Chapter 3,Bandpass Transmission Techniques for Mobile Radio,Bandpass Transmission Techniques for Mobile Radio,This chapter is concerned with method to mitigate the channel impairments identified and characterized in Chapter 2. The focus is: Digital modulation scheme The probability of transmission error in the presence of Rayleigh fading and AWGN Spread Spectrum,Chapter 3 - Lecture 1,Relative Groundwork,3.1 Relative Groundwork,2、Signal Space and Decision Regions,1、Introduction,3、QPSK and 2FSK,1、 Introduction,Elements of a digital communication systemBandpass Transmission,3.1 Relative Groundwork,1、 Introduction,Elements of a digital communication system,Signal design and receiver optimization together have the ability to combat fading and multipath effect:Modulation - signal designDemodulation optimized receiver,1、 Introduction,Elements of a digital communication system,Efficient radiationFacilitates channel assignment and reduces interference from other transmissions,1、 Introduction,Bandpass Transmission,1、 Introduction,Bandpass Transmission,The modulation can be classified into two categories:Linear modulationNonlinear modulation,an 1 0 1 1 0 1 0 0,2ASK,2FSK,2PSK,Bandpass Transmission,1、 Introduction,2ASK,2FSK,2PSK,Bandpass Transmission,1、 Introduction,For wireless communications, the criteria commonly used to evaluate the suitability of a modulation scheme include:Compact power spectral densityGood transmission performance Small (or no) envelope fluctuations after band pass filtering,The criteria of Bandpass Transmission,1、 Introduction,The amplitude of the carrier is constant, regardless of the variation in the message signal. It is the phase that changes.,Constant Envelope,1、 Introduction,Benefits of Constant Envelope :Power efficientLow out-of-band radiationSimpler receiver design can be usedHigh immunity against random AWGN and Rayleigh fading,Constant Envelope,1、 Introduction,2、 Signal Space and Decision Regions,Vector-Space Representation of M-ary SignalSignal Detection and Optimal Receiver,3.1 Relative Groundwork,To understand digital modulation, it is important to know that a signal can be equivalently represented both in the time domain and in the signal space domain. Each of the waveforms can represented as a point in an N-dimensional signal space over the interval 0 Ts.,2、 Signal Space and Decision Regions,Vector-Space Representation of M-ary Signal,The digital source generates digital symbols for transmission at a rate of Rs symbols per second, the symbols are taken from an alphabet of size M.,Each symbol is represented by a unique baseband waveform,2、 Signal Space and Decision Regions,Vector-Space Representation of M-ary Signal,Over each time interval of Ts=1/Rs, one of the M waveforms is selected for transmission,Each of the waveforms can be represented as a point in an N-dimensional signal space defined by orthonormal basis function over the interval,2、 Signal Space and Decision Regions,Vector-Space Representation of M-ary Signal,Thus, in the signal space defined by the , vm(t) ban be represented by the vector,2、 Signal Space and Decision Regions,Vector-Space Representation of M-ary Signal,2、 Signal Space and Decision Regions,Vector-Space Representation of M-ary Signal,Definition 3.1 The correlation coefficient between realvalued signals xm(t) and xk(t) is,The squared Euclidean distance between xk(t) and xm(t) is defined as:,2、 Signal Space and Decision Regions,The squared Euclidean distance,2、 Signal Space and Decision Regions,The squared Euclidean distance,The receiver can be divided into two components: The demodulator Decision device,2、 Signal Space and Decision Regions,Signal Detection and Optimal Receiver,The signal space representation leads itself conveniently to decision making. The received signal is,The received signal can be represented by a vector , where,2、 Signal Space and Decision Regions,Signal Detection and Optimal Receiver,2、 Signal Space and Decision Regions,Matched Filter,2、 Signal Space and Decision Regions,Matched Filter,2、 Signal Space and Decision Regions,Matched Filter,Given the demodulator output , the decision device is to perform a mapping from to an estimate of the transmitted symbol in a way that will minimize the probability of error in the decision making process.,ML Decision Rule: Set if for all and,2、 Signal Space and Decision Regions,Decision Regions,In other word, the decision rule is to choose the message point closest to the received signal point, which is intuitively satisfyiing.,2、 Signal Space and Decision Regions,Decision Regions,The receiver consisting of the matched-filter demodulator and the decision device using the ML decision rule is commonly referred to as matched filter receiver. The receiver is optimum in the sense that it minimizes the probability of transmission error in an AWGN channel.,