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Frequency Selective Multipath

The paper by Mahmoud and his colleagues describe the Performance of Bit Error Rate (BER) of the Direct Sequence Code Division Multiple Access (DS-CDMA). The DS-CDMA system is over a frequency selective multipath Rayleigh fading channel. The power control of the system is considered to be in perfect control. To evaluate the performance of Bit Error Rate of asynchronous DS-CDMA, the standard Gaussian Approximation is employed. The performance is analyzed using the varying numbers of multipath components, various process gain, and varying numbers of interfering cells. The factors of analysis of the performance of DS-CDMA affect the BER performance. Hence, they are also considered during examination of the performance of Bit Error Rate.

The writers embark on their research by defining the various parameters and terms involved in the research. The definitions and clarification are the main items in the introduction. According to the Mahmoud et al, Code Division Multiple Access is a radio communication technique that allows multiple users share the same spectrum simultaneously. The technique is regarded in the spread spectrum techniques as the highly investigated application. The spreading signal is the multiplied narrowband message by a large bandwidth signal. The means of generating the spreading signal introduces us to the pseudo-noise (PN) code. To generate spreading signal, pseudo-noise is convolved with a chip waveform that holds less duration than the symbol duration.  From the code sequences I realized that it is possible to share the same channel and frequency simultaneously by assigning users different code sequences. The paper describes further more terms that are essential in the research. The terms are inclusive of Multiple Access Interference (MAI) which is a phenomenon through which another user’s signal appears as noise in signals of other users. The phenomenon has an influence on BER since it degrades BER and system performance. Therefore, to describe the performance of CDMA it is essential to include MAI; its quantity and effect.

The writers proceed to explain the mathematical description of an asynchronous DS-CDMA system. The asynchronous DS-CDMA is described using the reverse link; the transfer in mobiles to base station. The explanation involves use of abstract data in symbols to explain the factors mathematically.

The system is assumed to hold k active users and Mc cells. The transmitted signal is presented mathematically, expressing all of its variables and the sequence of the system. The channel model gains center of analysis afterwards. The assumption held in the description is that the channel from the mobile phone to base station, with the given variables is a multipath Rayleigh fading channel.

In determining the system performance, the assumptions from which the Gaussian Approximation technique is based on is the argument that the bit decision statistic Zo may be designed as Gaussian random variable. The random variable is defined as the Standard Gaussian approximation. Central Limit Theorem is used in approximating the sum of Multiple Access Interference signals as an additive white Gaussian process. Accuracy of the standard Gaussian Approximation increases with an increase of the number of users according to the paper.

The results from the research are based on Standard Gaussian approximation. From the results the received power of the desired signal is normalized to 1. The results would be accurate if the number of users is large since from the graph of accuracy of Gaussian approximation increases with increase in the number of users. The results denoted that performance of the DS-CDMA system is largely dependent on quantity of interfering cells. I agree to the relation conceded by the result. The Bit Error rate performance is found to be also largely dependent on the multipath components. Using the Standard Gaussian Approximation, the process gain significantly influences the performance of Bit Error Rate. The results are agreeable according to the substantial data used and the variable inputs that were recognized in the formula.

Despite investigating and providing evidence to the existing factors that affect the performance of Bit Error Rate, some of the methods and steps carried out are still unclear. The researchers do not describe the steps to how they reached the final formula in finding the performance of Bit Error Rate using the existing factors. For example, the formula generated in correlation receiver and the performance determination using the Standard Gaussian Approximation.

The paper limited itself to the final formulas and not the step calculation of the effects. The variables used in drawing the different graph were also not clearly stated. The paper is more of a description of how the performance of Bit Error Rate maybe calculated and providing the various definitions involved in the formula. The general view of the paper is quite pleasing since it has a flow of orienting the reader with the terms essential in the paper before describing how they are made effective in the paper.

According to the variables used to describe the paper and the assumptions made during the calculation, it is agreeable that the authors’ conclusion is correct. The system involved use of the reverse link which has multipath due to the multiple users that are involved in using the mobile phones to the base stations. Therefore, the variables are multipath related, the conclusion that performance of Bit Error Rate is affected by multipath components holds true. 

Malcolm Potts Children of Darkness
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