1

OFDM Baseband Modulation Technology based on VHDL

Lin LinChangchun Institute of Optics, Fine

Mechanics and Physics, ChineseAcademy of Sciences

Graduate School of the Chinese

Academy of SciencesChangchun China; Beijing China

linlinat0218@yahoo.com.cn

Yan-feng QiaoChangchun Institute of Optics, Fine

Mechanics and Physics, Chinese Academy of Sciences

Changchun Chinaqiaoyf@ciomp.ac.cn

Wan-xin Su Changchun Institute of Optics, Fine

Mechanics and Physics, Chinese

Academy of Sciences

Changchun China

swx123456@mail.jl.cn

�Abstract—In order to improve the transmission velocity in

mulitipath fading wireless channel, the high speed OFDM

technology receives increasing attentions in mobile

communication. Modulation programs are designed with

VHDL based on the principle of OFDM in the paper. First,

after OFDM fundamental is introduced; two main advantages

are obtained via discussing spectrum utilization ratio of OFDM.

Then, from the results of VHDL simulation, the realization of

baseband operations, such as interleaver, subcarrier

modulation, IFFT and adding CP, are presented. Finally,

implemented programs are validated on the actual implement

system. Experimental results indicate that setup time

corresponding to transmission velocity is only 71.05μs and

steady time is approximately 6 times as setup time, that is, not

only achieving the high speed transmission, but also supplying

adequate modulation time.

Keywords: OFDM; VHDL; Baseband Modulation

I. INTRODUCTION

The growth of mobile communications and wireless internet access has produced a strong demand for advanced wireless techniques. The challenges for wireless communication designs come from the detrimental characteristics of wireless environments, such as multipath fading, Doppler Effect, co-channel interference, and intentional jamming in military communications. The objective of this paper is to provide an approach to solve the problem of transmission velocity of multipath fading by means of orthogonal frequency division multiplexing (OFDM) [1][2].

OFDM is a special form of multicarrier modulation, which was originally used in high frequency military radio. An efficient way to implement OFDM by means of a discrete Fourier transform (DFT) was found by Weinstein in 1971.The computational complexity could be further reduced by a fast Fourier transform (FFT). However, OFDM was not popular at that time because the implementation of large-size FFTs was still too expensive. Recent advances in VLSI technologies have enabled cheap and fast implementation of FFTs and IFFTs. In the 1980s, Cimini first investigated the use of OFDM for mobile communications. Since then, OFDM has become popular. In the 1990s, OFDM was adopted in the standards of digital audio broadcasting (DAB),

� 978-1-4244-5848-6/10/$26.00 ©2010 IEEE

digital video broadcasting (DVB), asymmetric digital subscriber line (ADSL), and IEEE802.11a. OFDM is also considered in the new fixed broadband wireless access system specifications [3] [4].

II. ALGORITHM BEHAVIOR

A. OFDM fundamental

Supposing N subchannels in OFDM system, one subchannel uses one subcarrier

� � � �kkkk tfBtx �� �� 2cos )1,,1,0( � Nk � (1)

where Bk is amplitude of the kth subcarrier which decidesinput code; fk is frequency of the kth subcarrier; φk is initialphase of the kth subcarrier [5]. The sum of N subcarriers isprovided

� � � �

�

��1

0

2cosN

k

kkk tfBts �� (2)

Rewriting (2) in complex field

� � kktfjN

k

k eBts�� �

�� 2

1

0

�

(3)

where kB�

is complex input of the kth subcarrier.If frequency interval of adjacent subcarrier is �f = 1/T

and )2/()( Tmkfk ��� )2,1,0( ��m , arbitrary two subcarriers is orthogonal in code duration T, that is

� � � � ���T

iikk dttftf0

02cos2cos ����

(4)

where Tnff ik /� )2,1,0( ��n and orthogonality is

independent of φk and φi . So this multicarrier system is called orthogonal frequency division multiplexing.Spectrum density of single subcarrier is showed as Fig.1.

Figure 1: Spectrum density of single subcarrier

f

fk+1/T

fk

2

Figure 2: Spectrum density of complex subcarriers

Because frequency interval of adjacent subcarrier is �f= 1/T, spectrum density of complex subcarriers is showed as Fig. 2.

There are two main advantages of the method: one is that signal could make the most of frequency band; the other is the flexibility of modulation of subcarriers.

B. OFDM spectrum utilization ratio

Supposing that N is the number of subcarriers, T is code duration and M is modulated M-system of every subcarrier.Frequency band width is

T

NBOFDM

1�� (5)

Utilization ratio of frequency band is transmitted bit ratio of unit bandwidth

MN

N

BT

MN

OFDM

BOFDM 22 log

1

1log

�����

(6)when N converges at , MBOFDM 2log�� [6].

If a subcarrier adopts M-system code to transmit, in order to obtain the same transmission velocity, utilization ratio of frequency band is expressed by

MN

T

T

MNBM 2

2 log2

1

2

log���� (7)

Comparing (6) and (7), OFDM technology makes utilization ratio of frequency band approximately increasetwice times.

III. VHDL IMPLEMENT

VHDL is a hardware description language that describeselectron circuitry and systemic behaves. Based on thedescription and interrelated software tools, one can gainanticipant circuitry or system. In the article, ISE9.2i achievesvarious operations of Virtex-5 FPGA such as program,synthesis, implement, restriction and simulation.

Figure 3: Simulation results of time sequence of interleaver

Inverse discrete Fourier transform (IDFT) is used tomodulate signal, since the expression of OFDM symbol is like that of IDFT

1

(2 )

0

1( ) ( )

Kj K nk

n

s k S n eK

�

�

�

(8)where k = 0, 1 K-1. Using K input codes in (2) to substitute into K disperse values S(n), s(k) becomes s(t) of (2)and φk = 0.

This section presents VHDL implement results of interleaver, subcarrier modulation, IFFT and adding CP.Next, these will be discussed respectively.

A. Interleaver

Interleaver is to disperse lost information to decreaseerror bit rate, in other words, when user information bits are lost among transmission process, lost information is part bits of some users, not all bits of one user and originalinformation can be recovered by the remaining information[7]. The process of interleaver is that data are read from the RAM where grouping data are stored, according to some rule.Here data are across read with equal interval, and the intervalis 4. Simulation results are showed as Fig.3.

B. Subcarrier modulation

Subcarrier modulation mostly uses three modes that are FSK (Frequency Shift Keying), PSK (Phase Shift Keying)and MQAM (Multiple Quadrature Amplitude Modulation)[8]. In the article employ BFSK (Binary Frequency Shift Keying), QPSK (QuadriPhase Shift Keying) and 16QAM(16-system QAM). Pilot modulation usually adopts BFSK that f1 and f2 correspond to "0" and "1" in Fig.4. For QPSK,phase 0, π/4, π/2 and 3π/4 are denoted by code "00", "01","10" and "11", respectively, and simulation results of time sequence are showed as Fig.5 (Maker region is thewaveforms of four phases). Frequency division and phase shift of QPSK are realized by taking count of system clock.

MQAM is amplitude and phase keying system where amplitude and phase are synchronously modulated as two independent parameters. The kth code is denoted as

� � � � � �TktkTtAts kkk 1cos 0 ����� ��(9)

Figure 4: Simulation results of time sequence of BFSK

3

Figure 5: Simulation results of time sequence of QPSK

where k = 0,1,2,3 , Ak and θk can choose different discrete values. When θk is 0 or π/2 and Ak is +A or –A, MQAM becomes QPSK, so QPSK is the simplest MQAM. In vectorgraph, every spot expresses amplitude and phase of one code, and MQAM signal is composed of two orthogonal vectors as Fig.6. The real and imaginary part of the spot express signal value has been modulated. Fig.7 shows simulation plot of time sequence of 16QAM where relevantspot is denoted by well-regulated combination of four values -- "0000100000" (32), "0001100000" (96), "1111011111" (-33) and "1110011111" (-97).

C. Realization of IFFT

Inverse fast Fourier transform (IFFT) is a fast realizationof IDFT and employs here. After mapping, data must be from frequency domain to time domain via IFFT, and synchronously accomplish OFDM modulation. The number of spots is 256. Data of frequency domain have been on corresponding subcarriers before IFFT. 256 subcarriers are 192 data subcarriers, 8 pilot subcarriers and 56 empty subcarriers including 28 protective subcarriers in lowfrequency region, 27 protective subcarriers in high frequencyregion and one DC (Direct Current) subcarrier. Indexes of 8pilot subcarriers are -88 -63 -38 -13, 13, 38, 63, 88 [9].

Data subcarriers map according to arrowhead directionfrom negative frequency to positive frequency as Fig.8. In implement process, sequence number of IFFT module is 0255, so subcarrier -128 127 transform subcarrier 0 255based on periodicity of IFFT, where 0 127 and 128 255are positive and negative frequency region, respectively. The plot is showed as Fig. 9.

Figure 6: Vectorgraph of 16QAM and 64QAM

Figure 7: Simulation results of time sequence of 16QAM

-128

-101

-100

-89

-88

-87

-64

-63

-62

-39

-38

-37

-14

-13

-12

-1

0

1

12

13

13

37

38

39

62

63

64

87

88

89

100

101

127

data subcarriers mapping direction-128 127

Figure 8: OFDM subcarriers mapping

0

1

12

13

14

37

38

39

62

63

64

87

88

89

100

101

127

128

155

156

167

168

169

192

193

194

217

218

64

87

219

242

243

244

255

data subcarriers mapping direction

0 255positive frequency

region

negative frequency

region

Figure 9: Regulated OFDM subcarriers mapping

Figure 10: Simulation results of time sequence of adding CP (GI = 4)

Realization of IFFT makes use of Fast Fourier Transform v5.0 that is an IP core of Xilinx ISE. Xilinx Co. supplies partly free IP cores for users which can be used via setting correlative parameters or making little modifications to save logic resources of mapping, operate steadily and shortendesign period. Here FWD_INV = 0, FWD_INV_WE = 1, NFFT = 64, 16, NFFT_WE = 1 and the others adopt defaults.

D. Adding CP

In OFDM systems, the entire channel is divided into Nnarrow subchannels and the high-rate data are transmitted in parallel through the subchannels at the same time. Therefore, the symbol duration is N times longer than that of single-carrier systems and the inter-symbol interference (ISI) is reduced by N times. Through adding a cyclic prefix (CP) ahead of each OFDM symbol, the ISI can be totally suppressed as long as the length of CP Tg is longer than the maximum channel delay τmax. Usually the length of CP is much smaller than the symbol duration; therefore, the spectrum efficiency decrease is negligible. To preserve the orthogonality, the subchannel spacing satisfies f = 1/ Ts,where Ts is the OFDM symbol duration [10] [11].

However, introduced guard interval (GI) brings loss of power and information velocity. The loss of power is defined as

���

����

��� 1log10 10

FFT

g

guardT

T�

(10)where Tg is the length of sample GI TFFT is the symbollength of OFDM after FFT without GI. From (10), when GIoccupies 20%, the loss of power is no more than 1 dB, but

Ak

�k

4

the loss of power could achieve 20%. The cost is worthybecause of eliminated ISI. Simulation results of time sequence of adding CP is showed as Fig.10.

IV. EXPERIMENT RESULTS

Fig.11 shows the actual implement system. The implement results enumerated in Table 1 indicate that the movement of programs is normal. Experiment conditions are data transmission rate - 25Mb/s, mobile velocity - 400 km/h, sampling frequency - 12.5MHz, FFT period - 3.84μs, and CP length - 0.96μs. Noted, the mix of Table 1 is the combine of 16QAM, QPSK and BPSK.

When the modulation modes alternately use to adaptchannel change, setup and steady time is 71.05μs and 440.03μs respectively, in other words, implement system has enough time to accomplish various baseband works and operation velocity satisfies the request of high speed.Moreover, memory resources consumed are only 7.6% andCFOs (carrier frequency offsets) error is also accurate within 1% of the subcarrier spacing.

V. CONCLUSION

OFDM Baseband Modulation Technology mentioned in the article, using VHDL as realization foundation reducessetup time and increases steady time which makecomplicated baseband works be accomplished well, and whose validity and feasibility are proved through the ISE simulation results and running on the actual implement system, respectively. It is exhibited that setup time corresponding to operation velocity is between 10 and 230μsimproving approximately one order of magnitude and steadytime can arrives at 65.53 1223.65μs. Next, much lessCFOs error will be researched with higher mobile velocity.

Figure 11: Implement system

TABLE I. EXPERIMENT RESULTS

modulation setup time

(μs)

steady

time (μs)

memory

resources (%)

CFOs

error

64QAM 213.23 1223.65 10.5% 0.00987

16QAM 55.74 381.77 7.8% 0.00966

QPSK 20.65 108.26 4.2% 0.00792

BPSK 12.33 65.53 2.0% 0.00654

mix 71.05

(average)

440.03

(average)

7.6%

(average)

0.00971

(average)

ACKNOWLEDGMENT

This work is supposed by the National High Technology Research and Development Program of China (863, No. 2008AA7034320B), and here thanks for constant guidanceof my advisors, Dr. Yan-feng Qiao and Wan-xin Su and opportunity supplied by conference organizers.

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