The Propagation Group Design of a GHz PN Generator -3 -Introduction Wireless systems have become a dominant presence in our lives. From voice communication to data transmission and general connectivity, wireless options existed that allow greater mobility and freedom than their wired counterparts. As more time and money was invested in the wireless industry, products began to show up on the market ranging from cell phones to wireless LAN devices to ad hoc Bluetooth type devices. With the growing need for more bandwidth and increased data rates, in combination with the saturation of existing wireless channels, the FCC is considering opening new spectrums centered at several tens of Gigahertz. While technology has allowed us to push the envelopes of the frequency spectrum and utilize ever-increasing frequencies for communication, our understanding of the propagation characteristics of such high frequency channels has lagged behind. The task proposed for this undergraduate research project was the design and construction of a Gigahertz sliding correlator channel sounder, an instrument used for the characterization and analysis of wireless channels [1]. This project greatly mirrors the work done by Chris R. Anderson as detailed in his Master’s thesis, which has served as an excellent reference for much of the information in this document [1]. The Multipath Problem At very low frequencies, wireless transmission may approach the textbook concept of transmitting and receiving a single signal [1]. However, as clock rates go up, so does the complexity of wireless transmission. Electromagnetic waves reflect, diffract, and scatter, alleviating the need for direct line of sight between transmitter and receiver, but also creating the complicated multipath problem. Multipath is the nearly infinite number of paths that a signal can take from transmitter to receiver, reflecting off smooth objects, scattering off rough objects, and diffracting around sharp corners [1]. When a high frequency signal is transmitted, it is received not once, but several times at the receiver. Signals that bounce around in the environment and have longer overall path lengths take a longer to reach the receiver. The more the signal bounces off and around objects along a given path, the longer it takes to reach the receiver and, generally speaking, the more it is attenuated. Introduction to Spread Spectrum The channel sounder works by sending a broadband signal over a given channel using a technique called “spread spectrum” [1]. Spread spectrum originated as a means of secure communication for the military, spreading a signal out in the frequency domain to give it a very low peak power. To observers, a spread spectrum signal looks similar to white noise, and thus has a Low Probability of Intercept (LPI). The noise-like properties of a spread spectrum signal are achieved by modulating the signal with a pseudo-random noise (PN) code, which is a pseudo-random binary sequence. PN codes are generated by shift registers configured with linear feedback taps, and this will be detailed in a later section. The PN code exhibits some interesting properties, which will be noted for the sake of completeness. 1) The Maximal Length Linear Shift Register (MLSR) sequence has a period of L chips, with L = 2N – 1. (That is, an N bit shift register can generate a PN code of L bits, where the maximum value of L is 2N – 1.)The Propagation Group Design of a GHz PN Generator -4 -2) The statistical distribution of “1’s” and “0’s” is the same as in a random sequence with the exception that the total number of “1’s” is always one larger than the total number of “0’s”, independent of the length of the code. (Note that this implies only codes of odd length are possible.) 3) The modula-2 sum of any m-sequence with a shifted version of itself produces another shifted version of the same sequence. 4) All possible N-bit words will appear in the sequence exactly once, except for the all-zeros combination. (The all-zeros combination should never occur because the shift register will become locked in this state.) 5) The autocorrelation of the PN sequence is given by Rxx(τ): ()⎪⎭⎪⎬⎫⎪⎩⎪⎨⎧>≤−=⎟⎠⎞⎜⎝⎛∆⎟⎟⎠⎞⎜⎜⎝⎛−∆⎟⎠⎞⎜⎝⎛+−=∑∞=−∞=cccccxxTtTttTTLTLLR,0,1trate) chip theasknown (also rateclock theis 111ττττlll The spectrum of the PN code follows a sinc2(f) envelope, with the nulls occurring at integral multiples of the clock frequency [1]. The spectrum is made up of discrete peaks between envelope nulls. The number of peaks between nulls is given by L – 1 where L is the length of the PN sequence. Figures 1 and 2 show the spectrum and autocorrelation of the PN code. Figure 1. Spectrum of an L = 7, fc = 1 kHz PN sequence.The Propagation Group Design of a GHz PN Generator -5 - Channel Sounder Fundamentals The sliding correlator channel sounder clocks the PN codes at very high frequencies to fill a wireless channel with noise-like content [1]. The PN codes are modulated onto the carrier frequency and transmitted across the channel. Some distance away, a receiver demodulates the signal and performs the “sliding correlation”. The received PN code, which is clocked by the transmitter at some frequency fT, is mixed with an identical PN code clocked by the receiver at some slightly slower frequency fR. Because the received PN code is clocked at a higher frequency than the PN code generated at the receiver, the received code slides past the slower receiver-generated code in time. When the faster code slides past the slower code such that they are momentarily perfectly aligned, the crosscorrelation will be very large. At points of poor alignment, the crosscorrelation will be -1/N. This was indicated by the autocorrelation of the PN code. A series of alignments due to the multipath environment will generate a series of triangular peaks in the crosscorrelation. This effectively is the impulse response of the channel. By taking the Fourier Transform of this impulse response, the frequency response of the channel may be found. PN Generator Overview The PN generator is based around a shift register configured with linear feedback [2]. Certain registers on the shift register are selected as feedback taps. The bits at these taps are XOR-ed together (modulo-2 addition). The output of the