The above problem solved by the Pulse Compression. Pulse compression shares the inkling of transmitting a long-range pulse with some modulation embedded which spreads the energy over the bandwidth necessary for the required resolution. Pulse compressed Wave forms have larger time bandwidth (BT) product compared to uncompressed pulses whose BT=1.The pulse compression technique in the waveforms is employed either in the Frequency coding or Phase coding. An LFM signal is a waveform of frequency modulated whose carrier frequency varies linearly with time, over a specific period. This is one of the oldest and frequently used waveforms. It finds application in CW and pulsed radars. Since an LFM waveform serves as a constant amplitude waveform, it makes sure that the amplifier works efficiently. Also, this waveform spreads the energy widely in frequency domain. A long pulse is divide in to a number of sub pulses of equal duration and the phase of each sub pulse is modulated with the different phases. This can be merely divided into binary and poly-phaser phase coding. In binary technique, the phase of any sub pulse takes any of the two values, either 1 or -1, in harmony with the sequence. In poly phase coding or Non-Binary coding , the phase of the sub pulse takes any of the M arbitrary values. The poly phase codes are Frank codes,p1 codes,p2 codes , P3 codes and p4 coded waveform are some of the commonly used sequences in Polyphase coding. The range side lobes for polyphase coded waveforms are lower than that of binary-coded waveform of same length, but the Doppler performance gets debilitated. # II. # Orthogonal Wave forms Orthogonal poly phase code consists of Length of the sequence (N c ),set size of the (L) and Phase of the sequence (M). Signals which probably containing N sub pulses represented by a complex number sequence, the set of the sequence is given by ?? ?? (??) = ?? ?? ? ?? (??)(1) Where n=1,2, ?., N c and l=1, 2, ?., L Where Øl (n), (0?Ø l (n)<2?) is the phase of sub pulse n of signal. umber of waveforms are used for radars signal. Several properties of radar waveforms are discussed in [10], [9], [7]. An un-modulated or modulated continuous signal is used in continuous wave radar. Such a system can detect targets using Doppler offset, but range measurements become difficult. Since the radar transmits continuous waves, the requirement for secondary antenna for reception arises which is considered as another short coming of such a system. Pulsed radar transmits signals at regular time intervals of time unlike the CW radar. pulsed radars could give range measurements. But the selection of pulse width is a co-operation among the required resolution of the system and the detectable maximum Range. Number of characteristics of the radar system such as the Range resolution, range accuracy, target detection, radar range and Doppler shift. are decided by the radar waveforms. For example, the shorter the pulse width, the more accurate rang resolution the system has. But at the similar instance of time, short pulse will not support a good detection range. ? ?? (??)?? ?0, 2?? ?? ?? , 2. 2?? ?? ?? , ? , (?? ?? ? 1). 2?? ?? ?? ? (2) ?? ?? (??) = ?ð??"ð??" 1 , ð??"ð??" 2 , ? , ð??"ð??" ?? ?? ? (3) # N Year Assume a set a poly phase codes with contains the set as Nc whose set size is L, one can briefly signify the phase values of S with following L× N c phase matrix. (??, ?? ?? , ?? ?? ) = ? ?? 1 (1) ?? 2 (2) ? ?? 1 (?? ?? ) ?? 2 (1) ?? 2 (2) ? ?? 2 (?? ?? ) ? ?? ?? (1) ? ?? ?? (2) ? ? ?? ?? (?? ?? ) ? (4) Here the phase sequence in row (1 ? l ? L) is the sequence of polyphase signal, and complete elements in the matrix can be elected from the set of phases. From the cross correlation and autocorrelation distinguishing of orthogonal polyphase codes, we get. ??(?? ?? , ??) = ? ? ? ? ? 1 ?? ?? ? exp ??[?? ?? (??) ? ?? ?? (?? + ??)] = 0 0 < ?? < ?? ?? ?? ?? ?1 ??=1 1 ?? ?? ? exp ??[?? ?? (??) ? ?? ?? (?? + ??)] = 0 ? ?? ?? < ?? < 0 ?? ?? ??=???+1 For l=1, 2, ?. L ( 5) ??(?? ?? , ??) ? ? ? ? ? ? 1 ?? ?? ? exp ????? ?? (??) ? ?? ?? (?? + ??)? = 0 0 < ?? < ?? ?? ?? ?? ??? ??=1 1 ?? ?? ? exp ????? ?? (??) ? ?? ?? (?? + ??)? = 0 ? ?? ?? < ?? < 0 ?? ?? ??=???+1 or p?q and p, q=1, 2, ? L where and are the aperiodic function of autocorrelation polyphase sequence and the function of cross correlation sequences and .Where k defined as the discrete time index. Therefore, crafting of an orthogonal polyphase code made corresponding to the building of a polyphase matrix in equation 6 with and constraints in equation 5 and equation 6.For the scheme of code sets of orthogonal polyphase used in MIMO radar systems, an the process of optimization is used not only to suppress the auto correlation side lobe peaks and the cross correlation peak but also to suppress the the total autocorrelation sidelobe energy and cross correlation energy in equation 7. Here ? is the weight factor if it is less than one means more weightage is given to auto-correlation and less weightage is given to cross-correlation. ?? = ? ? |??(?? ?? , ??)| 2 + ?? ? ? ? ???(?? ?? , ?? ?? , ??)? 2 ?? ?? ?1 ??=?(?? ?? ?1) ?? ??=??+1 ???1 ??=1 ?? ?? ??=1 ?? ??=1 (7) III. # Mimo Radar Signal Model A pure MIMO system is one that operates incoherently where as netted radar (NR) Systems operate Coherently and decentralized radar networks (DRNs) operate incoherently with a two stage processing [12].The basic form of the received signal in a MIMO network is the signal arriving at the k th receiver can be modeled as ?? ?? (??) = ? [( ?? ?? =1 ??0 1 ? ?? ,?? (??)?? ?? (?? ? ?? ?? .?? ) + ?? ?? ,?? (?? ? ?? ?? .?? )] + ?? ?? (??) + ?? ?? (??)(8) Where H o/1 is 0 or 1 depending the absence or presence of target respectively; s m is the m th transmitted signal, c m,k is the clutter, z k is the thermal noise, J k is an external disturbance (such as jamming), ? m,k and T m,k are the delays occurring during the path between the m th transmitter and the target/clutter respectively and the k th receiver and ?? ??,?? (?) is a coefficient that accounts for the parameters of the mono/bisatic radar equations, the phase shift ,and the RCS-distribution, specifically . ?? ??,?? (??) = ? ?? ?? ?? ? ?? ???? ?? ???? ? 2 ?? (4??) 3 ?? ?? 2 ?? ?? 2 ?????? ???? 2???? ?? .?? ? ?(9) Where G tx and G rx are respectively the gains of the transmitting and receiving antennas, ? is the RCS of the target, P t is the transmitting power, R m and R k are the transmitter-target and target-transmitter distances respectively and R m.k is the distance covered by the signal. The effects of the clutter are not considered, and hence this leads to the following expression for the received signal. The received output may be expressed as the result of the cross correlation of the received signal with the transmitted waveforms as follows. ?? ?,?? = ?? ?? ( ?? ) ? ?? ? (??) = ??0 1 ? ( ?? ?? =1 ? ?? ,?? (??)?? ?? (?? ? ?? ?? .?? )? ?? ? (??) +[?? ?? (??) + ?? ?? (??)] ? ?? ? (??) = ??0 1 ? ?,?? (??)?? ? (?? ? ?? ?.?? )+??0 1 ? ( ?? ?? =1 ?? ?? ? ?? ,?? (??)?? ?? .?? (?? ? ?? ?? .?? )+[?? ?? (??) + ?? ?? (??)] ? ?? ? (??) = ??0 1 ? ?,?? (??)?? ? (?? ? ?? ?.?? )+??0 1 ? ( ?? ?? =1 ?? ?? ? ?? ,?? (??)?? ?? .? (?? ? ?? ?.?? ) + ?? ?.?? (??)(11) Where R h (t) is the autocorrelation function of sm and R m,h is the cross-correlation function between s m and s h and n h,k is the component of the overall disturbance incoming in the k th receiver after the h th matched filter. Consequently a matrix M x signals from the same area may be written as follows. ?? ?? = ? ?? 11 ?? 12 ? ?? 1?? ?? 21 ?? 22 ? ?? 2?? ? ?? ? ?? ??1 ?? ??2 ?? ???? ?(12) Alternatively, this equation may be rearranged into vector X as follows ?? = [?? 11 , ? ?? 1?? , ?? 21 , ? ? ?? 2?? , ?? ??1 , ? . ?? 1?? ] ?? (13) Where T is the transpose operator. # IV. # Optimization Algorithms for Mimo Radar Many optimization methods have been developed for solving various types of engineering problems. Popular optimization algorithms include particle swarm optimization, neural networks, genetic algorithms, artificial immune systems, and fuzzy optimization. The particle Swarm concept originated as a simulation of simplified social systems. The Particle Swarm Optimization algorithm is basically a populationbased stochastic search algorithm and provides solutions to the complex non-linear optimization problems. PSO has the benefits of being more efficient when compared to most other optimization algorithms. V. # SIMULATION RESULTS In this paper Optimization of Orthogonal Polyphase Coded Waveform for MIMO Radar using Particle Swarm Optimization Algorithm is carried out. In the present work, Particle Swarm Optimization Algorithm is to optimize the six phase polyphase coded sequence to achieve good auto correlation properties and crosscorrelation properties. On the basis of projected algorithm the polyphase six phase coded sequences are set with lengths varying from 7 to 128 and number of transmitting ,receiving antennas L=3 and L=4. The auto correlation side lobe peak values obtained for different length of the sequences. the average value of ASPs is 0.0023 it is better than the literature values. The auto correlation side lobe peak values obtained for different length of the sequences the average value of ASPs is 0.0069 it is better than the literature values. # Conclusion Properties of Auto correlation side lobe peaks of Six phase produced order sets with three and four transmitting antennas for Sequence length N= 40 to 128 is obtained and compared with the literature values. From the design result, it conclude that the results obtained have great improvement in ASPs things of all the sequence lengths. In order to carry out the implementation of particle swarm optimization algorithm for the optimization of orthogonal poly phase sequences is developed for MIMO radar. 12![Fig. 1: Max (ASP) values of six phase sequence set L=3 designed using PSO compared with literature values](image-2.png "Fig. 1 :Fig. 2 :") 34![Fig. 3: Max (ASP) values of six phase sequence set L=4 designed using PSO compared with literature values.](image-3.png "Fig. 3 :Fig. 4 :") ![](image-4.png "") Six Phase Optimal Sequence Design for MIMO Radar?? ?? (??) = ??0??(?? ?? . ??)??(?? ?? . ?? ?? . ??)?? ???? ???? ??F??(?? ?? . ??)??(?? ?? . ?? ?? . ??)1 ? ( ?? ?? =1 ? ?? ,?? (??)?? ?? (?? ? ?? ?? .?? ) + ?? ?? (??) + ?? ?? (??) 1( ) Volume XVII Issue III Version Iof Researches in EngineeringGlobal Journal 2S.NoLength ofMax(ASP)Max(ASP)SequenceReportedLiterature170.03270.0792130.01790.07513170.01690.07204210.01260.07315290.00610.07216310.00620.07697370.00410.07778450.00360.07629490.00330.074410530.00260.073111610.00170.079212870.00150.077113950.00170.0762141030.00110.0741151130.00120.0734161170.00110.0733 © 2017 Global Journals Inc. (US) Year 2017 F © 2017 Global Journals Inc. (US) * Polyphase code design for orthogonal netted radar systems HDeng IEEE Transactions on Signal Processing 52 2004 * MIMO radar an idea whose time has come EFishler AHaimovich RBlum LCimini DChizhik RValenzuela Proc. of the IEEE Int. Conf. on Radar of the IEEE Int. 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Publication * Bounds on the Volume and Height Distributions for the MIMO Radar Ambiguity Function YuriIAbramovich GordonJFrazer IEEE Signal Processing Letters 15 2008 * MIMO Radar Ambiguity Properties and Optimization Using Frequency-Hopping Waveforms Chun-YangChen PPVaidyanathan IEEE Transactions on Signal Processing Dec.2008 56 III Version I