A new approach to bit error rate reduction and its impact on telecom performance

Transcription

1 Journal of Scientific AHUJA & Industrial & CHAKKA: ResearchA NEW APPROACH TO BIT ERROR RATE REDUCTION ON TELECOM Vol. 72, March 23, A new aroach to bit error rate reduction and its imact on telecom erformance Amit Kumar Ahuja and Ram Chakka 2*,2 Meerut Institute of Engineering and Technology, Meerut-255, India. Received: 3 Setember 22; revised :27 December 22; acceted: January 23 Imroved techniques for (Bit-Error-Rate) reduction at receivers are much needed in digital communications, in order to make it ossible to transmit bit streams effectively at lower SNRs (Signal-to-Noise-Ratio) and for other advantages. This aer rooses and evaluates a new scheme for reduction alicable to a large class of correlated digital signals. Substantial imrovements over classical method are realized and demonstrated. Its imact on telecommunications erformance measures is analyzed. Keywords: QoS, Performance analysis,, DSP, Matched filter, Baseband communication. Introduction Today, in telecommunications systems, meeting erformance objectives is crucial for the success of the vast advances that are taking lace in technologies, services, business models, their utility and deendability. Telecom erformance measures include cost effectiveness for the end user, rofitability for the rovider, link reliability, service reliability, QoS, exandability of services and caacity, environmental friendliness, etc. and above all safety - that is, not ossessing any ability to cause disease or death to living beings. Tyical QoS measures alicable at various layers can be,, SNR levels of oeration, Bandwidth (B.W.) utilization efficiency, etc. 2 at the hysical layer; acket loss robability, acket turn-around time, network resources utilization at higher layers. De-noising of different tyes of signals in diverse technologies is an imortant research toic today 3-6. Lowering by some means or the other can hel achieving more reliable communication. Certain systems can do this at the cost of reduced B.W. utilization efficiency or increased SNR levels of oeration (transmitting at higher signal ower can lead to higher Electromagnetic Field (EMF) exosure). On the other hand, mere reducing the SNR levels or increasing the B.W. utilization efficiency can give rise to higher and hence less reliable communication. Thus, imortant *Author for corresondence ramchakka@yahoo.com trade-offs exists among transmission SNR levels, B.W. utilization efficiency and levels. These trade-offs are studied and used by communications engineers carefully to achieve need-based otimal oerating oints. Safety and measures of safety deserve to be treated most imortant among all the QoS arameters. Technologies are shifting from restricted, uncomfortable wired domain to un-restricted and comfortable wireless domain. In this shift, living beings are exosed to a new kind of risk, that of EMF exosure. Many studies have been conducted to see if there is any relationshi between EMF exosures and induced human diseases with some conclusions, and much more such studies are the need of the hour. For examle, a consistent attern of an increased risk was reorted 7 for acoustic neuroma and glioma after years of mobile hone usage, recommending a revision of microwave exosure standards. Milham & Ossiander 8 reorted the effect of EMF exosure on childhood leukemia. Several such studies 9, demonstrated the relationshi between EMF exosure and various diseases. Recently, a grou of 3 scientists from 4 countries, meeting in Lyon, France, under the ausices of the International Agency for Research on Cancer (IARC) and World Health Organization (WHO), formally classified radio-frequency electromagnetic fields, ertaining to ubiquitous mobile handsets, as Grou B carcinogenic agents due to their otential to induce glioma, a articularly nasty tye of brain cancer. A wider database regarding the studies

2 5 J SCI IND RES VOL 72 MARCH 23 on the effect of EMF is available with WHO 2. The threat due to EMF s exosure does call for aroriate rovisioning in system design towards minimizing health risk without negatively effecting erformance and QoS. One such rovisioning can be the develoment of new signal recovery schemes that would result in lower at the receiver outut, when comared with the existing signal recovery schemes. Such imroved signal recovery schemes can also result in lower SNR levels of oeration as er vs. SNR trade-off, without affecting QoS. Lower can also result in lower B.W. requirement, hence cost savings too. The objective of this aer is to develo and imlement an efficient receiver, suitable for a wide class of correlated digital signals, which would lead to signal recovery with lower when comared with the conventional Matched-filter based receiver (MF receiver). Conventional MF receiver uses Single- Threshold Scheme (STS) for the otimum detection of uncorrelated transmitted digital signals corruted by Additive White Gaussian Noise (AWGN). In this aer, a new Two-Thresholds Scheme (TTS) is roosed and imlemented for use in MF receiver for correlated digital signals (defined later in this aer). These two receivers are termed in this aer as, STS-MF receiver (STS-based MF receiver or simly MF receiver) and TTS-MF receiver (TTS-based MF receiver) resectively. Transmitted signals chosen for this study are termed as -q signals (defined later in this aer) which fall into the class of digital correlated signals. These signals are transmitted through AWGN channel and recovered at the receiver end using both the receivers, searately., RF (Bit-Error-Rate-Reduction-Factor) and SPRRF (Signal-Power-Requirement-Reduction-Factor), defined later, are chosen as erformance indicators in this study. Extensive simulation results have indicated definitive imrovements of the TTS-MF receiver over the STS-MF receiver, for -q signals, when evaluated with resect to the above mentioned erformance arameters and in the SNR range of - db to +8 db. Though the develoment of the new scheme and the erformance study done in this aer are for baseband (wired) communication systems, the concets and the methodology can be aroriately extended to assband (wireless) communication systems with similar advantageous results as illustrated later in this aer. Such an extension to assband would only need certain modifications due to the differences in modulation schemes and a few other medium characteristics. In our use of terms (glossary), for examle, is used to refer Bit-Error-Rate as a technical term, while, (in italics) is used to refer Bit-Error-Rate as an identifier having some value. MATLAB (R28a) is used for the simulation work, carried out in this aer. Classical MF receiver MF receivers are used in a number of alications 3-6. General block diagram of digital baseband transmitter and conventionally used baseband receiver using Matched filter (MF receiver) exist in the literature 5,6. When the transmitted digital signals are uncorrelated (referred here as the r -r signals) and with their indeendent bit robabilities, r,r (r is the robability of bit occurrence, r that of bit ) known at the receiver end, MF receiver does otimal detection of the transmitted bits effected by AWGN 5-7. Not in all cases, the ractical transmitted digital signals are uncorrelated 8. There are numerous alications 9-2 in which either the source generates correlated bit stream, or uncorrelated bit stream generated by the source becomes correlated after some necessary re-rocessing (such as source coding and channel coding 5,6,22,23,24 ) before transmission. For examle, the use of channel coders, such as block codes and cyclic codes can induce correlation among adjacent bits 5,6,22,23. Also, the use of certain other channel coders such as convolutional encoders 24 can induce even higher orders of correlation, say K th order correlation, among the outut bits. As far as the sources that generate correlated bit streams are concerned, for examle, digital sensors 25,26 which send status information in either yes or no mode come under this category. Not only this, even correlated channels (examles include channels subject to fading) induce certain degrees of correlation among transmitted bits 2. Thus, correlated signals do exist, and are rather abundant in nature 8. Therefore, effective erformance analysis of communication systems having these correlated signals becomes imortant. Understanding Classical MF (STS-MF) Receiver The single otimal threshold (λ ot-uc ) used in the DD (Decision Device) section of the classical MF receiver, for r -r signals, is given by following relationshi 5 : N r λ ot uc = ln...() 4ATb r where N is the ower sectral density of white noise, A is the amlitude level selected for NRZ (Non-Return-to-Zero)

3 AHUJA & CHAKKA: A NEW APPROACH TO BIT ERROR RATE REDUCTION ON TELECOM r =.2, SNR = - db r =.4, SNR = - db r =.5, SNR = - db r =.6, SNR = - db r =.8, SNR = - db (a) Threshold (b) Threshold Fig. Otimality verification of λ ot-uc for r -r signals. vs. Threshold curve for various r,r. SNR levels - db (left), + db (right). Vertical lines on X-axis are exactly at λ ot-uc r =.2, SNR = + db r =.4, SNR = + db r =.5, SNR = + db r =.6, SNR = + db r =.8, SNR = + db SIM for r = ANL for r =. SIM for r = ANL for r =.3 SIM for r =.5 ANL for r =.5 SIM for r =.8 ANL for r = SI M at SNR = - db LTL99% at SNR = - db UTL99% at SNR = - db SI M at SNR = db LTL99% at SNR = db UTL99% at SNR = db (a) SNR (db) r (b) Fig. 2 Simulation validation and confidence levels: (left): Comaring SIM and ANL, (right): and its 99% uer and lower bounds for different SNR levels (right). line codes, T b is bit duration, and r,r are indeendent bit robabilities corresonding to bit and resectively. In Fig., vs. Threshold are lotted by evaluating at SNR levels of - db and + db, for a threshold range which is selected around λ ot-uc. The vertical lines in Fig. stand on the X-axis exactly at λ ot-uc, calculated according to Eq. (). The results are obtained by simulation along with Batch-Means Method (BMM), exlained in adequate detail later. It can be noticed that the minimum aears to occur nearly at λ ot-uc. This shows the otimality of MF at λ ot-uc. For the case of STS-MF receiver, analytical exression of robability of error ( e, which is equivalent to ) exists in the literature 5 and is given by, e r = erfc 2 A + λ N T b r + erfc 2 A λ N T b...(2) where λ is the threshold chosen for bit decision making in DD. So, when the threshold selected is otimal (λ=λ ot-uc ), robability of error (equivalently ) can be calculated from Eq. (2). To validate our simulation, we have comared the simulated ( SIM ) and obtained through the above analytical exression ( ANL ), for different arameter values of SNR and r,r. SIM vs. SNR and ANL vs. SNR lots for different values of r,r are shown in Fig. 2 (left). From Fig. 2 (left), it is clear that SIM and ANL coincide

4 52 J SCI IND RES VOL 72 MARCH 23 well, which validates our simulation results. The accuracy levels of simulation results are checked using Batch- Means Method (BMM) 27. bits are used in each simulation run, and the result is averaged over 2 such simulation runs. Corresonding 95% and 99% confidence intervals are comuted and found to be sufficiently accurate. vs. r curve corresonding to 99% confidence interval is shown in Fig. 2 (right). In the Fig. 2 (right), SIM is the simulated using bits averaged over 2 such simulations, LTL99% and UTL99% reresent 99% Lower Tolerance-Limit (LTL) and 99% Uer Tolerance-Limit (UTL) resectively. Out of the six lots in Fig. 2 (right), the lower three corresond to LTL99%, SIM and UTL99% at SNR = db, and the uer three lots corresond to those at SNR = - db, aroriately. A secial class of correlated digital signals, termed as the -q signals, is defined in the next section. A new Two-Thresholds Scheme based MF receiver (termed as, TTS-MF receiver) is roosed and develoed for this class of signals. Using extensive simulation results, it is shown later that for the case of -q signals, TTS-MF receiver dominates in erformance over the STS-MF receiver considerably. In other words, for the case of -q signals, the STS-MF receiver becomes rather sub-otimal. A Class of Correlated Digital Signals The -q signals are essentially a secial class of digital correlated signals. In these signals, the astdeendence is of order (first order ast-deendence). That is, the occurrence of a bit deends robabilistically on the realized revious bit. There are lenty of alications 8-2 in which -q signals occur, as exlained in a revious section. So, analysis of communication systems using these signals becomes imortant. Mathematically the evolution of -q signals haens as: = Pr(/) = Pr{ (New bit to be transmitted is going to be ) /(Previously transmitted bit is )}; q = Pr(/) = Pr{ (New bit to be transmitted is going to be ) /(Previously transmitted bit is )}; which also mean, -= Pr(/) = Pr{(New bit to be transmitted is going to be )/(Previously transmitted bit is )}; -q= Pr(/) = Pr{(New bit to be transmitted is going to be )/(Previously transmitted bit is )}; (3) Let r and r be the unconditional robabilities of a given bit to be or resectively, in a -q signal. Then they can be obtained from,q as: q r = 2 q and, so that, r r = q r = 2 q...(4)...(5) Interesting henomenon occurs when + q =.. It is shown below that, a -q signal becomes an uncorrelated r -r signal when + q =., and also the converse. If + q =., it can be seen from Eqs. (3) that Pr{(New bit to be transmitted is going to be )/ (Previously transmitted bit is )} = =. q = Pr{(New bit to be transmitted is going to be )/ (Previously transmitted bit is )}. Also, Pr{(New to be transmitted bit is going to be )/(Previously transmitted bit is )} = - = q = Pr{ (New bit to be transmitted is going to be )/(Previously transmitted bit is )}. These imly no correlation with reviously transmitted bits. For the converse, when an uncorrelated r -r signal is characterized as a -q signal, it can be seen from Eqs. (3), that = r and q = r, hence + q = r + r =.. Using Eq. () and Eq. (5), λ ot-uc can be exressed in terms of arameters,q as N q λ ot uc = ln...(6) 4ATb Derivation of the Two-Thresholds Scheme (TTS) In this section, the develoment of the Two- Thresholds Scheme (TTS) is exlained. Performances of both TTS-MF and STS-MF receivers are evaluated and comared in the next section, using simulation. This is done for the case when transmitted digital signals are correlated and of -q tye. In Eq. (), for given T b, A and N, the λ ot-uc is a logarithmic function of indeendent bit robabilities ratio (r / r ). Here, r can be seen as the robability that the new occurrence (next bit) is going to be, and r as the robability that the new occurrence is going to be. In case of the -q signals, the occurrence

5 AHUJA & CHAKKA: A NEW APPROACH TO BIT ERROR RATE REDUCTION ON TELECOM 53 of new bit deends on the revious bit, hence it is assumed, in the develoment of the TTS, that the robability of the newly occuring bit to be or does deend on the recovered revious bit. Hence, the ratio, /Pr( the newly occuring bits is )/ Pr( the newly occuring bits is ), can be seen to be deendent on the nature of the reviously recovered bit (unlike in the case of r -r signal). This imlies that the threshold value also can be considered to be deendent on the reviously recovered bit. Hence, two thresholds are ossible in case of -q signals, one is valid when the reviously recovered bit is and the other is alicable when the reviously recovered bit is. Analytically, these thresholds are derived, aroximately, as follows: Case-: When the reviously recovered bit is, then the robability that the next bit would be is assumed here to be instead of r, in the exression for threshold λ otuc in Eq. (). And similarly, the robability that the next bit would be is assumed to be - instead of r in the same exression. Using this, the new threshold corresonding to the case when reviously recovered bit is, can be obtained by simly relacing r with, and r with - in the r.h.s. exression of Eq. (). The corresonding threshold, termed as λ ot-c (in subscrit, c indicates correlated signals, and indicates the case of reviously recovered bit is ), is given by following exression: N λ ot c = ln...(7) 4ATb Case-: When the reviously recovered bit at the outut of MF receiver is, then r and r can be relaced by - q and q resectively by using similar lines of argument as above, and the corresonding threshold (λ ot-c ) becomes: N q λ ot c = ln...(8) 4ATb q Hence, when the signals are of -q tye with and q known at the receiver end, using TTS-MF receiver involves using two-thesholds, λ ot-c and λ ot-c, according to Eqs. (7) and (8), deending uon whether the reviously recovered bit is or, resectively. Classical way is rather to use the STS-MF receiver with single threshold λ ot-uc given as in Eq. (6). In TTS, the new bit detection will be decided by comaring the samled outut of matched filter with one of two thresholds, that is, λ ot-c when reviously recovered bit is, and λ ot-c when reviously recovered bit is. If the samled value of the matched filter outut is greater than or equal to the aroriate threshold, DD roduces bit, else bit, as the recovered new bit. Using extensive simulation, it is shown in the next section that the TTS-MF receiver erforms substantially better than the classical STS-MF receiver for the case of -q signals, transmitted over a large SNR range of our exerimentation. Performance Issues for Comarison When a new method is roosed, extensive erformance study is needed for comaring the method with the existing methods. It is roosed to carry out the necessary erformance analysis study and comarison with resect to the imortant telecommunication erformance measures that are outlined below. Simulations are carried out for both the methods searately. RF: Bit-Error-Rate-Reduction-Factor (RF) is defined as the ratio of TTS and STS (i.e., TTS / STS ), where TTS and STS are Bit-Error-Rates at the outut of the TTS-MF receiver and the STS-MF receiver resectively, with signal ower and B.W. being the same in both the cases. Sueriority of the roosed scheme over the classical one with resect to reduction would be indicated if RF <.. Obviously, smaller RF that is less than. would imly larger imrovement due to the new receiver. SPRRF: Signal-Power-Requirement-Reduction-Factor (SPRRF) is defined as the ratio of SP TTS and SP STS (i.e., SP TTS / SP STS ), where SP TTS and SP STS are transmitted signal owers (in actuals, not in logarthemic scale) required in cases of TTS-MF receiver and STS- MF receiver resectively in such way that the channel B.W. required and quality of data recovered (in terms of ) are same in both the cases, i.e. with TTS = STS. Signal ower requirement and are interrelated. vs. SNR is usually a non-increasing (or decreasing) function. For examle, refer to the lot vs. SNR in Fig. 3, obtained by simulation, for both STS- MF and TTS-MF receivers, and for a case when RF <.. This lot is further exlained later. As shown in Fig. 3, for a articular value of, = c, the corresonding values of SNR in the case of TTS-MF and STS-MF receivers are SNR c STS and SNRc TTS resectively. So, for the case in context, the ratio of

6 54 J SCI IND RES VOL 72 MARCH 23 Fig. 3 vs. SNR curve for STS-MF and TTS-MF receivers, for = q =.9. SNR c and TTS SNRc becomes SPRRF. As demonstrated, STS SNR c < TTS SNRc, hence the resulting SPRRF becomes STS less than.. Obviously, if SPRRF <. can be achieved, for same channel B.W. and (quality of data recovered) using the two receivers indeendently, that would mean better erformance of the new receiver in terms of reduced signal ower requirement (without any change in ). From the EMF exosure oint of view, SPRRF can be considered as a very imortant measure since any reduction in signal ower requirement (SPRRF <.), with unchanged quality of data recovered (similar ) and channel B.W., would result in lower EMF exosure, and hence better erformance and indeed better safety as well 7-2. BWRRF: Bandwidth-Requirement-Reduction-Factor (BWRRF) is defined as the ratio of W TTS and W STS ( W TTS / W STS ), where W TTS and W STS are the channel B.W. (in Hz) requirements for the cases of TTS-MF receiver and STS-MF receiver resectively, in such a way that quality of recovered data at both the receivers outut is same ( STS = TTS ), also with the same transmitted ower in both the cases. In other words, gain obtained by the roosed receiver in terms of RF can be translated or converted into certain corresonding gain in B.W. Reduction (BWRRF). Obtaining accurate or aroximate exressions for BWRRF by quantitative analysis is highly involved. Hence we consider this as an imortant toic for further research. Results and Discussion In this section, extensive numerical results obtained by simulation corresonding to both the receivers are resented. The results clearly show that the TTS-MF receiver dominates in erformance over classical STS- MF receiver. Performance analysis study of both the receivers are carried out under the following arametric assumtions: Transmitted digital signals are correlated, and of - q tye in nature, with and q values known at the receivers. Bits are transmitted after olar NRZ line coding. This is for baseband communications. Channel is of AWGN tye. Performance is evaluated in the SNR range of - db to +8 db. Batch-Means Method (BMM) is used to check the accuracy levels of the results. In each batch, bits are used and the mean result of 2 such batches is taken as the reorted result in each simulation run. From Eq. (4), it is clear that when correlation arameters and q are given, r and r can be found uniquely. However, it is to be noted that the converse is not true, that is, there exist several airs of,q value sets that can give rise to the same r value. For examle, the four {,q} value sets {.5,.85}, {.5,.8342}, {.5,.988} and {.95,.992} give rise to the same r (r =.5, r =.85) which can be verified by using Eq. (4), though the correlations in these four signals are different. How would correlations affect the erformance of STS-MF receiver and TTS-MF receiver is an imortant question. It is then also interesting to comare the erformance within the set of -q signals that have the same r and r, in order to see the effect of correlation arameters and q, in a systematic manner. These may be accomlished as follows. Let us consider a ossible set of -q signals, with all ossible,q values that give rise to the same r and r bit robabilities. Each -q signal in this set may have a different air of,q values from another, however, with the same r and r. For given r and r, obtaining the range of ossible,q values (or sets of (,q) ) that have the same r can be done as follows. From Eqs. (4) and (5), for certain convenience, let us exress and q as follows: = ( 2r ) + r q ; r q = ( 2r ) r + r...(9) In the left one of Eqs. (9), for a given value of r, notice that is an increasing function of q. Also, q can

7 AHUJA & CHAKKA: A NEW APPROACH TO BIT ERROR RATE REDUCTION ON TELECOM STS at SNR = - db TTS at SNR = - db STS at SNR = db TTS at SNR = db STS at SNR = + db TTS at SNR = + db r =.4, r = (a) STS at SNR = - db TTS at SNR = - db STS at SNR = db TTS at SNR = db STS at SNR = + db TTS at SNR = + db r =.4, r = q STS at SNR = - db TTS at SNR = - db STS at SNR = db TTS at SNR = db STS at SNR = + db TTS at SNR = + db r =.4, r = (b) q (c) Fig. 4 Simulated for STS-MF and TTS-MF receivers for different SNR levels: (a) vs., for r =.4 and r =.6, (b) vs. q, for r =.6 and r =.4, (c) vs. q, for r =.4 and r =.6 vary from to., corresondingly would vary from (-2r )/(-r ) to.. This way, the whole range of (,q) air values, having same r,r, can be obtained. Notice that the left one of Eqs. (9) can be used when r.5, then only (-2r )/(-r ) can be non-negative. In the similar way, the right one of Eqs. (9) can be used to find the range of (,q) values when r >.5. Here, that is when r.5, the range of can be from to. and the corresonding range of q would be from (-2r )/(-r ) to.. Thus, aroriately Eqs. (9) can be used to find the range of (,q) air values that give rise to the same given r and r. In the following figures, simulation results are shown. Fig. 4(a) shows vs. (for both STS and TTS ) lot for r =.4, r =.6, and Fig. 4(b) shows vs. q lot for r =.6, r =.4. Both lots are corresonding to SNR values, - db, db and + db. STS vs. (or q) is flat as exected, that is because STS does not deend on and q, for given r and r. vs. q lot for r =.4, r =.6 is shown in Fig. 4(c). In this lot, notice 2 r that the value of q can be only as q = r 3 in accordance with what is exlained above. RF vs. and RF vs. q lots corresonding to various sets of r,r air values ({.2,.8},{.8,.2},{.5,.5}) and SNR (- db to +6 db) are shown in Fig. 5 (a), (b) and (c). From the results shown in Figs. 4 and 5, following conclusions can be drawn: vs. (for r,r ) and vs. q ( with r,r values reversed) curves are almost similar (refer to Fig. 4 (a) and (b)). Because of this, the corresonding RF curves are also similar, as shown in Fig. 5 (a), (b), and (c).

8 56 J SCI IND RES VOL 72 MARCH 23 RF SNR = - db SNR = db SNR = + db SNR = +2 db SNR = +4 db SNR = +6 db r =.2, r = (a) RF RF (c) SNR = - db SNR = db SNR = + db SNR = +2 db SNR = +4 db SNR = +6 db.3 SNR = - db SNR = db SNR = + db SNR = +2 db SNR = +4 db SNR = +6 db r =.2, r = q r =.5, r =.5 Fig. 5 Simulated RF for different SNR levels: (a) RF vs., r =.2 and r =.8, (b) RF vs. q, r =.2 and r =.8, (c) RF vs., r =.5 and r =.5. (b) In almost all considered arameter range of or q (.5 to.95) and SNR (- db to +6 db), notice that TTS < STS (refer to Fig. 4 (a), (b) and (c)). In Fig. 5, this imrovement is indicated by RF <.. At larger values of or q, the imrovement is better. Notice that, in Eqs. (9), = r q = r. Also notice that STS = TTS and RF =. when = r, in all the figures. This is in accordance with what is exected since at = r, + q = r + r =. imlying the -q signal becoming r -r signal, making the erformances of TTS-MF receiver and STS-MF receivers equal. In Fig. 5 (a), (b), and (c) this is shown by RF =.. Even at high noisy condition (SNR = - db), TTS- MF receiver works better than the STS-MF receiver. Maximum imrovement of uto 72% in is observed, among the resented results, when r =.2, r =.8 (and, r =.8, r =.2) and SNR = +6 db (refer to Fig. 5 (a) and (b)). For any given r,r, imrovement observed is higher at higher values of SNR. Considering the average RF over the entire range of (or that of q), one can see that the average RF is erhas largest at r =.5 comared with other values of r (refer to Fig. 5 (a), (b) and (c)). This result is imortant and of secial significance, as in many communication systems, the value of r is often sought at.5, in order to hel the roer clock recovery at the receiver 28.

9 AHUJA & CHAKKA: A NEW APPROACH TO BIT ERROR RATE REDUCTION ON TELECOM 57 SPRRF SNR STS (db) (a) =., q =.3 =.3, q =.3 =.5, q =.3 =.7, q =.3 =.9, q =.3 SPRRF SNR STS (db) (b) =., q =.5 =.3, q =.5 =.5, q =.5 =.7, q =.5 =.9, q =.5 SPRRF SPRRF (c) Fig. 6 Simulated SPRRF vs. SNR STS for values of : (a) with q =.3, (b) with q =.5, (c) with q =.9, (d) for various values of = q. (d) As discussed reviously in detail, the QoS arameters,, SNR (and hence signal ower, SP) and channel B.W. are exchangeable. In other words, imrovement obtained in terms of -reduction can be translated or transferred, in rincile, into imrovement in terms of Signal-Power-Requirement-Reduction-Factor (SPRRF), and Bandwidth-Requirement-Reduction- Factor (BWRRF). Fig. 3, already discussed to some extent in revious section, shows how imrovement in RF can be translated into the corresonding imrovement in SPRRF. Plots corresonding to SPRRF vs. SNR are resented in Fig. 6 (a), (b), (c) and (d), for various sets of and q values. In this figure, arameter is varied from. to.9 with ste size of.2 while keeing q constant. Results corresonding to different values of and q, are thus obtained. From the results shown in Figs. 3, and 6, following conclusions can be drawn: It is assumed that when the signal level increases, the accuracy of detection also increases. This is clearly demonstrated in Fig. 3 for an examle case. It is this observation that makes it ossible to think of finding ways of translating the obtainable advantages in to an aroriate advantage in SPRRF instead. A future research idea is to extend this research in order to identify the nature the lots in Fig. 3 by curve-fitting methods. It is observed that SPRRF is minimum (corresonding to maximum imrovement) when,q values are either very small or very large (look at the cases when, = q =. and when = q =.9, as shown in Fig. 6(d)).

10 58 J SCI IND RES VOL 72 MARCH 23 Maximum imrovement corresonding to aroximately 28% reduction in signal ower requirement is observed. This is an imortant result since this causes lowering in transmitted ower requirements and hence reduced EMF exosure, accordingly, comared to the conventional scheme while getting the same quality of the recovered bits at the receiver outut. This would reduce the ossible risk due to EMF exosure. Another benefit is reduced ower consumtion, or ower saving. It is observed that SPRRF deends on SNR STS. For examle in Fig. 6 (a), (b), (c) and (d), at higher values of,q, SPRRF is low when SNR STS is either low or high. Value of SPRRF is. corresonding to the case when +q =.. This is exected since, when +q =., -q signals become r -r signals, making the erformance of two receivers equal. Conclusion and Future Scoe The classical MF receiver is otimal for r -r uncorrelated signals corruted by AWGN, if r is known at the receiver. In ractise, many signals generated or transmitted are not entirely uncorrelated, this is due a number of reasons that are exlained in the aer. The question that is addressed in this aer is, is it ossible to design better receivers than classical MF receiver for these signals if the correlation arameters are known at the receiver? This question is successfully and ositively answered, as well as demonstrated by extensive simulation study. A large class of correlated digital signals termed here as the -q signals are conceived. With correlation arameters and q assumed to be known at the receiver end, a new detection algorithm termed as the TTS-MF receiver, based on two thresholds, is suggested and derived for these signals. The classical MF receiver is based on single threshold, and it is also refered as STS-MF receiver in this aer. Both the receivers are alied indeendently to the generated -q signals corruted by AWGN. The s of the recovered digital signal for these two receivers are comared judiciously for a number of well-conceived - q signals and exeriments. The results clearly establish the sueriority of the suggested new scheme (TTS) over the classical scheme (STS) when alied to -q signals, with resect to. In any receiver, it can be assumed that would deend on the signal strength (transmitted signal ower) and the B.W. utilized, this relation is rather wellestablished in the literature in cases of STS-MF receiver. The ossibility to translate the reduction in by the new receiver into aroriately equivalent advantages in terms of reduced signal ower requirement is also investigated. We have then established the sueriority of TTS over STS in obtaining advantage in terms of signal ower requirement reduction, for -q signals. Sensitivity study with resect to,q arameters is also attemted. Numerical results obtained by simulation and analysis are illustrated by lots, necessary conclusions of the exeriments are summarized in the sections. Further research oenings include extending the method to larger classes of correlations that are ossible in digital signals. Though our imlementations and exerimentation is carried out for baseband with NRZ signals, the concets and analysis can be modified and extended to suit other alications such as assband, wireless domains. References Joint Software Systems Safety Engineering Workgrou, Joint Software Systems Safety Engineering Handbook, Version. (Deartment of Defense, USA) 2. 2 Information Resource Management Association, Networking and Telecommunications: Concet, Methodology, Tools and Alications, st edn (IGI Global, USA) 2. 3 Ramya C & Rani S S, Video denoising without motion estimation using K-means algorithm, J Sci Ind Res, 7 (2) Babu C G, Vanathi P T, Ramachandran R, Rajaa M S & Vengatesh R, Performance analysis of voice activity detection algorithm for robust seech recognition system under different noisy environment, J Sci Ind Res, 69 (2) Patil A A & Singhai J, Image denoising using curvelet transform: an aroach for edge reservation, J Sci Ind Res, 69 (2) Deea D & Shanmugam A, Enhancement of noisy seech signal based on varience and modified gain function with PDE rerocessing technique for digital hearing aid, J Sci Ind Res, 7 (2) Hardell L, Carlberg M, Söderqvist F, Mild K H & Morgan L L, Long-term use of cellular hones and brain tumours: increased risk associated with use for years, Occu Environ Med, 64 (27) Milham S & Ossiander E M, Historical evidence that residential electrification caused the emergence of the childhood leukemia eak, Med Hyotheses, 56 (2) Lennart H & Cindy S, Biological effects from electromagnetic field exosure and ublic exosure standards, Biomed & Pharmacotheray, 62 (28) 4-9. BioInitiative reort: a rationale for a biologically-based ublic exosure standard for electromagnetic fields (ELF and RF) 27, htt:// IARC Monograhs on the Evaluation of Carcinogenic Risks to Humans. Non-Ionizing Radiation, PART II: Radiofrequency Electromagnetic Fields (Includes Mobile Telehones, Microwaves and Radars), Lyon, France, 2 (2).

11 AHUJA & CHAKKA: A NEW APPROACH TO BIT ERROR RATE REDUCTION ON TELECOM 59 2 WHO s EMF database, htt://as.who.int/eh-emf/research/ database [accessed ]. 3 Gholamiour A H, Gorcin A, Celebi H, Toreyin B U, Saghir M A R, Kurdahi F & Eltawil A, Reconfigurable filter imlementation of a matched-filter based sectrum sensor for cognitive radio systems, in IEEE Int Sym on Circuit and Syst (ISCAS) (Rio de Janeiro, Brazil) 5-8 May, 2, Jiang C, Li H & Rangaswamy M, On the conjugate gradient matched filter, IEEE Trans on Signal Pr, 6 (22) Hykin S, Communication Systems, 4 th edn (John Wiley and Sons Inc, USA) 28, , Lathi B P & Ding Z, Modern Digital and Analog Communication Systems, 4 th edn (Oxford University Press, UK) 2, 56-52, , , Turin G, On the estimation in the resence of noise of the imulse resonse of a random, linear filter, IRE Trans on Infom Theory, 3 (957) Cariolaro G & Puolin S, Moment of correlated digital signal for error robability evaluation, IEEE Trans on Infom Theory, 2 (975) Shubair R M, Jimaa S A, Hamila R & AI-Tunaije M A, On the detection and estimation of correlated signal using circular antenna arrays, in Int Conf on Commun and Infom Tech (ICCIT) (American International University, Bangladesh), 29-3 March, 2, Pradhan S S, Choi S & Ramchandran K, A grah-based framework for transmission of correlated sources over multile-access channels, IEEE Trans on Infom Theory, 53 (27) Grossmann M & Schneider C, Grouwise frequency domain multiuser MMSE turbo equalization for single carrier block transmission over satially correlated channels, IEEE J Selected Toics in Signal Pr, 5 (2) Cover T M & Thomas J A, Elements of Information Theory, 2 nd edn (Wiley Interscience, NJ) 26, 3-34, Lint V & Hendricus J, Introduction to Coding Theory, 3 rd edn (Vol. 86) (Sringer-Verlag, NJ) 999, 22-45, Dholakhia A, Introduction to Convolutional Codes with Alications, Vol. 275 (Kluwer Academic Publisher, USA) Fraden J, Handbook of Modern Sensors: Physics, Design and Alications, 4 th edn (Sringer-Verlag, Heidelberg) Smart Sensors and MEMS, Proc of NATO Advanced Study Institute on Smart Sensors and MEMS, Yurish S Y & Gomes M T S R (editors), (NATO Science Series) Remenyi D, Onofrei G & English J, An Introduction to Statistics using Microsoft Excel, st edn (Academic Publishing International, UK) 2, Kobayashi H, A Survey of Coding Schemes for Transmission or Recording of Digital Data, IEEE Trans Commun Tech, 9 (97) 87-.