 shows the incremental redundancy decoding performance of a PBCCH packet. It is clear that decoding of PBCCH rarely takes all 16 transmissions. High geometry users are more likely to need less redundancy for less processing gain to decode the packet as compared to edge users. It, therefore, takes less time for high geometry users to acquire the system significantly reducing the acquisition time.

A decoding failure may also be the consequence of a false detection of TDM Pilots 1 to 3. If decoding fails even if the LLR buffer has combined 16 consecutive PBCCH transmissions, the acquisition procedure restarts.

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Fig. 6 PBCCH decoding performance at various levels of redundancies

(channel model: PedB 3km/h, one receive antenna).

Upon a successful decoding of the PBCCH packet, the access terminal confirms that the information acquired from TDM Pilot 1-3 is correct and a UMB system indeed exists at this carrier frequency. In addition, it obtains the system information including superframe index, system FFT size and number of guard subcarriers, etc, from the PBCCH packet. This information is necessary for decoding the following SBCCH packet.

F. SBCCH Decoding

If the current superframe index is odd, the access terminal starts to acquire SBCCH. Four OFDM symbols from 1 to 4 are sampled and transformed to frequency domain using an FFT. Using the number of guard subcarrier information from the PBCCH as well as the Preamble Frequency Reuse mode, the actual guard subcarriers are zeroed out, the modulation symbols are demodulated, descrambled, de-interleaved and decoded. The seed to the descrambling sequence is generated using the procedure described in Section II, C.

By now the access terminal has all the information necessary to access the system and completes the system acquisition.

IV. CONCLUSION

Flexible system configuration is highly desirable in optimizing system performance for variable deployment environments. Preamble design and system acquisition for flexible systems is challenging. This paper uses UMB as a paradigm to illustrate the preamble design schemes and system acquisition techniques for any OFDMA systems in general. The UMB system allows flexible configurations to meet different deployment needs. It supports bandwidth from 1.28 MHz to 20 MHz with variable guard subcarriers and scalable in unit of 154 kHz. It allows for synchronous and asynchronous FDD and variable partitioning TDD. It has configurable cyclic prefix duration for variable deployment environments and full/half duplex operation for different access terminals. This flexibility also makes the design of UMB preamble challenging as compared to

conventional systems. This paper describes these challenges, as well as the solution provided by the UMB

standard. The UMB preamble design meets the requirements and ensures the initial system acquisition for an access terminal is efficient, i.e., low overhead, low latency, and low complexity.

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