Frequency diversity through hopping results in performance gain (fig. 1). Expectably, performance is better over larger delay spread channel VehB.

Naturally, performance is improved as the interleaving depth is increased (fig. 2). However, the gain from employing frequency hopping as opposed to plain block interleaving is reduced. This is because the attainable frequency diversity between two time slots decreases with their time difference Δt, due to the multiplicative factor Jo(2πfDΔt) in the channel correlation function.

The effect of the Doppler spread depends on the channel (fig. 3).

Substantial gain can be attained if only a subset of the hopping patterns is used, such that any hop is at least 20 tones (fig. 4).

FH-OFDM for Mobile Broadband Wireless AccessFH-OFDM for Mobile Broadband Wireless AccessKostas Stamatiou, John G. Proakis

AbstractAbstract We are studying the deployment of Frequency Hopped OFDM

(FH-OFDM) at the downlink of a cellular mobile radio system. Each user in a cell is assigned a number of tones by the base-station, which change over time according to a predetermined hopping pattern. The construction of the hopping patterns is based on orthogonal latin squares, which have desirable properties regarding intra-cell interference avoidance and inter-cell interference averaging.

In this work, the performance in terms of the bit-error-probability is evaluated analytically for two coded modulation schemes, i.e. TCM and BICM, combined with a block interleaver, without taking into account the adjacent cell interference. Our objective is to quantify the effect of the channel parameters, the hopping pattern selection and the interleaver depth on the performance of a coded FH-OFDM link.

MotivationMotivation

OFDM

Orthogonal multiple access: No intra-cell interference (potential for higher capacity than CDMA)

High data rates without the need for equalization (simple receiver design)

Frequency Hopping

Frequency diversity (gain through coding)

Inter-cell interference averaging (higher frequency reuse)

Candidate technology for 802.20

FH-OFDM Downlink FH-OFDM Downlink

Each mobile is assigned a number of tones, according to its

demand in bandwidth

The tones change over time according to a hopping pattern

MS 2BS

MS 1

1 2 1 1

2 1 2 1

1 2 1 1 2

2 1 1 1

1 2 1

1 1 2 1

1 2 1 2

2 1 1

1 1 1

1 2f

t

Ban

d wid

th

OFDM symbol

Interference Interference

Different hopping patterns are assigned to adjacent cells in order

to average inter-cell interference

1

1

1

1

1

1

1

1

1

1

1 3 2

2 1 3

1 3 2

3 1 2

3 1 2

2 1 3

2 1 3

3 1 2

2 3 1

2 1 3

1

2

3

Cell 1 Cell 2

Parameters Parameters

Carrier frequency 2 GHz

Bandwidth 1.25 MHz

OFDM symbol duration, Ts 100 μsec

Cyclic prefix duration, Tcp ~ 11,1 μsec

Tone spacing, 1/T 11.25 KHz

FFT size, N’ 128

Number of tones used, N 113

Period of hopping sequences

113

Tcp T

Ts

t

OFDM symbol

Channel Model Channel Model Channel impulse / frequency response:

where gk(t) are WSS, independent, CN (0,2σk2)

Jakes’ model for each tap (fD is the Doppler frequency)

Correlation function:

Noise is AWGN

M

kkk tgtg

1

)()();(

M

k

fjk

ketgtfG1

2)();(

tfJttgtgE Dkkk 22)]()([ 02*

M

k

fjkDoGG

ketfJttffGtfGEtf1

22* )2(2);();();(

Vehicular Test Environments Vehicular Test Environments

UMTS macro-cellular channel model also considered for 802.20

Vehicular Test Environments (TE) VehA and VehB

Latin Squares Latin Squares For α = 1,…,N-1 define an NxN matrix Aα by setting

Aα(i,j) = αi + j (modN)

where i,j = 0,…,N-1 and N is a prime number. The set {Aα} is a family of N-1 mutually orthogonal latin squares.

Example: N = 50 1 2 3 4

1 2 3 4 0

2 3 4 0 1

3 4 0 1 2

4 0 1 2 3

Cell A1

0 1 2 3 4

2 3 4 0 1

4 0 1 2 3

1 2 3 4 0

3 4 0 1 2

Cell A2

Properties Properties

The rows and columns of Aα represent the OFDM tones and time slots respectively

If an element of Aα is assigned to a user, a N-periodic hopping pattern is constructed for that user

Hopping patterns within cell are orthogonal

There can be only one collision between any pair of hopping patterns in two different cells (interference randomization)

Δf between two consecutive tones in the hopping pattern of any user in cell Aα is either -(α-1)modN or N-(α-1)modN

TCM TCM Base-station with Trellis Coded Modulation (TCM)

TCM

EncoderTCM

Encoder

Block

Symbol

Interleaver

(depth β)

Block

Symbol

Interleaver

(depth β)

Hopping pattern

generatorHopping pattern

generator

Coded streams of

other users

Symbol

mapperSymbol

mapper

One tone/user/OFDM symbol

Latin squares, N = 113

Rate 2/3, 8-state Ungerboeck code with 8-PSK (Lmin = 2)

OFDM Mod.

OFDM Mod.

Binary

SourceBinary

Source

Performance - TCMPerformance - TCMThe bit-error-probability is approximated by

where

E is the set of dominant error events (L 3, S = 4)

is the number of bit errors for the symbol error

event e (obtained from code error-state-diagram)

H is the hopping pattern event of span S

Perfect channel estimation

Block interleaver span α >> S

Eb PwEP

eH Hee )|()(

2

1

)(ew

BICM BICM

Rate 1/2, 8-state Convolutional Code with 16-QAM

Higher diversity order (dfree = 4), but half the trellis complexity

Same information rate (20kbps)

Conv.

EncoderConv.

Encoder

Binary

SourceBinary

Source

Block Bit

Interleaver

(depth βb)

Block Bit

Interleaver

(depth βb)

OFDM Mod.

OFDM Mod.

Hopping pattern

generatorHopping pattern

generator

Coded streams of

other users

Gray

mapperGray

mapper

Bit-interleaving and Gray mappingBit-interleaving and Gray mapping

c1

c2

c3

cα

cα+1

cα+2

cα+3

c2α

c(β-1)α+1

c(β-1)α+2

cβα

c(β-1)α+2

c2α+1

c2α+2

c2α+3

c3α

c3α+1

c3α+2

c3α+3

c4α

16-QAM symbol x1

α

βb

16-QAM symbol x2

0010 0110

01110011

01010001

01000000

1010

1011

1001

1000

1110

1111

1101

1100

dmin

αβb = codeword length

α >> dfree

Performance - BICMPerformance - BICM

The bit-error-probability is approximated by the expression

where P(dfree|H) is the probability of the only minimum distance binary error event (1000111), for given hopping pattern event H

Generally a very complicated problem to compute P(dfree|H) (very complex metrics)

Simplification: For high SNR, probability of erroneous decision on a bit transmitted in symbol xk is dominated by the closest neighbor of xk with the complementary bit

This neighbor is unique for Gray mapping

)]|([ HH freeb dPEP

Results - TCM Results - TCM

Base-station with Bit-interleaved Coded Modulation (BICM)

Results - BICM Results - BICM

Fig. 1 – TCM performance Fig. 2 – Effect of interleaving

Fig. 3 – Effect of Doppler spread Fig. 4 – Effect of hopping pattern selection

Conclusions - TCM Conclusions - TCM

Conclusions - BICM Conclusions - BICM The BICM scheme outperforms the TCM one (fig. 5), since the diversity order of the convolutional code (dfree = 4) is higher than the diversity order of the Ungerboeck code (Lmin = 2, which is the minimum symbol error event length). Moreover, while the information rate achieved by both schemes is 2 bits/symbol, the trellis complexity of BICM is half that of TCM.

Increasing the interleaver depth leads to greater performance gain than in the TCM case (fig. 5). Inversely, frequency hopping as opposed to plain block interleaving also provides more significant gain for BICM compared to TCM (compare fig. 6 and fig. 1,2).

The above observations are related to the fact that the higher the diversity order of a code, the more ‘difficult’ it is for it to be acquired for a given degree of channel correlation. Additional time or frequency diversity thus leads to greater performance gain, as the diversity order of the code is increased.

Future work Future work

Consider a multi-cellular system with frequency re-use factor 1

Effect of interference randomization on the outage capacity

Deployment of MIMO techniques to increase data rate, increase diversity and suppress the interference

Imperfect channel estimation

Iterative decoding (e.g. LDPC)

Fig. 5 – Comparison of BICM and TCM Fig. 6 – Effect of frequency hopping on BICM performance