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Muti-Carrier CDMA Overview with BPSK Modulation In Rayleigh Channel
Pragya Pallavi Dept. Of Electronics & Telecommunication Kalinga Institute of Industrial Technology,
KIlT University Bhubaneswar, India [email protected]
A�lFtIcl-Multi-carrier code division multiple access (MCCDMA) is an attractive choice for high speed wireless communication as it mitigates the problem of inter symbol interference (lSI) and also exploits frequency diversity. In orderto support multiple users with high speed data communications, the MC-CDMA technique is used to address these challenges. In this paper working of Transmitter and Receiver model of MCCDMA system is presented. This work also derives simulation through MA TLAB of average bit error rate (BER) versus bit energy to noise ratio (Eb/No) of Multi Carrier Code Division Multiple Access (MC-CDMA) systems using various detection techniques which are used for both uplink & downlink MCCDMA systems i.e. Maximal Ratio Combining (MRC) and Equal Gain Combining (EGC) with synchronization errors over Rayleigh channel using HPSK modulation and Additive White Gaussian Noise, which shows the reduction in HER performance.
Keywonls-MCCDMA,· BPSK Motlulfllion,. RlIYleig" c"flllllel,· AW6N,· EGC,· MRC
I. INTRODUCTION
With a surging increase in demand for personal wireless radio communications within the past decade, there is a growing need for technological innovations to satisfy theses demands. Future technology must be able to allow users to efficiently share common resources, whether it involves the frequency spectrum, computing facilities, databases, or storage facilities.[l]The multicarrier(MC) technique has grown an important alternative for wireless indoor communications. One large advantage of this technology is its robustness in case of multipath propagation. MC-CDMA is one representative of the MC technique. It has emerged as another feasible option for forward-looking MC communications systems by exploiting the flexibility and potential offered by the combination of OFDM and CDMA
With a surging increase in demand for personal wireless radio communications within the past decade, there is a growing need for technological innovations to satisfy theses demands. Future technology must be able to allow users to efficiently share common resources, whether it involves the frequency spectrum, computing facilities, databases, or storage facilities.[l ]The multicarrier(MC) technique has grown an important alternative for wireless indoor communications. One large advantage of this technology is its robustness in case of multipath propagation. MC-CDMA is one representative of the MC technique. It has emerged as
978-1-4244-5540-9/10/$26.00 ©2010 IEEE
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Pradipta Dutta Dept. Of Electronics & Telecommunication Kalinga Institute of Industrial Technology,
KIlT University Bhubaneswar, India cr _ [email protected]
another feasible option for forward-looking MC communications systems by exploiting the flexibility and potential offered by the combination ofOFDM and CDMA
II. MULTI-CARRIER CDMA OVERVIEW
A. Multi-carrier CDMA (MC-CDMA) Two main variations of the MC spread spectrum systems
are the MC-CDMA (frequency domain spreading) and MC direct sequence CDMA (MC-DS-CDMA) (time domain spreading). One way of looking at MC-CDMA is as a combination of CDMA and OFDM, resulting in better frequency diversity and higher data rates. In MC-CDMA, each symbol is spread using code chips and transmitted on several subcarriers. There is no necessity for the number of carriers to be equal to the code length; thus offering a degree of flexibility in our design.MC-DS-CDMA differs in the fact that the data is spread in time domain rather than in frequency; with each sub channel representing a regular DSCDMA system. The principle of MCCDMA is that a single data symbol is transmitted on multiple narrow band subcarriers. Indeed, in MCCDMA systems, spreading codes are applied in frequency domain transmitted over independent subcarriers. The eminent advantage of MC-CDMA is the increase in bandwidth efficiency; the reason being the multiple access made possible through proper systems design using orthogonal codes.
B. Needfor MCCDMA MC-CDMA takes advantage of both OFDM and CDMA
and makes an efficient transmission system by spreading the input data symbols with spreading codes in frequency domain. It uses a number of narrowband orthogonal subcarriers with symbol duration longer than the delay spread. This makes it unlikely for all the subcarriers to be affected by the same deep fades of the channel at the same time thereby improving performance .Synchronization during transmission becomes easier with longer symbol durations. As the number of paths increases the performance of the two systems improves at first due to diversity, then, it starts to deteriorate due to the increased interference from large number of paths of all users. In general, there is an optimum number of paths that depends on the system used and the number of users. As the number of users increases, interference from all users through all paths increases. Therefore, the optimum number of paths decreases.
III. MCCDMA SYSTEM MODEL
In this section, we describe the transmitter and receiver model of MCCDMA system. Here, symbols are modulated on many subcarriers to introduce frequency diversity instead of using only one carrier like in CDMA. Thus, MC-CDMA is robust against deep frequency selective fading compared to DS-CDMA [10]. Each user data is first spread using a given high rate spreading code in the frequency domain. A fraction of the symbol corresponding to a chip of the spreading code is transmitted through different subcarriers [8].
A. MCCDA1A Transmitter mode!
...
.' / �
-
...
-
Figure 1. MCCDMA Transmitter.
In this figure, the main difference between MCCDMA & OFDM is that the MC-CDMA scheme transmits the same symbol in parallel through several subcarriers whereas the
OFDM scheme transmits different symbols. . . . . . c(t) = [cf ,c{ , ... , �.,,] is the spreading code of the J I user in
the frequency domain, G MC denotes the processing gain, sometimes called the spreading factor. The input data stream
is multiplied by the spreading code of length GMC' Each chip of the code modulates one sub carrier. The number of
subcarriers is N = G MC' The users are separated by different codes. All data corresponding to the total number of sub carriers are modulated in baseband by an inverse fast Fourier transform (IFFT) and converted back into serial data. Then, a cyclic prefix is inserted between the symbols which is a repeat of the end of the symbols at beginning, to combat the inter-symbol interference (ISI) and the inter-carrier interference (ICI) caused by multipath fading. And hence the cyclic prefix length is chosen such that it is greater than the delay spread of the channel, so that the effects of multipath are mitigated effectively. Finally, the signal is digital to analog converted and up converted for transmission.
In MC-CDMA transmission, it is essential to have frequency nonselective fading over each sub carrier. Therefore, if the original symbol rate is high enough to become subject to frequency selective fading [8], the input data have to be serial to parallel (SIP) converted into P
parallel data sequences [�,a;, ... ,0] and each SIP output is
multiplied with the spreading code of length GMC • Then,
each sequence is modulated using GMC subcarriers. Thus, all
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sub carriers N = P XG MC are also modulated in baseband by the IFFT.
Figure 2 shows the modified version of the MC-CDMA transmitter.
In order to improve the performance of the system, an appropriate approach for channel estimation is, to use dedicated pilot symbols that are periodically inserted in the transmission frame (in the time domain) , also known as block-type pilot channel estimation. The pilot tones can also be inserted into each symbol (in the frequency domain) with a given frequency spacing; this is known as comb-type pilot channel estimation [4,5].
,: :t�,-----, , ...
- I.
Figure 2. Modified version of the MC-CDMA Transmitter.
Block-type pilot channel estimation has been developed under the assumption of a slow fading channel, i.e. the channel transfer function does not change very rapidly. Whereas comb-type pilot channel estimation has been developed under the assumption that the channel changes from one OFDM block to the other. It estimates the channel at pilot frequencies & the frequency response of the channel at frequencies where pilot tones are not located & can be interpolated using various interpolation techniques such as linear, spline, FFT or low pass filtering [5]. Pilot tones may be inserted in both time and frequency domains as shown in Figure 3, where we can see the rectangular pilot insertion grid with pilot tones inserted every third frequency and every fourth time slot. The pilot density is thus 1112 , that is, 1112 of the whole capacity is used for channel estimation.
.000.000.000.000.000. �looooooooooooooooooooo . . 000000000000000000000
.000.000.000.000.000. 000000000000000000000
000000000000000000000 .000.000.000.000.000.
000000000000000000000 � 000000000000000000000 � .000.000.000.000.000.
r 000000000000000000000 000000000000000000000 .000.000.000.000.000.
Tirue 4Ts Figure 3. Example of a pilot tone grid.
B. MCCDA1A Receiver mode! The MCCDMA receiver configuration for the jth user is
shown in Figure 4. The received signal is first down
converted. Then, the cyclic prefix is removed and the remaining samples are serial to parallel converted to obtain the m-subcarriers components (corresponding to the q;� data), where m = 1,2, ... , GMC .The m-subcarriers are first demodulated by a fast Fourier transform (FFT) (OFDM demodulation) and then multiplied by the gain qjm to combine the received signal energy scattered in the frequency domain. In [8], the decision variable is given by:
d - "" m�l ( 1) - L...J GMC qmYm Y ="" j�l zI d d + n
111 �J 111 m m (2)
lY(d
orr
Figure 4. MC-COMA Receiver.
where, Ym and nm are the complex baseband component of the received signal and the complex Gaussian noise at the nI" subcarrier, respectively. zJ,n and aj are the complex envelope of the nih sub carrier and the transmitted symbol of l" user, respectively. J is the number of active users. As we mentioned in section A, pilot symbols are periodically inserted in the transmission frame because coherent demodulation requires knowledge of the channel. The channel estimation is processed from the pilot symbols received at the beginning of each data frame. An optimum Wiener estimator is used [9, 11], and the channel estimation is processed across the time axis or the frequency axis or both.
In the remainder of the report, we will consider simulation of MC-CDMA systems.
IV. SIMULATION OF MCCOMA
Here we discuss BER for BPSK in a Rayleigh multipath channel. In discussion on Rayleigh channel, a circularly symmetric complex Gaussian random variable is considered, which is of the form, h = hre + jhim where, real and imaginary parts are zero mean independent and identically distributed (iid) Gaussian random variables with mean 0 and variance 0"2 .The magnitude 1 hi which has a probability density,
-t?
p(h) = --; e2°', h:?: 0 is called a Rayleigh random variable. 0"
This model, called Rayleigh fading channel model, is reasonable for an environment where there are large number of reflectors._[12]
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The received signal in Rayleigh fading channel is of the form, Y = hx+ n ,where ' Y' is the received symbol, h' is complex scaling factor corresponding to Rayleigh
multipath channel, 'x' is the transmitted symbol (taking values +1' s and -1' s)and 'n' is the Additive White Gaussian Noise (A WGN) Assumptions:
1) The channel is flat fading - means that the multipath channel has only one tap. So, the convolution operation reduces to a simple multiplication.
2) The channel is randomly varying in time - meaning each transmitted symbol gets multiplied by a randomly varying complex number 'h' . Since 'h' is modeling a Rayleigh channel, the real and imaginary parts are Gaussian distributed having mean 0 and variance 112.
3) The noise 'n' has the Gaussian probability density function with with pen) = (11 .J 2 nO" 2 )e-(n-Ill' 12IT' J1 = 0 and 0"2 =JV;,12.
4) The channel ' h ' is known at the receiver. Equalization is performed at the receiver by dividing the received symbol y by the h y= yl h= (hx+n)1 h= x + h ,where, h= nl his the additive noise scaled by the channel coefficient.
S Bit Error Rate BER computation in A WGN, the probability of error for
transmission of either + 1 or -1 is computed by integrating the tail of the Gaussian probability density function for a given value of bit energy to noise ratio Ebl No. The bit error rate
is, � = � eifc( � E;, I � ) .However in the presence of channel � h' , the effective bit energy to noise ratio is 1 h 12 E;, I � . So the bit error probability for a given value of , h' is,
1 il hi' E, 1 C 1 hi' h; �//; =-eifc( ---=-erfi:("y), wherey =---I 2 � 2 N
To find the rror probability over all random values of 1 h f , one must evaluate the conditional probability density function �/" over the probability density function of y
Probability density./imction oj" y :From our discussion on chi-square random variable, we know that if 1 hi is a Rayleigh distributed random variable, then 1 h 12 , is chisquare distributed with two degrees if fteedom. Since 1 h 12 , is chi square distributed, y is also chi square distributed The probability density .fUnction 0.1 y is,
-y
P( ) 1 E 1 N S h b b·l· . y = --- e b " y:?: 0 . 0 t e error pro a 1 Ity IS, E;,/� � = f� � eifi. dy This equation reduces to
�=�d-(E;,/�)) 2 (Eb/�)+l
1) Simulation Model: Procedure for Matlab simulation of a BPSK transmission
and reception in Rayleigh channel is as follows:-First we generate random binary sequence of + l' s and
l ' s,then multiply the symbols with the channel and then add A WGN.At the receiver, we equalize (divide) the received symbols with the known channel & perform hard decision decoding and count the bit errors.Finally we repeat
for multiple values of � I N;, and plot the simulation results. SEA feu 8PSK modulatllln '" Raylltlgh dI�
lO''---:;--7--�lO;--�'5;--�:D;----:;25�----;!O;:;-�3S e ...... d6
Figure 5. BER Vs ¥u{Zr in Rayleigh channel
C Channel Model
The transmitted waveform gets corrupted by noise 'n' typically referred to as Additive White Gaussian Noise (AWGN).
Additive: As the noise gets ' added ' (and not multiplied) to the received signal
White: The spectrum of the noise if flat for all frequencies. Gaussian: The value of the noise n follows the Gaussian probability distribution function,
D. Computing the probability of error:
The received signal, y = SI + n when bit 1 is transmitted
and y = So + n when bit ° is transmitted. The conditional probability distribution function (PDF) of y for the two cases are:
1 -(y-,[EtY 1 _(y+JEb)2 p(y /Sl) = r::;:o e No & p(y /so) = r::;:o e No
v n N o vrrNo
-jE;, I
o +jE;, I
Figure 6. Conditional probability density function with BPSK modulation
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Assuming that p(rlsO) and p(rls1) are equally probable i.e.
+.JE: & -.JE: have equal probability, the threshold ° forms the optimal decision boundary. If the received signal is
+.JE: ' which is greater than 0, then the receiver assumes
[per l SI)] of SI was transmitted. If the received signal is
-.JE: ' which is less than or equal to 0, then the receiver
assumes [p(rl so)] of So was transmitted. i.e.
y> ° � SI and y:O; ° � So • Probability of error given SI
transmitted was
With this threshold, the probability of error given SI IS
tran . . . _2 1 0
-(Y-JEbJ 1 00 2 p(e/s ) =- J . e No dy = ---;=I rr-e-z dz 1. ;'f(No -en Vrr . i� \I No
= � erfC(f!i: where, erfC(x) = l t e-r'd.x is the
complementary error function.
• Probability of error given So was transmitted Similarly the probability of error given
So is transmitted is 00 � 2
1
J -(y+,1 Eb) 1
J pee/so) = -- e No dy = - e-z2 liz .JnNo .jTI ,�. -a ,'Eb/No = �erfcUEb/No ) .
2 Total probability of bit error
� = P(SI )p(el SI) + p(so)p(el so)
Given that we assumed that SI and So are equally probable
l.e. P(SI) = P(S2) =112 the bit error probability
is,� = �erfC(�Ebl N;,) E. Simulation mode!-
We performs the following procedure:-Initially, we generate random BPSK modulated symbols
+1's and -l's, then we pass them through AWGN channel after that we demodulate the received symbol based on the location in the constellation, then we count the number of
errors finally repeat the same for multiple � I N;, value
Bn etrar probability CIJrIo'tl far BPSK modulaMn in "WCN Cunn.I
mo$L-�.2 ---::-----:!--�. ,---7-----:�-----'--7. EblNo, d'S
rlgUJt: I. D.c� V S Db 1 .iY 0111 J-\. VVUi'll L11i:tIl11t:1
By analyzing figure 6 & 7 together, we will get the figure,
as shown below which is BER Vs � / A: on Rayleigh Channel with A WGN for MCCDMA system
BER Vs EblNo on Rayleigh Channel
10.5 O�--=----:--:---:':--�lO:----C':'=-2 --:':14
-
--'16�-'=-B
-
-::20 EblNo, dB
Figure 8. BER Vs � / A: on Rayleigh Channel
In the above graph, Blue & Green line shows:Simulated BER for BPSK for user-1&2 with AWGN on Rayleigh Channel
V. DETECTION STRATEGIES FOR BOTH DOWNLINK
MCCDMA
MCCDMA receiver combines the received signals scattered in the frequency domain. Signal combining strategies include Orthogonality Restoring Combining (ORC), Controlled Equalization(CE),Minimum Mean Square Error Combining(MMSEC),Equal Gain Combining(EGC) and Maximal Ratio Combining(MRC). However, EGC and MRC are not constrained and they are adopted herein, since detection strategies which are used at the receiver side in MCCDMA for both uplink and downlink is EGC and MRC.
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This work derives the average bit error rate (BER) of the uplink and downlink MCCDMA.
EGC:-With two receive antennas, the BER with EGC is,
1; =l..[1 - (�� / A:(� / A: +2) / Eb/ A: +1)] .We perform
the fotowing procedure for simulation: Initially, we generate random binary sequence of +l's and -l's then we multiply the symbols with the channel & add A WGN, after that we equalize each receive path by compensating with the known channel phase at the receiver & then we accumulate the equalized symbols from all receive paths, then we perform hard decision coding & count the bit errors. Finally, we
repeat it for multiple values of � / A: & plot the simulation results.
BER for BPSK modulation with Equal Gain Combining in Rayleigh channel
EblNo, dB
Figure 9. BER for BPSK with EGC in Rayleigh Channel
MRC:- Error rate with Maximal Ratio Combining (MRC): From the discussion on chi-square random variable,
we know that, if hi is a Rayleigh distributed random variable,
then h; is a chi-squared random variable with two degrees of
freedom. The pdf of Yi is P(yJ = [l/(Eb / A:)]e-YiI(Ehi N,,) •
Since the effective bit energy to noise ratio y is the sum
of N such random variables, the pdf of y is a chi-square
random variable with 2N degrees of freedom. The pdf of y is,
If we see above, in the post on BER computation in
A WGN, with bit energy to noise ratio of � / A: ' the bit error rate for BPSK III A WGN IS derived as
I;, = � eriC( � � / A:) Given that the effective bit energy to
noise ratio with maximal ratio combining is y , the total bit error rate is the integral of the conditional BER integrated
00 OVt
This equation reduces to
#-\ P" = p#�)N-I+k)(1-pi'
I I I -\/2 where, p=---(1+--) 2 2 -0,INo
BER Simulation Model: We perform the same procedure for simulation ofMRC as ofEGC, the only difference is,
BER felf el"'SK modulltloo 'MIIh Mulm81 Rallo Combining in R''Ylelgh chlnn,l
10'
10'
10'� O:---!------;IO!:---:'.!:---=l0:-'- --="':----=..,:----=:)5 CbfNo. dB
Figure 10. BER for BPSK with MRC in Rayleigh Channel
here in MRC, we have to choose the received path & then equalize the received symbols per MRC.
VI. CONCLUSION
In this paper we have tried to study and implement the Multi- Carrier CDMA system and derive the BER Vs Eb/No performance for MCCDMA communication system using variable number of bits with BPSK modulation on Rayleigh channel and Additive White Gaussian Noise. Here detection strategies are also analyzed which are used for both uplink and downlink MCCDMA that is Equal Gain Combiner(EGC) and Maximal Ratio Combiner(MRC).Simulation ofBER Vs
-0, I N;, with EGC and MRC in Rayleigh Channel with BPSK modulation shows that as BER performance decreases, the
bit energy to noise ratio, Eb I No increases. Here, in MCCDMA signals received will never be
corrupted because copy of same signals are transmitted over all subcarriers and error or overlapping of signals will never take place because of orthoganility property
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