Advanced Wireless Networks Lecture 5: : Diversity Techniques in Multi-Carrier System Here, as in Lecture 4, instead of one carrier, we consider N carriers. This allows us to have the following advantages. Thus, as was shown in previous lecture, we define for the channel with flat slow or fast fading the average SNR as: Each branch has an instantaneous SNR= and then probability of error . The probability that a single branch has SNR less than some threshold is the cumulative distribution function defined as: Lectures 1 & 2: Overview Adv. Wireless Comm. Sys.

Diversity Techniques in Multi-Carrier System Now, the probability that all M independent diversity branches receive signals which are simultaneously less than some specific SNR threshold is: If any branch with number I achieve SNR> then the probability of that is The PDF is found as derivative of CDF of all braches to achieve threshold, i.e., Then, the mean SNR can be defined as and Lectures 1 & 2: Overview Adv. Wireless Comm. Sys.

Diversity Techniques in Multi-Carrier System Example: Consider four branches, which each branch is independent Rayleigh fading channel. The average SNR . Find: The probability that the SNR will drop below threshold . Solution: We see that . Then using above formulas, we get for four independent branches: When diversity is not used, this formula can be evaluated using M=1, i.e., It is clear to see that without diversity the SNR drops below the specified threshold of 10 dB with a probability that is three order of magnitude greater than if four branches diversity is used. Lectures 1 & 2: Overview Adv. Wireless Comm. Sys.

Diversity Techniques in Multi-Carrier System Frequency Diversity Why OFDM? Frequency diversity transmits information on more than one carrier frequency. Here frequencies are separated by more than coherent bandwidth of the channel and, therefore, will not experience the same fades. This means that the channel bandwidth (coherence bandwidth) of each sub-channel denoted as bw, will be much smaller than , that is, By use of N carriers, we finally have: Lectures 1 & 2: Overview Adv. Wireless Comm. Sys.

Frequency Diversity – OFDM (Cont.) In Figure is shown example on how we can split the channel bandwidth on N sub-channels with bandwidth bw very narrow to exclude effects of deep fading. Lectures 1 & 2: Overview Adv. Wireless Comm. Sys.

Frequency Diversity – OFDM (Cont.) Then, each independent sub-signal will have in frequency domain a rectangular shape of power spectral density (PSD) which in frequency domain has sharp presentation f . PSD And conversely, rectangular shaping function in time domain (a pulse), has in frequency domain a shape of ideal Nyquist filter time shaping function Lectures 1 & 2: Overview Adv. Wireless Comm. Sys.

Frequency Diversity – OFDM (Cont.) We now assume that the transmitted signal passing the fading channel consisting N sub-carriers (e.g., N paths) can be generally presented via the attenuation factor for signal received in nth sub-channel and its own independent phase, , i.e., where The sub-carriers of OFDM are orthogonal on the interval , from which is followed that Lectures 1 & 2: Overview Adv. Wireless Comm. Sys.

Frequency Diversity – OFDM (Cont.) The corresponding splitting allows us to obtain a signal for the each carrier in the following manner: where and is a set of constellation’s points containing L points . and OFDM implementation is based on direct and inverse fast Fourier transform (denoted FFT and IFFT, respectively), which we will described below. Lectures 1 & 2: Overview Adv. Wireless Comm. Sys.

Frequency Diversity – OFDM (Cont.) The corresponding discrete-form presentation of IFFT/FFT algorithm is the following: where Lectures 1 & 2: Overview Adv. Wireless Comm. Sys.

Frequency Diversity – OFDM (Cont.) Here we denoted the following parameters: Finally, we get: or schematically: Then, at the receiver just FFT on sampled is used. Lectures 1 & 2: Overview Adv. Wireless Comm. Sys.

Time Diversity One modern implementation of time diversity involves the use of RAKE receiver, working as n-delay line through which the received signal is passed. Its action is somewhat analogous to an ordinary garden rake, and consequently, the name "RAKE receiver" has been used for this receiver structure by Price and Green in 1958. The RAKE receiver collects the time-shifted versions of the original signal by provide a separate correlation receiver for each of the multipath signals. Usually for CDMA, a RAKE receiver utilizes multiple correlators to separately detect the M multipath components with deep fading (i.e., strongest multipath components). . Lectures 1 & 2: Overview Adv. Wireless Comm. Sys.

Time Diversity – OFDM (Cont.) The outputs of the M correlators are denoted as . They are weighted by , respectively. The weighting coefficients are based on the power or the SNR from each correlator output. As in the combining diversity scheme, the overall signal is given The weighting coefficients are normalized to the output signal power of the correlator in such a way that the coefficients sum limits to unity, shown by the following formula: Lectures 1 & 2: Overview Adv. Wireless Comm. Sys.

Time Diversity – OFDM (Cont.) Choosing weighting coefficients based on the actual outputs of the correlators yields better RAKE receiver performance. This performance gives a conditional error probability in the form of where for the orthogonal signals, and for the antipodal signals. Here For the Rayleigh flat fading channel, we get probability for instantiations SNR . where, as above, is an average SNR for the kth path (kth sub-channel). Lectures 1 & 2: Overview Adv. Wireless Comm. Sys.

Spatial Diversity One modern implementation of time diversity involves the use of RAKE receiver, working as n-delay line through which the received signal is passed. Its action is somewhat analogous to an ordinary garden rake, and consequently, the name "RAKE receiver" has been used for this receiver structure by Price and Green in 1958. The RAKE receiver collects the time-shifted versions of the original signal by provide a separate correlation receiver for each of the multipath signals. Usually for CDMA, a RAKE receiver utilizes multiple correlators to separately detect the M multipath components with deep fading (i.e., strongest multipath components). . Lectures 1 & 2: Overview Adv. Wireless Comm. Sys.

MIMO Systems for Spatial Diversity Propagation Channel M N Lectures 1 & 2: Overview Adv. Wireless Comm. Sys.

QOS Performance for MIMO Systems Lectures 1 & 2: Overview Adv. Wireless Comm. Sys.

Signal Data Parameters in the MIMO Systems Shannon Formulation Lectures 1 & 2: Overview Adv. Wireless Comm. Sys.

K-Parameter of Fading Lectures 1 & 2: Overview Adv. Wireless Comm. Sys.

QOS Performance for MIMO Systems Bit Error Rate Lectures 1 & 2: Overview Adv. Wireless Comm. Sys.

Bit Error Rate (Cont.) Lectures 1 & 2: Overview Adv. Wireless Comm. Sys.

QOS Performance for MIMO Systems – Numerical Results Lectures 1 & 2: Overview Adv. Wireless Comm. Sys.