IRJET- Performance Analysis of a Synchronized Receiver over Noiseless and Fading Channels

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 06 Issue: 11 | Nov 2019 www.irjet.net p-ISSN: 2395-0072
© 2019, IRJET | Impact Factor value: 7.34 | ISO 9001:2008 Certified Journal | Page 14
Performance Analysis of a Synchronized Receiver over Noiseless and
Fading Channels
Ramulu Prashanth Goud
1Research Assistant, Dept. of ECE, CMR Engineering College, Kandlakoya, Medchal-501401, India
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Abstract – This paper presents a baseband communications system that implements the data phase transmission using a single-
tone waveform. In our contribution, the behavior of received signal when transmitted over a noiseless channel and a fading
frequency selective channel with AWGN is analyzed in-terms of the output power spectrum, estimate of the cross-spectral phase
between the equalizer input and its output, control signal used to drive the Farrow fractional delay, scatter plot of the equalizer
input, output and descrambler output.
Key Words: AWGN, Equalization, Fading, Phase modulation, RLS.
1. INTRODUCTION
Wireless communication is turned out to be one of the greatest endowments from the telecommunication industry for the
development of one’s nation. The continually expanding interest for high data rates in wireless networks requires the
productive use of the restricted data transfer bandwidth available, while supporting a high review of portability in differing
propagation conditions [1]. The limit and the achievable integrity of correspondence frameworksaretoa greatdegreesubject
to the system’s knowledge concerning the channel conditions experienced. Consequently, the arrangement of an exact and
strong channel estimation system is an essential figure accomplishing a high performance. The estimation is finished by
equalizing the channel [2]. The equalization alludes to expelling the impactsofthechannel.Inmultipathpropagationthesignal
data goes through a diverse way and may bring fading of the signal, in this manner there comes a delay in achieving the
destination. At the point when the delay spread (Td) is lesser than a symbol period, the contortion is called flat fading, if the
delay spread is more than a symbol period called as frequency selective fading. Data exchange is seriously constrained at the
deep fade frequencies [3]. The channel conditions are assessed and its belongings are evacuated by channel equalization. It
monitors the movement in the channel by creating updates of the channel estimates utilizing equalizing algorithms (RLS)and
at long last tries to limit those estimated errors [4]. The Equalizer is set at the recipient front end to evacuate the channel
impairments by refreshing the weights.
The synchronization writing is so incomprehensible as to involve more than 1000 technical papers with applications in
differing territories, for example, communications, telemetry, time and frequency control, and instrumentation frameworks.
This colossal accumulation of information has been incorporated and expounded in brilliant books like those by Viterbi [5],
Stiffler [6], Lindsey [7], Lindsey and Simon [8], Gardner [9], Meyr and Ascheid [10], and in the ESA specialized report by
Gardner [11]. Digital synchronization strategies, which implies that to recover timing,phaseandcarrierfrequencybyworking
just on signal tests taken at appropriate rate. This is interestingly with the recognizable analog methods which work on
continues time waveforms. On the other-hand, continues phase modulation (CPM) strategies have turned into a serious
research territory in the eighties, around with the production of the book by Anderson et al [10].
2. SYSTEM MODEL
The received signal from a transmitter is processed through RLS Equalizer to avoid the noise introduced by the channels. RLS
equalizer is designed as shown in Figure 1. The extra delayis introduced to align the Randomizing sequence with theEqualized
signal. The Equalizer introduces a delay equal to the length of a frame. An extra delay is intended in Frame Alignment block to
align the signal to the beginning of the interleaver frame [12]-[14]. This block collects a block of data equal to size of the
interleaver matrix depending on the data rate and interleaver length. The function of Symbol Extraction block is to convert the
tribit that results from the modulation into one, two or three bit channel symbols depending on the data rate. Finally the
deinterleaved data is passedto the FEC decoderandthedataisdecoded.Theinputsignalandreceivedsignalsaregivenasinputs
to BER block to analyze the performance of various blocks and will be discussed more in Section.

Figure 1: RLS Equalizer.
3. NUMERICAL ANALYSIS
In basic linear model, let us consider estimation of vector θ in model that is linear in θ. Classical linear form can be defined as
(1)
where Y
i
is i th measurement, h
i
is corresponding “design vector,” and n
i
is unknown noise value. This model is used
extensively in control, statistics, signal processing, etc. However, many estimation/optimization criteria based on “squared-
error"-type loss functions which leads to criteria that are quadratic in θ and Unique (global) estimate θ. This Criterion (loss
function) has form
(2)
where Y
k
= [y
1
,y
2
,....,y
i
] and H
k
is k × p concatenated matrix of h
T
i row vectors. Classical batch least-squares estimate is
(3)
Popular recursive estimates (LMS, RLS, Kalman filter) may be derived from batch estimate. However, batch form may not be
convenient in many applications, for example, data arrive over time and want “easy” way to update estimate at time i to
estimate at time k+1.
Least-mean-squares (LMS) method is very popular recursive method which is a Stochastic analogue of steepest descent
algorithm and LMS recursion can be written as
(4)
Suppose process is modeled according to autoregressive (AR) form:

(5)
where x
i
represents state, γ and α
i
are unknown parameters, u
i
is control, and n
i
is noise. Let target (“desired”) value for x
i
be d
i
, Optimal control law known (minimizes mean-square tracking error) as
(6)
An alternative to LMS is Recursive Least Squares (RLS) which is a stochastic analogue of Newton-Raphson(“secondorder”
method) and faster convergence than LMS in practice. The two recursions of RLS algorithm are
(7)
It is common to have the underlying true θ evolve in time (e.g., target tracking, adaptive control, sequential experimental
design, etc.). Prototype recursive form for estimating θi is
(8)
where choice of A
i
and I
i
depends on specific algorithm.
4. RESULTS AND DISCUSSION
The full receiver which shown in Figure 2 mainly comprises of four blocks such as Acquired Passband Waveform, Frequency
Translator and Channel, Receiver and Byte Error display [15], and the internal operations of the receiver is shown in Figure3.
Figures 4, 5 show the behavior of received signal when transmitted over a noiseless channel and a fading frequency selective
channel with AWGN, respectively. Figure 4 depicts the plots for a noiselesschannel (a)Thechannel outputpowerspectrum(b)
Estimate of the cross-spectral phase between the equalizer input and its output (c) Control signal used to drive the Farrow
fractional delay (d) Scatter plot of the equalizer input (e) Equalizer output (f) Descrambler output. It can be observed that a
distortion in the signal due to the effect of the noise in the fading channel [15] - [20].
Figure 2: Basic block diagram of receiver.
Figure 3: Synchronization operations involved in receiver.

Figure 4: Plots for a noiseless channel (a)The channel output power spectrum (b)Estimate of the cross-spectral phase
between the equalizer input and its output (c) Control signal used to drive the Farrow fractional delay (d) Scatter plot of
the equalizer input (e) Equalizer output (f) Descrambler output.

Figure 5: Plots for a fading frequency selective channel with AWGN (a)The channel output power spectrum (b)Estimate of
the cross-spectral phase between the equalizer input and its output (c) Control signal used to drive the Farrow fractional
delay (d) Scatter plot of the equalizer input (e) Equalizer output (f) Descrambler output.
5. Conclusion
This paper presented the receiver with RLS equalization properties and also analyzed the behavior of a signal over various
channels. The mathematical analysis is also presented with relevant expressions. It is observed that a distortion in the signal
due to the effect of the noise in the fading channel. In future, different equalizers will be analyzed for various fading channels.
REFERENCES
[1] Navdeep Singh Randhawa, Shally Sharma and Rakesh Kumar Dubey, A Survey of Equalization Techniques for an Effective
Equalizer Design in MIMO-OFDM Systems, International Conference on Circuit, Power and Computing Technologies
[ICCPCT], 2015.
[2] Kai-Kit Wong; Ross D. Murch;KhaledBenLetaief,“PerformanceEnhancementofMultiuser MIMO WirelessCommunication
Systems", IEEE Transactions on Communications, vol. 50, NO. 12, December 2002.
[3] Chan, Albert M.; Gregory W. Wornell, “A class of block-iterative equalizers for intersymbol interference channels", In
Communications, ICC 2000, IEEE International Conference on, vol. 1, pp. 31-35, 2000.
[4] Foschini, Gerard J.; Michael J. Gans, “On limits of wireless communications in a fading environment when using multiple
antennas", Wireless personal communications, Springer, vol. 6, no. 3, pp. 311-335.
[5] A.J. Viterbi, Principles of Coherent Communication, New York. McGraw-Hill, 1966.
[6] Stiffler, Jack Justin. Theory of synchronous communications. Prentice Hall, 1971.
[7] Lindsey, William C. "Synchronization systems in communication and control." (1972).

[8] Lindsey, William C., and Marvin Kenneth Simon. Telecommunication systems engineering. Courier Corporation, 1973.
[9] Gardner, Floyd M. Phaselock techniques. John Wiley & Sons, 2005.
[10] H. Meyr and G. Ascheid, Synchronization in Digital Communications, vol. 1, New York; John Wiley&Sons, 1990.
[11] Gardner, Floyd M. "Demodulator reference recovery techniques suited for digital implementation." ESA, 1988.
[12] MathWorks, Communication toolbox-DefenseCommunications:USMIL-STD-188-110BBasebandEnd-to-EndLink,R2017.
[13] MIL-STD-188-110B: Interoperability and Performance Standards for Data Modems, U.S. Department of Defense, 2000.
[14] ITU-R Recommendation 520-2: Use of High Frequency Ionospheric Channel Simulators, 1978/1982/1992.
[15] MathWorks, Communication toolbox-Defense Communications: US MIL-STD-188-110A Receiver, R2017.
[16] Wilhelmsson, Leif, and Lars Sundstrom. “Automatic gain control of a received signal using a power target." U.S. PatentNo.
9,350,313. 24 May 2016.
[17] Levesque, Martin, and David Tipper. "A survey of clock synchronization over packet-switched networks." IEEE
Communications Surveys & Tutorials 18.4 (2016): 2926-2947.
[18] Mahmood, Aneeq, et al. “Clock Synchronization Over IEEE 802.11â”A Survey of Methodologies and Protocols," IEEE
Transactions on Industrial Informatics 13.2 (2017): 907-922.
[19] Kanthimathi, M., and R. Amutha. "Energy Efficient Constellation Rotation for Multiple-Symbol Differentially Encoded
Communications." Journal of Computational and Theoretical Nanoscience 14.9 (2017): 4236-4240.
[20] Guo, Lianping, et al. "Decomposing Numerically Controlled Oscillator in Parallel Digital Down Conversion Architecture."
Journal of Circuits, Systems and Computers 26.09 (2017): 1750126.

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