maximum Doppler shift fp; an important factor to be considered when developing channel equalization and estimation techniques The autocorrelation function of the impulse response is also commonly used to characterize multipath fading channels. The autocorrelation function of h(t; T)is defined as 重h(t1,t2;n1,n2)=E[b(t;n)h'(t2:2) Most radio channels can be accurately modeled as wide sense stationary uncorrelated scattering(wSSUS)channels. For wide sense stationary channels, the correlation functions depend only on the time difference For uncorrelated scattering channels. paths of different delay are uncorrelated. The autocorrelation function for WSSUS channels is then simplified to Eh(t;n)h(t+△t;72)=西h(△;n)6(r1-n2) 210) The function n(O;)= n(G)is called the power delay profile. The power delay profile gives the average power at the channel output as a function of time delay T. An effective measure of the time dispersiveness of the channel is the rMs delay spread, defined as (T-F).Rn)dr 更h() (211) Pa(T)dr 重h(T) The range of values of r over which n()is essentially nonzero is called the multipath spread of the channel and is denoted by im
The reciprocal of the multipath spread is a measure of the coherence bandwidth of the channel; i.e., B (213) where b is the coherence bandwidth of the channel. Signals with frequency sepa- ration greater than Bc are affected differently by the channel. If the bandwidth of an information-bearing signal is small in comparison to Bc, all frequency components of the signal experience the same response, and the channel is said to be frequency nonselective or at. On the other hand, if the bandwidth of the information-bearing signal is large in comparison to Be, different frequency components of the signal are ffected diferently, and the channel is said to be frequency-selective. In this case. the signal is severely distorted by the channel. Multipath fading channels with Aat frequency response are called jat fading or time-selective channels. Flat fading is often a reasonable model for indoor mobile wireless communications where the multipath spread is small and or lower data rate systems where the signal bandwidth is small. Multipath fading channels that are frequency-selective are said to be frequency-selective fading channels. Frequency selective fading is the more appropriate model for outdoor and high data rate systems Frequency-selective fading is in effect both frequency-selective and time-selective and is the more difficult environment for mobile wireless communications. Mitigating the detrimental effects of frequency-selective fading is the main focus of this thesis
2.1.2 Simulation of Multipath Fading Channels Computer simulation is an essential tool in the development of wireless communi- cation systems. Multipath fading channel simulators can provide an accurate and controlled means of evaluating system performance over a wide range of expected channel conditions. Two popular methods of constructing fading channel simula tors are the filtered white Gaussian noise technique [19] and the so called Jakes' 2.1.2.1 Filtered White Noise Method The filtered white noise technique is a straightforward method of constructing a fading channel simulator by modulating the in-phase and quadrature-phase components of the carrier with a lowpass filtered Gaussian noise source. Therefore, the complex baseband equivalent of the simulator is simply a complex white Gaussian noise source followed by a lowpass filter. If a zero-mean white gaussian noise source is used, the simulator produces a Rayleigh fading envelope; otherwise, a Ricean fading envelope is generated. The frequency response of the lowpass alter is chosen to approximate the fading spectrum in(2.8). Although the filtered white noise technique is simple, a complicated lowpass filter is required to provide an accurate simulator. 2.1.2.2 Jakes' method Jakes'method is less intuitive than the filtered Gaussian noise approach but tends to produce better results. In this method, one oscillator at frequency fp and M oscilla- tors with=(2,n=12…,M,则heeM=(号- nd N is the assumed number of discrete multipaths are used to generate waveforms
x(u) Z h(ao)减;n)2) h(u: L-1) n (u) ∑ Figure 2. 1: Discrete-time tapped delay line model for a frequency-selective fading channel(22 that are added together to produce both the in-phase and quadrature-phase compo- nents of the channel simulator. The oscillators are appropriately weighted to produce the desirable fading characteristics. For a Rayleigh fading envelope, the amplitudes of the oscillators are all unity, except for the oscillator at frequency fD that has an amplitude of 1//2. The main advantage of Jakes'method is that it can closely approximate an isotropic scattering environment with a simulator of reasonable com- plexity 2.1.2.3 Simulation of Frequency-selective Fading Channels In this thesis, the T-spaced model is used for the simulation of frequency-selective fading channels[ 12, 21]. As shown in Figure 2.1, the discrete-time complex baseband equivalent channels are modeled as transversal filters with the tap spacing equal to the symbol duration Ts. The tap coefficients, h(u; r ), are approximated as uncorrelated zero-mean complex Gaussian random processes, i.e., assumed absent of any LOS or pecular component. For the simulations throughout this thesis the Jakes' method of generating a rayleigh fading carrier for 2-D isotropic scattering channels he CosT207 six-ray power delay profiles in Table 2. 1 are used to set the variances
Table 2.1: COST207 six-ray power delay profiles Typical Urban(TU) Bad Urban(BU Delay(uS) Power Delay(us)Power 0 0.5 0.56 0.2 0.3 05 0.63 10 16 0.25 1.6 032 0.16 66 0.4 of the tap coefficients 23]. The maximum delay, or the order of the channel impulse response(CIR), is given by L=「Tm/Ts here r] denotes the smallest integer equal to or greater than I 2.2 Diversity Techniques The mobile wireless channel suffers from multipath fading that severely attenuates the received signal during periods of deep fades. The severe signal attenuation makes it impossible for the receiver to determine the transmitted signal reliably unless larger amplitude replicas of the same information-bearing signal are made available to the receiver. Providing duplicate signals to the receiver is referred to as diversity, and it is the single most effective means of improving the performance and reliability of wireless communications in fading environments. Essential to the success of any diversity technique is that replicas of the information-bearing signal experience in- dependent fading processes. The three main forms of diversity commonly exploited