07-06-2010, 12:14 AM
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CELLULAR AND MOBILE COMMUNICATIONS DS-CDMA
Presented By:
V.VIJAYA KUMAR, IV B.Tech E.C.E
SREE VIDYANIKETHAN ENGINEERING COLLEGE ,TIRUPATI
ABSTRACT
So far transmission errors have been described as evil entity in communication literature. Introducing error intentionally can save power and reduce interference. This has been proved by scientists Jik Dong Kim (South Korea), Sang Wu Kim (USA) and Young Gil Kim (South Korea). It is about combined power and error control in multicarrier DS-CDMA systems which are most popular in various indoor and mobile communication systems. This paper explains new scheme devised by them along with performance comparison with older systems to prove it is better than existing systems. This work originally appeared in IEEE transactions on communications in August 2004.
I. INTRODUCTION
A combined power control and error control coding in multicarrier direct- sequence code-division multiple-access (DS-CDMA) systems is explained in this paper. The transmission power is controlled in such a way that channel fading in each subchannel is compensated for only when the channel gains in all subchannels are above a prescribed cutoff fade depth 0; otherwise, no power is allocated for the corresponding symbols (i.e., power truncation), and erasures are generated at the receiver. The motivation for this technique is that the symbols with low channel gain is likely to be error and yet, if transmitted, consumes the energy resources and generate interference to the other users. Truncating the power for those symbols has the effect of reducing the interference to other users and allocating more power on symbols with high channel gain (there by reducing the error probability). Since block codes can correct twice as many erasures as errors, the coded performance can be improved by properly combining the power control with the error-control coding.
II. SYSTEM MODEL
We consider a multicarrier DS-CDMA system with K active transmitters communicating with a common receiver (base station). The block diagrams of the transmitter and receiver are shown in Fig. below. Each packet of data is encoded by an (n, k) extended Reed-Solomon (RS) code over GF (Q), where n is equal to Q and is a power of two. In order to randomize error bursts, an ideal interleaver/deinterleaver is assumed. A code symbol (Q-ary) is converted into M (= log2 Q) parallel bits, and each bit is spread by a random sequence pk(t). The substreams are modulated on M subcarriers with a carrier spacing that provides nonoverlapping subbands. The subchannels are assumed to experience an independent flat fading. This assumption can be justified by choosing the number of subcarriers and the bandwidth of each subband, such that the carrier spacing between adjacent subcarriers, f, is greater than the coherence bandwidth, Bc, and the delay spread is less than the chip duration of each subchannel.
Let k,i be the channel power gain in the ith subchannel for transmitter k. We assume that {k, i} are independent and identically distributed (i.i.d) random variables with probability density function (pdf) given by
(1)
Where = E [k, i] for all i and k. We also assume that = k,1, k,2¦ k,M can be estimated perfectly at the receiver, and fed back to the transmitter k through a reliable feedback channel for power control. The channel state changes at a rate slow enough (slow fading) for the delay on the feedback channel to be negligible. However, the side-information error may occur if the receiver fails to identify the correct gain (due to the low SNR of pilot) or the feedback channel is not reliable.
The receiver signal r (t) at the base station can be expressed as
(2)
Where Pi( ) is the transmission power, dk,i(t) and pk(t) are the data and random spreading waveforms, respectively, fi is the carrier frequency, tk is the propagation delay and k,i is the carrier phase, all for transmitter k at the ith subchannel. We will assume a raised-cosine chip waveform with rolloff factor a, n(t) represents the thermal noise and is modeled by a zero mean white Gaussian noise with two-sided power spectral density N0/2.
If the channel power gains of all M subchannels are greater than a threshold 0 (i.e., k,i = 0, for all i), then the corresponding Q-ary code symbol is transmitted with a power Pi( ),i = 1, 2,¦.,M. Otherwise, it is not transmitted (i.e.,
(A) TRANSMISSION FOR THE kth USER
(B) RECEIVER FOR THE kth USER
Pi( ),i = 0, for all i), and an erasure is generated for the corresponding Q-ary code symbol at the receiver. Thus the probability of symbol erasure is given by
(3)
The erasure probability is also the activity factor; each user turns off its power with probability . Thus, the power truncation will reduce the average number of interfering users from K-1 to (K-1) , thereby reducing the symbol-error probability (SEP). Notice that the conventional power control corresponds to a special case of 0 being equal to zero.
III. MATHEMATICAL ANALYSIS
Because an (n, k) RS code can correct any set of s erasures and t errors provided s+2t = n-k, the probability of incorrect decoding PE is given by
(4)
Where per and pc are the symbol (Q-ary) erasure probability and the correct symbol (Q-ary) probability, respectively. Below, we will derive the correct symbol probability pc for two types of power control.
A. Power Truncation Only (Scheme B)
In this subsection, we consider the following power control:
(5)
for some constant P. The required feedback information for this type of power control is one bit indicating whether the channel power gains of all M subchannels are greater than a threshold o (i.e., k,i = o, for all i). The special case of 0 = 0 corresponds to the conventional errors-only decoding without power control. The coherent correlation receiver calculates a decision statistic Zk,i
(6)
where T is the bit duration, and dk,i is the channel bit in the ith subchannel. The first term in (6) is the desired signal term. The second term
(7)
represents multiuser interference, where f is a random variable uniformly distributed over [0, 2p). According to the central limit theorem, the distribution of IM is approximately Gaussian with mean zero and variance
(8)
(9)
where is a constant that depends on the chip waveform, N Ë T/Tc is the processing gain, and Tc is the chip duration of each subchannel. For the rectangular chip waveform and raised-cosine chip waveform with a rolloff factor a, is 1/3 and (1- a /4)/2, respectively. The third term in (6) represents the background white Gaussian noise with mean zero and variance N0/2. Thus, Zk,i is a Gaussian random variable with
(10)
where
(11)
Therefore, the conditional probability pc( ) of correct symbol (Q-ary) is
(12)
where
(13)
In (12), we assumed that the Q-ary code symbol is correct only when all log2Q bits constituting the code symbol are correct, i.e., if atleast one bit constituting the code symbol is in error, the probability of correct symbol pc is given by (14)-(15).
(14)
(15)
In deriving (14), we assumed that the k,i™s for i=1,2,¦.,M are i.i.d. It follows from (5) and the assumption that the k,i™s for i=1,2,¦.,M are i.i.d. that the average transmission power per channel bit is
(16)
(17)
Therefore, the average received energy per information bit is
(18)
(19)
Where r=k/n is the code rate.
B. Truncated Channel Inversion (Scheme A)
In this subsection, we consider the following power control:
(20)
for some constant PR. This type of power control makes the fading channel appear as a time-variant additive white Gaussian noise (AWGN) channel during nontruncation periods. The required feedback information for this type of power control is the channel gains of all subchannels (k,1, k,2,¦¦,k,M), which is much more than what power truncation only (scheme B) requires. The special case of 0=0 corresponds to the conventional errors-only decoding with channel inversion.
It follows from (8) and (20) that the variance of the multiple access interference is
(21)
The equivalent noise spectral density Ne/2 can be then obtained form (11) and (21). Therefore, the probability of the correct symbol (Q-ary) is given by (22).
(22)
It follows form (16) and (20) that the average channel bit power PT is
(23)
The average received energy per information bit can be obtained from (18) and (23).
IV. NUMERICAL RESULTS AND DISCUSSION
Fig. 1 is a plot of the probability of incorrect decoding PE versus the normalized cutoff threshold /¯. We find that there exists an optimum threshold that minimizes PE , and the optimum choice of for scheme A can reduce PE by almost two orders of magnitude, when compared with the conventional errors-only decoding with channel inversion (0 = 0). Also, scheme A provides a better performance than scheme B. This can be explained as follows.
Scheme A (per-carrier adaptation) makes the channel appear as an AWGN channel during nontruncation periods, and thus, provides a better performance over scheme B. However, if the available energy resources is limited (i.e., very low Eb/N0), then the truncation period for scheme A may be too long (i.e., too many erasures to correct), so that its decoding-error probability may become higher than scheme B.
Fig. 2 is a plot of the probability of incorrect decoding PE versus Eb/N0 with several erasure-generation methods, where the simulation results for the proposed scheme are included for the validation of the analysis. We find that the combined power control and error-control coding scheme (A and B) provide a much lower PE over the conventional error-control coding without power control (C, D, and E), particularly at high Eb/No. This is because the proposed scheme suppresses the multiuser interference
Fig. 4. Probability of incorrect decoding PE versus Eb/No: (512,170) RS code, N=64, K=30, M=9, a=0.25, A=truncated channel inversion, B= power truncation only, C= convolutional code of rate with an optimum distance profile of the generator polynomial (4 564 754) in octal number and constraint length of seven. and saves the energy resources by truncating the transmission power during unfavorable channels, and allocates the saved energy on symbols on high channel gain. shows that the combined power control and error-control coding provides a significant capacity gain over conventional schemes.shows the characteristic steep slope of the RS code versus the graceful degradation of the convolutional code.
We also find that the convolutional-coded system provides a lower PE than the RS-coded system in the low SNR region, but exhibits an error floor and provides a higher PE in the high SNR region(interference-limited region).
V. CONCLUSIONS
We explained that the probability of incorrect coding can be significantly reduced by combining the power control with the error-control coding. It is also seen that power can be saved and interference can be reduced.
How much power can be saved
In reference 4 it has been explained that for a large communication network every one dB saving in power will result in savings of many millions of dollars annually.
Will Reliance India mobile which uses CDMA technology save crores of rupees by implementing this technique
These two questions will be answered when we meet in ERODE SENGUNTHAR Engg college on 22nd & 23rd of September 2005.
REFERENCES :
1. Jik Dong Kim (South Korea), Sang Wu Kim (USA) and Young Gil Kim (South Korea), COMBINED POWER CONTROL AND ERROR CONTROL CODING IN MULTICARRIER DS-CDMA SYSTEMS, IEEE TRANSACTIONS ON COMMUNICATIONS VOL. 52, No. 8, AUGUST 2004.
2. Dr. KAMILO FEHER Wireless Digital Communications, PHI 2002
3. WILLIAM C.Y.LEE, Mobile communications engineering, 2¬¬¬nd edition MC Graw-Hill.
4. K.SAM SHANMUGAM, digital and analog communication systems, John Wiley.
CELLULAR AND MOBILE COMMUNICATIONS DS-CDMA
Presented By:
V.VIJAYA KUMAR, IV B.Tech E.C.E
SREE VIDYANIKETHAN ENGINEERING COLLEGE ,TIRUPATI
ABSTRACT
So far transmission errors have been described as evil entity in communication literature. Introducing error intentionally can save power and reduce interference. This has been proved by scientists Jik Dong Kim (South Korea), Sang Wu Kim (USA) and Young Gil Kim (South Korea). It is about combined power and error control in multicarrier DS-CDMA systems which are most popular in various indoor and mobile communication systems. This paper explains new scheme devised by them along with performance comparison with older systems to prove it is better than existing systems. This work originally appeared in IEEE transactions on communications in August 2004.
I. INTRODUCTION
A combined power control and error control coding in multicarrier direct- sequence code-division multiple-access (DS-CDMA) systems is explained in this paper. The transmission power is controlled in such a way that channel fading in each subchannel is compensated for only when the channel gains in all subchannels are above a prescribed cutoff fade depth 0; otherwise, no power is allocated for the corresponding symbols (i.e., power truncation), and erasures are generated at the receiver. The motivation for this technique is that the symbols with low channel gain is likely to be error and yet, if transmitted, consumes the energy resources and generate interference to the other users. Truncating the power for those symbols has the effect of reducing the interference to other users and allocating more power on symbols with high channel gain (there by reducing the error probability). Since block codes can correct twice as many erasures as errors, the coded performance can be improved by properly combining the power control with the error-control coding.
II. SYSTEM MODEL
We consider a multicarrier DS-CDMA system with K active transmitters communicating with a common receiver (base station). The block diagrams of the transmitter and receiver are shown in Fig. below. Each packet of data is encoded by an (n, k) extended Reed-Solomon (RS) code over GF (Q), where n is equal to Q and is a power of two. In order to randomize error bursts, an ideal interleaver/deinterleaver is assumed. A code symbol (Q-ary) is converted into M (= log2 Q) parallel bits, and each bit is spread by a random sequence pk(t). The substreams are modulated on M subcarriers with a carrier spacing that provides nonoverlapping subbands. The subchannels are assumed to experience an independent flat fading. This assumption can be justified by choosing the number of subcarriers and the bandwidth of each subband, such that the carrier spacing between adjacent subcarriers, f, is greater than the coherence bandwidth, Bc, and the delay spread is less than the chip duration of each subchannel.
Let k,i be the channel power gain in the ith subchannel for transmitter k. We assume that {k, i} are independent and identically distributed (i.i.d) random variables with probability density function (pdf) given by
(1)
Where = E [k, i] for all i and k. We also assume that = k,1, k,2¦ k,M can be estimated perfectly at the receiver, and fed back to the transmitter k through a reliable feedback channel for power control. The channel state changes at a rate slow enough (slow fading) for the delay on the feedback channel to be negligible. However, the side-information error may occur if the receiver fails to identify the correct gain (due to the low SNR of pilot) or the feedback channel is not reliable.
The receiver signal r (t) at the base station can be expressed as
(2)
Where Pi( ) is the transmission power, dk,i(t) and pk(t) are the data and random spreading waveforms, respectively, fi is the carrier frequency, tk is the propagation delay and k,i is the carrier phase, all for transmitter k at the ith subchannel. We will assume a raised-cosine chip waveform with rolloff factor a, n(t) represents the thermal noise and is modeled by a zero mean white Gaussian noise with two-sided power spectral density N0/2.
If the channel power gains of all M subchannels are greater than a threshold 0 (i.e., k,i = 0, for all i), then the corresponding Q-ary code symbol is transmitted with a power Pi( ),i = 1, 2,¦.,M. Otherwise, it is not transmitted (i.e.,
(A) TRANSMISSION FOR THE kth USER
(B) RECEIVER FOR THE kth USER
Pi( ),i = 0, for all i), and an erasure is generated for the corresponding Q-ary code symbol at the receiver. Thus the probability of symbol erasure is given by
(3)
The erasure probability is also the activity factor; each user turns off its power with probability . Thus, the power truncation will reduce the average number of interfering users from K-1 to (K-1) , thereby reducing the symbol-error probability (SEP). Notice that the conventional power control corresponds to a special case of 0 being equal to zero.
III. MATHEMATICAL ANALYSIS
Because an (n, k) RS code can correct any set of s erasures and t errors provided s+2t = n-k, the probability of incorrect decoding PE is given by
(4)
Where per and pc are the symbol (Q-ary) erasure probability and the correct symbol (Q-ary) probability, respectively. Below, we will derive the correct symbol probability pc for two types of power control.
A. Power Truncation Only (Scheme B)
In this subsection, we consider the following power control:
(5)
for some constant P. The required feedback information for this type of power control is one bit indicating whether the channel power gains of all M subchannels are greater than a threshold o (i.e., k,i = o, for all i). The special case of 0 = 0 corresponds to the conventional errors-only decoding without power control. The coherent correlation receiver calculates a decision statistic Zk,i
(6)
where T is the bit duration, and dk,i is the channel bit in the ith subchannel. The first term in (6) is the desired signal term. The second term
(7)
represents multiuser interference, where f is a random variable uniformly distributed over [0, 2p). According to the central limit theorem, the distribution of IM is approximately Gaussian with mean zero and variance
(8)
(9)
where is a constant that depends on the chip waveform, N Ë T/Tc is the processing gain, and Tc is the chip duration of each subchannel. For the rectangular chip waveform and raised-cosine chip waveform with a rolloff factor a, is 1/3 and (1- a /4)/2, respectively. The third term in (6) represents the background white Gaussian noise with mean zero and variance N0/2. Thus, Zk,i is a Gaussian random variable with
(10)
where
(11)
Therefore, the conditional probability pc( ) of correct symbol (Q-ary) is
(12)
where
(13)
In (12), we assumed that the Q-ary code symbol is correct only when all log2Q bits constituting the code symbol are correct, i.e., if atleast one bit constituting the code symbol is in error, the probability of correct symbol pc is given by (14)-(15).
(14)
(15)
In deriving (14), we assumed that the k,i™s for i=1,2,¦.,M are i.i.d. It follows from (5) and the assumption that the k,i™s for i=1,2,¦.,M are i.i.d. that the average transmission power per channel bit is
(16)
(17)
Therefore, the average received energy per information bit is
(18)
(19)
Where r=k/n is the code rate.
B. Truncated Channel Inversion (Scheme A)
In this subsection, we consider the following power control:
(20)
for some constant PR. This type of power control makes the fading channel appear as a time-variant additive white Gaussian noise (AWGN) channel during nontruncation periods. The required feedback information for this type of power control is the channel gains of all subchannels (k,1, k,2,¦¦,k,M), which is much more than what power truncation only (scheme B) requires. The special case of 0=0 corresponds to the conventional errors-only decoding with channel inversion.
It follows from (8) and (20) that the variance of the multiple access interference is
(21)
The equivalent noise spectral density Ne/2 can be then obtained form (11) and (21). Therefore, the probability of the correct symbol (Q-ary) is given by (22).
(22)
It follows form (16) and (20) that the average channel bit power PT is
(23)
The average received energy per information bit can be obtained from (18) and (23).
IV. NUMERICAL RESULTS AND DISCUSSION
Fig. 1 is a plot of the probability of incorrect decoding PE versus the normalized cutoff threshold /¯. We find that there exists an optimum threshold that minimizes PE , and the optimum choice of for scheme A can reduce PE by almost two orders of magnitude, when compared with the conventional errors-only decoding with channel inversion (0 = 0). Also, scheme A provides a better performance than scheme B. This can be explained as follows.
Scheme A (per-carrier adaptation) makes the channel appear as an AWGN channel during nontruncation periods, and thus, provides a better performance over scheme B. However, if the available energy resources is limited (i.e., very low Eb/N0), then the truncation period for scheme A may be too long (i.e., too many erasures to correct), so that its decoding-error probability may become higher than scheme B.
Fig. 2 is a plot of the probability of incorrect decoding PE versus Eb/N0 with several erasure-generation methods, where the simulation results for the proposed scheme are included for the validation of the analysis. We find that the combined power control and error-control coding scheme (A and B) provide a much lower PE over the conventional error-control coding without power control (C, D, and E), particularly at high Eb/No. This is because the proposed scheme suppresses the multiuser interference
Fig. 4. Probability of incorrect decoding PE versus Eb/No: (512,170) RS code, N=64, K=30, M=9, a=0.25, A=truncated channel inversion, B= power truncation only, C= convolutional code of rate with an optimum distance profile of the generator polynomial (4 564 754) in octal number and constraint length of seven. and saves the energy resources by truncating the transmission power during unfavorable channels, and allocates the saved energy on symbols on high channel gain. shows that the combined power control and error-control coding provides a significant capacity gain over conventional schemes.shows the characteristic steep slope of the RS code versus the graceful degradation of the convolutional code.
We also find that the convolutional-coded system provides a lower PE than the RS-coded system in the low SNR region, but exhibits an error floor and provides a higher PE in the high SNR region(interference-limited region).
V. CONCLUSIONS
We explained that the probability of incorrect coding can be significantly reduced by combining the power control with the error-control coding. It is also seen that power can be saved and interference can be reduced.
How much power can be saved
In reference 4 it has been explained that for a large communication network every one dB saving in power will result in savings of many millions of dollars annually.
Will Reliance India mobile which uses CDMA technology save crores of rupees by implementing this technique
These two questions will be answered when we meet in ERODE SENGUNTHAR Engg college on 22nd & 23rd of September 2005.
REFERENCES :
1. Jik Dong Kim (South Korea), Sang Wu Kim (USA) and Young Gil Kim (South Korea), COMBINED POWER CONTROL AND ERROR CONTROL CODING IN MULTICARRIER DS-CDMA SYSTEMS, IEEE TRANSACTIONS ON COMMUNICATIONS VOL. 52, No. 8, AUGUST 2004.
2. Dr. KAMILO FEHER Wireless Digital Communications, PHI 2002
3. WILLIAM C.Y.LEE, Mobile communications engineering, 2¬¬¬nd edition MC Graw-Hill.
4. K.SAM SHANMUGAM, digital and analog communication systems, John Wiley.