Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.

Performance Analysis of Multiuser Detection Schemes for DS CDMA Systems

2,331 views

Published on

Published in: Technology

Performance Analysis of Multiuser Detection Schemes for DS CDMA Systems

  1. 1. ECE 4601: Communication SystemsPerformance Analysis of Multiuser Detection Schemes for DS-CDMA Systems Anya Skomorokhova Muath Altuwayjiri Date Submitted: November 28, 2012 1
  2. 2. Table of ContentsAbstract ......................................................................................................................................................... 31 Introduction ............................................................................................................................................... 4 Organization of Paper ............................................................................................................................... 72 Main Body .................................................................................................................................................. 8 2.1 Theory ................................................................................................................................................. 8 2.1.1 Sending Signal .............................................................................................................................. 8 2.1.2 Receiving Signal............................................................................................................................ 9 2.1.3. Matched Filter Detector.............................................................................................................. 9 2.1.4 Successive Interference Cancellation (SIC) Detector ................................................................. 10 2.2 Conventional Matched Filter using Orthogonal Input Signals .......................................................... 11 2.2.1 Procedure ................................................................................................................................... 11 2.2.2 Output at the Matched Filter ..................................................................................................... 11 2.2.3 Outcomes ................................................................................................................................... 12 2.3 Conventional Matched Filter using Non-Orthogonal Input Signals .................................................. 13 2.3.1 Procedure ................................................................................................................................... 13 2.3.2 Output at the Matched Filter ..................................................................................................... 14 2.3.3 Percent Error at Output ............................................................................................................. 15 2.3.4 Outcomes ................................................................................................................................... 16 2.4 Successive Interference Cancellation Multi-User Detector Using Non-Orthogonal Input Signals ... 17 2.4.1 Procedure ................................................................................................................................... 17 2.4.2 Output at the Matched Filter ..................................................................................................... 18 2.4.3 Percent Error at Output ............................................................................................................. 19 2.4.4 Outcomes ................................................................................................................................... 20 2.5 Comparison ....................................................................................................................................... 213 Conclusion ................................................................................................................................................ 22References .................................................................................................................................................. 23Appendix A: Simulation 1 Code – Orthogonal Waveforms Using Conventional Matched Filter ................ 24Appendix B: Simulation 2 Code – Non-Orthogonal Waveforms Using Conventional Matched Filter ........ 24Appendix C: Simulation 2 Code – BEP vs. Number of Users Graph ............................................................ 24Appendix D: Simulation 3 Code – Non-Orthogonal Waveforms Using SIC Multi-user Detector ................ 24Appendix E: Simulation 3 Code – BEP vs. Number of Users Graph ............................................................ 24 2
  3. 3. AbstractCode Division Multiple Access (CDMA) is a popular method used in multiple access channels. CDMA usesspecial coding to multiplex multiple users across one channel where each user is assigned a signaturewaveform. There are two types of codes: synchronous – orthogonal codes and asynchronous –pseudorandom codes. When using synchronous codes to modulate the transmitting signal, each signaluses a code that is orthogonal to the other signal’s codes, resulting in zero interference. Asynchronouscodes use pseudo-random binary sequences that can be reproduced by the receiver. A large number ofthese binary sequences transmitting at once can cause multiple access interference (MAI) that can betreated as Gaussian noise. This system suffers from two problems: capacity and the near/far effect.Capacity of the channel is limited by signal interference; hence it is vital to reduce this term. Thenear/far effect is the problem where user signals located far away from the base station are received atlower power than those of users near the base station.To combat these two problems, multiuser detection is used. Multiuser detection is largely done to limitthe effect of multiple access interference. The output of the filter is a summation of three terms: thedesired information, multiple access interference, and noise. The MAI term can be reduced using avariety of techniques. With decreased interference (the MAI term of the equation), the capacity of thechannel is increased and the near/far effect is minimized.This paper examines schemes of CDMA Multiuser Detection through literature and MATLAB simulation.The schemes explored are 1) the conventional matched filter detector for orthogonal waveforms, 2) theconventional matched filter detector for non-orthogonal waveforms, and 3) the successive interferencecancellation multi-user detector. The simulations consist of receiving and subsequently detecting datasent over the CDMA coded channel. Multicarrier Modulation is used to establish and detect the system,and the different multiuser detection schemes are used to extract the desired data. The paper comparesthe results and performance analysis of these techniques. 3
  4. 4. 1 IntroductionCode Division Multiple Access (CDMA) is a popular technique in multiple access communicationchannels. CDMA uses special coding to multiplex multiple users across one channel where each user isassigned a signature waveform. Unlike the Time Division Multiple Access (TDMA) channel accessmethod, where users are called “time orthogonal”, CDMA allows users to transmit data simultaneously.Additionally, unlike the Frequency Division Multiple Access (FDMA) channel access method, where usersare called “frequency orthogonal”, CDMA also allows all users to transmit data using the entirefrequency band. [1]A well-known analogy illustrates the differences between the channel access techniques. Suppose thatthere is a room full of people (a channel), where all individuals wish to talk to each other at the sametime (transmit information simultaneously). To avoid mixing conversations and losing comprehension ofthe ongoing conversation (signal interference corrupting data), they have three options. Firstly, theycould take turns having conversations, which is similar to how TDMA is used to assign users time slots totransmit information. Secondly, they could speak using different pitches, which is similar to how FDMAis used to assign users frequencies at which they could transmit. Alternatively, the people in the roomcould carry on conversations in different languages, which is similar to CDMA. In this way, they do nothave to take turns speaking, nor do they have to speak using different frequencies to distinguishconversations. The listener (receiver) tunes into the conversation (waveform) that they have the tools tocomprehend and all other data floating around the room is regarded as noise.The particular channel access technique used in this paper is Direct-Sequence Code Division MultipleAccess, or DS-CDMA. DS-CDMA uses a particular procedure for producing spread-spectrumtransmissions. Direct Sequence Spread Spectrum, or DSSS, works by modulating a sine wave with avector of pseudo noise codes to transmit the signal. The signal that is transmitted across the channel iswider than the actual information signal and thus it is better equipped to handle interference. 4
  5. 5. Pseudorandom waveforms have two distinctive properties. They can be generated using precisemathematical rules at both at the transmitter and receiver. They also nearly satisfy the requirements fora random sequence and have low correlation coefficients between user signals. [1]There are two types of codes: synchronous – orthogonal codes and asynchronous – pseudorandomcodes. Orthogonal codes are based on orthogonal vectors– two signals that result in zero dot product.When using synchronous codes to modulate the transmitting signal, each signal uses a code that isorthogonal to the other signal’s codes, resulting in a cross-correlation of zero and no interferencebetween the signals. While the lack of interference between signals is highly desirable, there is a limit tothe use of orthogonal codes because the number of waveforms available is inherently limited to O(WT),where T is time duration and W is bandwidth. This limitation is not beneficial to cellular networks, wherethe number of users may be unknown and it may be difficult to generate perfectly orthogonalwaveforms. [2]Asynchronous codes use pseudo-random binary sequences that can be reproduced by the receiver.These are most often used when the sender and the receiver cannot be synchronized, as is the case withmobile phones and base stations. PN (pseudo-noise) codes are used to encode and decode a data signalin the same way as orthogonal codes, but for asynchronous systems instead of synchronous systems.Unlike synchronous systems, asynchronous systems are not limited by the number of waveformsgenerated. However, asynchronous systems are susceptible to signal corruption and are thus limited incapacity by the channel noise. [2]A large number of these binary PN sequences transmitting at once can cause multiple accessinterference (MAI) that can be treated as Gaussian white noise. MAI is a result of correlation among thewaveforms traveling on the channel. The amount that MAI interferes with the transmission of the signaldepends on the number of users simultaneously transmitting data. When the system is over-saturatedwith signals, the effects of MAI need to be minimized. While it is possible to treat MAI as a noise term, 5
  6. 6. the conventional multi-user detector will suffer from significant output waveform errors, as will beshown in Section 2.3. [3]The asynchronous system using PN sequences suffers from two problems: capacity limitations and thenear/far effect. With non-orthogonal waveforms, the number of channels the system can have isunlimited. However, capacity of the channel is limited by signal interference; hence it is vital to reduceinterference to increase the capacity of the channel. The near/far effect is the problem where usersignals located far away from the base station are received at lower power than those of users near thebase station. [4]To combat these two problems, multiuser detection is used. Multiuser detection is largely done to limitthe effect of signal interference. The output of the filter is a summation of three terms: the desiredinformation, the MAI term, and white Gaussian noise. The MAI term can be reduced by either using anadaptive filtering algorithm or canceling out the interfering signals [5]. With decreased MAI interference,the capacity of the channel is increased and the near/far effect is minimized. In [6], the author statesthat an effective multiuser detection algorithm should be able to: 1. Improve the Bit-to-Energy-Percentage (BEP) 2. Improve the capacity of the channel 3. Inhibit the near/far effect 4. Efficiently use power to have higher data ratesTo demodulate the receiving signal, a matched filter detector is used. The conventional matched filterdetector consists of an array of matched filters, each corresponding to a user’s signal. Once applied, thisfilter demodulates each signal independently. As mentioned above, the signal consists of three parts:the information signal, a MAI term, and a noise term. Because the conventional filter is designed fororthogonal waveforms, it treats the MAI term as a noise term, causing a larger error probability in thesignal. However, this filter can be optimized to treat the MAI term differently and reduce the probability 6
  7. 7. of error and the near/far problem. There are many types of optimizations available. A few that wereexplored in [2] are:1. Linear detector – applies a linear transformation of the correlation matrix to the output2. Decorrelating detector –applies the inverse of the chip signal correlation matrix to the output3. Minimum mean-squared error (MMSE) detector – minimizes the mean squared error at the receiver using a linear mapping of the signal4. Successive interference cancellation (SIC)– cancels out interfering signals in order of diminishing power from the filter outputs5. Parallel interference cancellation (PIC)– cancels out the interfering signals in an iterative parallel processThe optimization considered in this paper is the SIC non-linear multi-user detector.Organization of PaperThe rest of the paper is organized as follows. Section 2 investigates the performance of three multiuserdetection schemes: 1. Orthogonal waveforms using a conventional matched filter 2. Non-orthogonal waveforms using a conventional matched filter 3. Non-orthogonal waveforms using a Successive Interference Cancellation (SIC) multi-user detectorSection 2.1 investigates the underlying theory and mathematics of the techniques. Sections 2.2 to 2.4detail the procedure and results of the three simulations. Section 2.5 compares of the effectiveness andlimitations of the techniques. Lastly, Section 3 concludes the study with final remarks. 7
  8. 8. 2 Main Body2.1 Theory2.1.1 Sending SignalThe signal model used for the user signals is AWGN (additive white Gaussian noise) and uses BPSKsignaling (binary phase shift keying). At the transmitter of the DS-CDMA channel with K total users, thekth user signal can be expressed by () ( ) (1)where Ak is the amplitude at the kth user signal, bk is an element of {-1,1} and Tb is the bit duration. Thespreading code sk can be expressed as ( ) ∑ ( ( ) ) (2) √where Tc is the duration of the chip, and N is the spreading gain found by Tb/Tc, and rect(t) is therectangular step function ( ) ( ) (3) ( )with bounds of ( ) (4) (5)Equations 1 – 5 were used in [2] to model the AWGN signal.Orthogonal SignalsIf the user signals are orthogonal, the signals must satisfy (6) and (7), where J is the spreading factor [8]. (6) (7) 8
  9. 9. A simple way to generate orthogonal waveforms is to use orthogonal variable spreading factor, or OVSFcodes. The PN matrix is an N x N matrix where N is the number of channels. The OVSF codes areillustrated using a recursive tree structure, with all vectors containing only +1 or -1. From this treestructure, one can look up the number N of channels needed and note the corresponding vectors. [9]For example, a spreading factor of 4 yields the matrix (8) (8) [ ]This matrix is then multiplied by the user signals, causing all the xk signals to be orthogonal to oneanother. The limitations of this technique are that the number of channels has to be a multiple of 2n andthere is a limit to the total number of channels one could have.2.1.2 Receiving SignalThe signal received at the receiver of an AWGN synchronous channel can be written as ( ) ∑ () ( ) ( ) ( ) (9)Where n(t) is a noise signal. Subscripts k and i distinguish the users. [2]2.1.3. Matched Filter DetectorOnce the signal arrives at the receiver end, it must be demodulated. The received signal is of the form ( ) (10)The filter detector consists of an array of matched filters, one of which can correctly demodulate thesignal. The MAI term of r(t) is zero if the input signals are orthogonal. When this is not the case, the MAIterm is evaluated as noise in the conventional matched filter. Hence, the output of the matched filter is (11) ∫ ( ) ( ) 9
  10. 10. Further evaluation of this equation yields (12) ∑ ()Where the correlation term is ∫ ( ) ( ) (13)Finally, the demodulated receiving signal can be written as ̂ ( ) (14)Equations 11-15 were used in [2] to design the conventional multi-user detector.The conventional detector is popular due to the uncomplicated nature of its implementation. Nochannel parameters or user attributes are required to be known in order to use this detector. Theconventional detector was designed for orthogonal waveforms and works ideally in orthogonalchannels. However, it has several drawbacks when processing non-orthogonal waveforms. Treating theMAI term of the output as noise can cause an error probability, whether or not any noise is actuallypresent on the channel. Additionally, it is influenced by the near/far effect where one user’s higherpower transmission will be reflected in a higher BEP for the other users’ signals. Thus, adjustments needto be made to this filter to treat the MAI term differently and to control the power of different users. [2]2.1.4 Successive Interference Cancellation (SIC) DetectorDue to the fact that the MAI term is different from the noise term in statistical terms, it needs to betreated as a non-noise term to improve the probability of error. There are many ways to optimize themulti-user detector, using both linear and non-linear methods. One way that is evaluated in this paper isa non-linear detector that uses SIC. This method organizes the signals in order of decreasing power andcancels out the interfering signals in that order. The output then becomes 10
  11. 11. ̂ ( ∑ ̂ ) (15)This form of the multi-user detector is straightforward to implement. However, the detector propagateserrors that occurred during transmission and also necessitates the need for channel estimates at thereceiving branch. [7]2.2 Conventional Matched Filter using Orthogonal Input Signals2.2.1 Procedure 1. General variables. The simulation allows the user to change input variables such as the number of users, the number of bits per user, the spreading gain, the number of samples taken by the detector, and the AWGN power. 2. Simulating the users. Orthogonal signature waveforms are created using the OVSF matrix with the values found in Equation 8. The user data signals are created using a random number generator. 3. Sending the data. The transmitted signal is constructed using Equation 1 by multiplying the orthogonal signature terms with the user signal and dividing by the square root of the spreading gain. This is then multiplied by the amplitude vector to simulate the near/far effect. 4. Receiving the data. The receiver receives a summation of a WGN (White Gaussian Noise) signal and the data signals from step 3. 5. Demodulating the received signals. Each signal is convolved using a conventional matched filter 6. Detecting bits from the result of the convolution. The output signal is assembled using Equation 13.2.2.2 Output at the Matched FilterThe output of the matched filter can be found in Figure 1. The output for each user input signal had anerror percentage of 0%. The input waveforms were carefully picked to be orthogonal to one another. As 11
  12. 12. long as that statement holds true and noise does not overwhelm the signal, the output waveforms should be error free. The code used to generate this graph is found in Appendix A.Figure 1. Orthogonal Input v. Output Signals using Conventional Matched Filter for Four Users. 2.2.3 Outcomes The conventional matched filter performs very well when the input signals consist of orthogonal waveforms. As long as this is the case, there will be no error in the output for low WGN powers. Hence the BEP ratio is very close to zero or is equal to zero. Though the condition of orthogonality guarantees no interference, it limits the capacity of the channel to the same capacity as TDMA and FDMA schemes, with a maximum number of waveforms allowed to be O(WT), where T is the time duration and W is the bandwidth [2]. Because of this limitation, there seems to be no visible advantage to using the CDMA technique over TDMA or FDMA techniques in 12
  13. 13. cellular systems, where capacity considerations of the system are very important to the overallperformance. Thus, the technique is unable to improve the capacity of the channel.The filter inhibits the near/far effect due to the lack of signal interference in the output. There is verylittle to none near/far effect visible at the output.Additionally, the filter efficiently uses power to provide higher data rates due to its effectiveness atfighting noise and signal interference.This system is very effective in fighting the effects of noise and unwanted signals. From Equation 9, it isevident that the MAI term is zero due to the orthogonality of the signals. So long as the white noise termn(t) does not overwhelm the desired signal, this system performs well. When white noise increases, theperformance of the filter drops. However, the performance drop is not as severe as that in non-orthogonal waveform systems because the orthogonal system still does not have to fight the additionalMAI term.When the number of waveforms exceeds the capacity of the channel, the waveforms become non-orthogonal and are very often demodulated with significant percent error. This case is investigated inthe next section using the same conventional matched filter.2.3 Conventional Matched Filter using Non-Orthogonal Input Signals2.3.1 Procedure 1. General variables. The simulation allows the user to change input variables such as the number of users, the number of bits per user, the spreading gain, the number of samples taken by the detector, and the AWGN power. 2. Simulating the users. PN signature waveforms are created using a random number generator with values 0 or 1. The user data signals are created using a random number generator. 13
  14. 14. 3. Sending the data. The transmitted signal is constructed using Equation 1 by multiplying the PN signature terms with the user signal and dividing by the square root of the spreading gain. This is then multiplied by the amplitude vector to simulate the near/far effect. 4. Receiving the data. The receiver receives a summation of a WGN (White Gaussian Noise) signal and the data signals from step 3. 5. Demodulating the received signals. Each signal is convolved using a conventional matched filter 6. Detecting bits from the result of the convolution. The output signal is assembled using Equation 13.2.3.2 Output at the Matched FilterOne output at the matched filter for four users is found in Figure 2. Due to the randomly generatedsignature waveforms and data, the output and percentage error differ with every run of the simulation. Figure 2. Non-orthogonal Input v. Output Signals using Conventional Matched Filter for Four Users.This trial produced mixed results. The output of user 1 was quite accurate and produced 0% error.however the output of the other 3 users was inaccurate due to the near/far effect and errorpropagation. The error worsened with each subsequent user because the power of the other user 14
  15. 15. signals interfered with the desired signal. Additionally, it is evident from the outputs of user 2 and user 4that the matched filters do not correct error propagation. The code used to generate this graph is foundin Appendix B.2.3.3 Percent Error at OutputThe percent error found at the output was 0% for User 1, 12.5% for User 2, 25% for User 3, and 37.5%for User 4. The average percent error for this trial is 18.75%. This is a significant amount of error and isunacceptable for any real implementation. The cause of this error is multiple access interference, or theMAI term of Equation 9. This filter treats the term as white noise, which causes the noise term to bevery large. The large noise term increases the probability of error.Figure 3 shows the average bit error percentage rate for an increasing number of users and anincreasing signal-to-noise-ratio SNR. This graph was generated by averaging 200 instances of theoutcome for each number of users. The code used to generate this graph is found in Appendix C.For the original SNR ratio SNR0, the BEP average hovers around 20% for 5 users. As the number of usersincreases to 10, the BEP increases to 28%. As the number of users increases to 20, the BEP increases to35%. For the SNR ratio [SNR0 – 5] dB, the noise is increased by 5 dB from the original level. Though anadditional 5 dB of noise was added, the plot closely follows the ratio of the original SNR plot.For the SNR ratio [SNR0 – 10] dB, the BEP ratio starts out around 22% with 5 users and increases to 37%for 20 users.For the final case where the SNR noise ratio is 15 dB more than the original noise level, the BEP with 5users is 26% and increases to 37% with 20 users. 15
  16. 16. During multiple simulations, it was discovered that adding white noise with a power up to 15 dB did notchange the BEP ratio because it was insignificant when compared to the size of the MAI term. The graphclosely resembled the SNR0 line in Figure 3. Figure 3. Non-Orthogonal Input using Conventional Matched Filter Bit Error Percentage.2.3.4 OutcomesThe conventional matched filter performs poorly when the input signals consist of non-orthogonalwaveforms. The BEP started at 20% for 5 users and approached 40% for 20 users.This technique does improve the capacity of the channel by lifting the limit on the number of waveformsallowed. However, the capacity now becomes limited by the amount of noise and MAI that the outputsignal has. More than white noise, the MAI term becomes a very important element that needs to bereduced in order to improve both capacity and the BEP. 16
  17. 17. Due to the abundance of signal interference in the output, the filter does not do a good job inhibitingthe near/far effect nor does it use power as efficiently as possible.This system is plagued by the large MAI term increasing noise, the probability of error, and decreasingcapacity. The biggest improvement in these factors would be seen from decreasing or nullifying the MAIterm. The next section demonstrates improvement in the output when the MAI term is reduced usingthe SIC detector.2.4 Successive Interference Cancellation (SIC) Multi-User Detector Using Non-Orthogonal Input Signals2.4.1 Procedure 1. General variables. The simulation allows the user to change input variables such as the number of users, the number of bits per user, the spreading gain, the number of samples taken by the detector, and the AWGN power. 2. Simulating the users. PN signature waveforms are created using a random number generator with values 0 or 1. The user data signals are created using a random number generator. 3. Sending the data. The transmitted signal is constructed using Equation 1 by multiplying the PN signature terms with the user signal and dividing by the square root of the spreading gain. This is then multiplied by the amplitude vector to simulate the near/far effect. 4. Receiving the data. The receiver receives a summation of a WGN (White Gaussian Noise) signal and the data signals from step 3. 5. Demodulating the received signals. Each signal is convolved using a conventional matched filter 6. Detecting bits from the result of the convolution. The output signal is assembled using Equation 15. To reduce the MAI term, start detecting bits in order of strongest to weakest user. Subtract the convolution of a user’s matched filter with each stronger users’ matched filter multiplied by their already detected bits and amplitude from the users matched filter output. 17
  18. 18. 2.4.2 Output at the Matched Filter One output at the matched filter for four users is found in Figure 4. Due to the randomly generated signature waveforms and data, the output and percentage error differ with every run of the simulation. It is evident in the user outputs that the SIC filter reduces the MAI term. The output of the filter is the dashed line that loosely follows the pulsing input. The solid line is the output after the SIC filter has been applied and the MAI term subtracted. It follows the peaks and nulls of the input signal more closely. This is most evident in the graph of user 3. The solid line (reduced MAI) clearly follows the movement of the input pulse but the dotted line (original output) at times departs significantly from the input. Through the graph of user 4 it is also evident that error propagates this system with ease. Provided that there is no propagation error, the SIC detector improves the output of the filter. The code used to generate this graph is found in Appendix D.Figure 4. Non-Orthogonal Input v. Output using SIC Detector. 18
  19. 19. 2.4.3 Percent Error at OutputThe percent error found at the output was 0% for User 1, 0% for User 2, 12.5% for User 3, and 0% forUser 4. The average percent error for this trial is 3.125%. While this is still a significant amount of error,the technique significantly improved the amount of error present. The cause of this error is the MAIterm of Equation 9. This detector attempts to measure the amount of MAI in each output signal andsubtract that amount from the output. It works relatively well in reducing percent error. However,because the algorithm treats each signal serially, any propagation error already in the signal willpropagate to the MAI-treated output.Figure 5 shows the average bit error percentage rate for an increasing number of users and anincreasing signal-to-noise-ratio SNR. This graph was generated by averaging 200 instances of theoutcome for each number of users. The code used to generate this graph is found in Appendix E. Figure 5. Non-Orthogonal Input using SIC Detector Filter Bit Error Percentage. 19
  20. 20. For the original SNR ratio SNR0, the BEP average is around 16% for 5 users. As the number of usersincreases to 10, the BEP increases to 24%. For the SNR ratio [SNR0 – 5] dB, the noise is increased by 5dB from the original level. Though noise was added, the plot closely follows the original SNR plot.For the SNR ratio [SNR0 – 10] dB, the BEP ratio starts out around 20% with 5 users and increases to 25%for 10 users. For the final case where the white noise is 15 dB more than the original noise level, theBEP with 5 users is 26% and increases to 31% with 10 users.Adding WGN powers between 0 dB and 5 dB not significantly alter the BEP because the MAIinterference term dominates. However, when adding the 10 dB or more of noise, the performance ofthe filter starts to worsen. At 15 dB of additional noise, the SIC detector output is comparable to that ofthe Conventional Matched Filter – as though the MAI term was never reduced by the SIC detector.2.4.4 OutcomesThe SIC detector performs moderately well when in comparison to the conventional matched filter. Theaverage BEP started at 16% for 5 users and reached 24% for 10 users. This is a significant improvementover the conventional matched filter, but could still be improved. Additionally, the SIC detector makesno improvements to the BEP if there is a significant amount (30 dB or more) of noise in the signal.This technique improves the capacity of the channel allowing any number of waveforms and reducingthe amount of MAI that is present in the system. However, the capacity is still very limited by theamount of noise in the signal because the SIC detector does not treat white noise.The detector is decent at inhibiting the near/far effect by reducing the MAI term and regulating thepower of user input signals. It uses power with some efficiency, however a lot of power would bewasted if SIC is applied over a noisy channel.This system experiences the negative effects of MAI, as the detector can only reduce it and notcompletely nullify it. The detector could be improved by treating the noise term or more effectivelyreducing the MAI term, particularly for a larger number of users. 20
  21. 21. 2.5 ComparisonThe conventional matched filter performs ideally when orthogonal waveforms are passed through it.Because of the orthogonal requirement, there is no interference and the MAI term is zero. Out of thethree cases considered, this system would perform best. However, it suffers a limited capacity due tothe need for a synchronized system, as well as a restricted number of orthogonal waveforms that can begenerated. Because of the severely limited capacity, it does not have any improvement over TDMA orFDMA, and is thus relatively useless in cellular environments.The conventional matched filter performs poorly when non-orthogonal waveforms are passed throughit. It treats MAI as white noise and thus produces a large bit-energy percent error. However, its capacityis limited by the amount of error in the output. To improve the output of the conventional matchedfilter, the output needs to be passed through an additional detector that can reduce the MAI term, andreduce the white noise on the channel. The SIC detector used reduces the MAI term but does not reducethe white noise.As seen in Table 6, there is significant BEP improvement when using the SIC Detector to reduce the MAIterm in the output of the matched filters. When BEP error can be attributed only to the MAI term, theSIC detector improves the BEP by 15%-20%, depending on the number of users. When both MAI and amoderate amount of noise are responsible for the BEP error, the SIC detector improves the BEP by 9% -14%, once again depending on the number of users. If there is 30 dB or more of white noise present inthe system (SNR0 has a power of 15 dB), the SIC detector does not significantly improve the BEP ratio. Table 6. BEP Improvement when using the SIC Detector Conventional SIC Detector BEP Percent Percent Matched Filter BEP Improvement for Improvement for 10 SNR 5 Users 10 Users 5 Users 5 Users 10 Users Users SNR0 20% 28% 16% 24% 20.0% 14.3% SNR0 – 5dB 20.5% 28.5% 16.5% 24.5% 19.5% 14.0% SNR0 – 10dB 22% 29% 20% 25% 9.1% 13.8% SNR0 – 15dB 26% 34% 26% 32% 0.0% 5.9% 21
  22. 22. 3 ConclusionConventional matched filters are not designed for non - orthogonal waveform inputs. They are notequipped to treat multiple access interference, and thus the system suffers from high bit-energy errorrates, the near/far effect, and reduced capacity.On the contrary, using orthogonal waveform inputs with conventional matched filters yields zero biterror and zero signal interference. However, the system is required to be synchronized, and is severelylimited in capacity by the number of orthogonal waveforms that can be created. Because CDMA is verypopular for cellular environments where it is often difficult to synchronize a base stations and a mobiledevice, the best solution is to use non-orthogonal waveforms and create additional filters or detectorsthat will remove signal interference and noise.The solution discussed in this paper is the SIC detector. Following a conventional matched filter, the SICdetector reduces the MAI term of the output signal by serially subtracting correlation terms from theuser signals. It successfully reduces BEP by 15% in minimum noise filled channels, and 10% in moderatenoise filled channels.If the system multi-user detection is required on is capable of being synchronized and does not havevery large numbers of simultaneous users, the orthogonal waveform using a conventional matched filteris the best combination to use. If the system is difficult to synchronize and has a large number ofsimultaneous users, the non-orthogonal waveform using a conventional matched filter and anoptimization is the best combination to use. Depending on the channel and the system needs, differentoptimization can be well-suited. The SIC optimization is best used on a channel with low white noise,power control (reducing the near/far effect), and less number of users. 22
  23. 23. References 1. Viterbi, A.J.; , "The orthogonal-random waveform dichotomy for digital mobile personal communication," Personal Communications, IEEE , vol.1, no.1, pp.18-24, 1st Qtr. 1994 doi: 10.1109/98.295356 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=295356&isnumber=7300 2. Garg, Mohit. "Multi-User Detection." Mohrahit. Indian Institute of Technology - Bombay, n.d. Web. 25 Nov 2012. <http://www.mohrahit.in/find/multi-user-detection.pdf>. 3. Nguyen, H.H.; , "Synchronous CDMA systems with group-orthogonal signature waveforms," Vehicular Technology Conference, 2003. VTC 2003-Fall. 2003 IEEE 58th , vol.2, no., pp. 897- 901 Vol.2, 6-9 Oct. 2003 doi: 10.1109/VETECF.2003.1285150 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1285150&isnumber=28569 4. Duel-Hallen, A.; Holtzman, J.; Zvonar, Z.; , "Multiuser detection for CDMA systems," Personal Communications, IEEE , vol.2, no.2, pp.46-58, Apr 1995 doi: 10.1109/98.382531 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=382531&isnumber=8673 5. Ahmed, M.; El-Mahdy, A.; El-Barbary, K.; , "Performance analysis of adaptive Hard Decision Parallel Interference Cancellation receiver in asynchronous Multicarrier DS-CDMA system," Radio Science Conference (NRSC), 2011 28th National , vol., no., pp.1-9, 26-28 April 2011 doi: 10.1109/NRSC.2011.5873603 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5873603&isnumber=5873575 6. Hongzheng Li; Zhao Feng; , "Multi-user detection technology of CDMA system," Electronics and Optoelectronics (ICEOE), 2011 International Conference on , vol.2, no., pp.V2-210-V2-212, 29-31 July 2011 doi: 10.1109/ICEOE.2011.6013216 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6013216&isnumber=6013156 7. Garg, Mohit, and Professor U.B. Desai. "Multi-user Signal Processing Techniques for DS-CDMA Communication Systems." Mohrahit. Indian Institute of Technology - Bombay, Dec 2004. Web. 25 Nov 2012. URL: http://www.mohrahit.in/learn/MohitGargDDPThesis-ppt.pdf 8. Beachy, John. "Lecture 18: CDMA." MATH 523, Summer 2008. Northern Illinois University, n.d. Web. 27 Nov 2012. URL: http://www.math.niu.edu/~beachy/courses/523/cdma_lec.pdf 9. . "OVSF Code Generator." Documentation Center – R2012b. The Mathworks, Inc., n.d. Web. 27 Nov 2012. URL: http://www.mathworks.com/help/comm/ref/ovsfcodegenerator.html 23
  24. 24. Appendix ASimulation 1 Code – Orthogonal Waveforms Using Conventional Matched FilterAppendix BSimulation 2 Code – Non-Orthogonal Waveforms Using Conventional MatchedFilterAppendix CSimulation 2 Code – BEP vs. Number of Users GraphAppendix DSimulation 3 Code – Non-Orthogonal Waveforms Using SuccessiveInterference Cancellation (SIC) Multi-user DetectorAppendix ESimulation 3 Code – BEP vs. Number of Users Graph 24

×