Spatial Diversity Effect on the Experimental Gain of Capacity of the Outdoor Mobile Radio Channel in the 700 MHz Band

From measurements performed in the 700 MHz band, this paper analyzes the effect of spatial diversity on the channel capacity through the propagation of an OFDM mobile radio signal and compares with the results of a single branch providing what improvement of the capacity is attained with the SIMO system.

performing measurements in order to corroborate the simulations. Then, the purpose is to determine the channel capacity in a SIMO system from the experimental gain of spatial diversity on the reception of an OFDM mobile radio signal. To accomplish this, the paper follows with Section II, which describes the theoretical aspects necessary to calculate the channel capacity. Section III describes the transmission and reception systems and the measurement environment whereas Section IV provides the results. Section V presents the conclusions.

A. Mobile Radio Channel Transfer Function
The randomness of the mobile radio channel makes stochastic the transfer function h, that defines the behavior of the propagation channel [8]. Based on the measurements performed, this function is experimentally determined for the 760  10 MHz band in both diversity branches: transmitter-receiver 1 (TX-RX1) and transmitter-receiver 2 (TX-RX2). Based on [8,9] if the received signal passes through a filter matched to the transmitted signal (s(t)), the transfer function of the channel is the output of this filter when an impulsive input is used. Then, the filtering process is equivalent to a correlation process (RS), which will result in the instantaneous transfer function h(ti, ) of the channel probed along the delays: in which stands for delay, Ci is the complex amplitude of the received signal Ci = Re(s') + j Im(s') and s' is the quadrature signal measured at the reception by the signal analyzer. From h(ti,), the mean delay and delay spread parameters, which quantify the temporal dispersion of the signal in the transmission channel, can be determined. For this purpose, in each ti, instantaneous power delay profiles are calculated from [8]: The average delay ( ̅ ) is calculated as the first center moment, or the average, of the instantaneous power delay profile Ph(τ). Due to the discrete acquisition, Ph(i) is the relative power on the delay τi, with N representing the number of correlation peaks within a power delay profile (named PDP), which characterizes the valid multipath. Then, its definition is: The RMS delay spread (T) is the standard deviation of the probability density function, which characterizes the arrival time of the multipath in the receiver [8]. This is calculated by the square root of the second center moment, variance, of the power delay profile Ph(τ). In discrete form, the RMS delay spread is [8]: with  meaning the mean signal-to-noise ratio (SNR = S/PN) at the receiving antenna, h is the complex channel gain calculated as described previously, and B is the band of the signal. The same process occurs in memoryless wideband SIMO system, in which each reception channel is independent from the other. In this case, if  is a constant mean in the environment of a Gaussian noise, the maximum channel capacity, in bps, is calculated from: in which hi is the channel gain related to each branch of diversity, calculated from (1), therefore, |hi| 2 means the absolute value of the power delay profile, calculated from (2), and N is the number of receiving antennas. In a random time variant channel, the maximum capacity due to the diversity in a SIMO receiver (CSIMO) is [10]: with H meaning the N X 1 channel gain, H H is the transposed matrix of H, and N is the number of receiving antennas. If two diversity branches are used: in which H11 and H12 represent the channel gains on the diversity branches TX-RX1 and TX-RX2, respectively, i.e., H11 = ℎ 1 ( , ) and H12 = ℎ 2 ( , ). It is noteworthy that for different points, with different distances from the receiver to the transmitter, the value of the SNR will be different and the normalized gain of the channel will be different in each situation too.

III. SETUP SPECIFICATIONS AND MEASUREMENT ENVIRONMENT
The measurements were carried out in the neighborhood of Higienópolis, suburb of the city of Rio de Janeiro, Brazil, in a suburban environment with high vehicular traffic and many constructions, following the route shown in Fig.1

A. Measurement Setup Description
The systems specifications used in the channel sounding are in Table I   In order to obtain the mean signal-to-noise ratio  used in (8)  As the noise presents normal statistics, (5) and (8) are used, respectively, for calculating SISO and SIMO system capacity. Therefore, firstly the capacity (C/B) of each receiving branch is calculated from (5) and the results are in Fig. 6. It is worth remembering that the channel function is time-  Complementing the results, Table II Fig. 7 depicts the distributions that best fit the normalized capacity values for each antenna. For the antenna 1, the cumulative distributions that best fit to the data were the exponential, for the smaller capacity values, and the normal, for the larger values. For antenna 2, they were normal and Nakagami distributions. The last, with low-value for the parameter m (distribution parameter of Nakagami probability density function) [8] best fitted to the lowest normalized capacity values up to approximately 5 b/s/Hz. This distribution, with m values in the range 0.5 ≤ m < 1.0 indicates low SNR, worse than Rayleigh, that is, the power of the received signal is due to weaker multipath, without a dominant path, which explains the smaller values of the normalized capacity. The normal distribution was best adjusted for normalized capacity values greater than 5 b/s/Hz. Recalling that the normal distribution is a Rice distribution with factor K >> 1 [8], the environment is characterized by the presence of a dominant path, which suggests that there is sight to the transmitter.
For the calculation of the joint capacity, the profiles of the left (1) and right antennas (2), synchronized, corresponding to the points of the same coordinate, were accounted. After synchronization, the SIMO system capacity according to (8), or the "joint capacity" resulted in: For observing better the capacity gain of the SIMO system, Fig. 8 provides the difference between the joint capacity and the individual capacity of each antenna, showing that the diversity effect of the