Cyclic Code Shift Keying (CCSK) is a non-orthogonal signaling scheme consisting of the 32 phases of a 32-chip sequence. Each symbol represents 5 bits of data and indicates which phase of the base sequence to transmit. For example, generating the transmitted symbol corresponding to the data word 00010 requires a two position left cyclic shift of the base sequence. The sequence used in this project is 01111100111010010000101011101100.

In order to improve performance in environments with multipath and multiple-access interference, the signal is modulated by a signature sequence before transmission. In a multiple-access scenario, multiple signature sequences would be used. For example with several transmitters and one receiver, each transmitter would have a unique sequence.

In traditional direct-sequence spread spectrum (DSSS) systems, the signature sequence has a higher chip rate than the data sequence. The signature sequence, referred to in these cases as a spreading sequence, increases the bandwidth of the signal. In this project, though, the signature sequence has the same chip duration as the CCSK signals and therefore does not contribute to the spreading of the signal.

In this project the performance of CCSK is examined in noisy, multipath, and multiple-access environments. 32-ary orthogonal signaling in a noisy, interference-free environment provides a benchmark for the results.

CCSK is the modulation scheme used by the military's Link-16 system, which is used for communication between terminals, such as two fighter aircraft. CCSK was chosen because a receiver requiring less hardware than a traditional bank of 32 matched-filters exists. When the system was devised, this simplicity was a big gain over 32-ary orthogonal signaling. Link-16 also uses a signature sequence with the same chip duration as the data sequence and uses the same base sequence mentioned above. The signature sequence of Link-16 changes in order to keep the transmitted data secure, but to protect against multipath and multiple access interference, the signature sequences only need to have good autocorreation and crosscorrelation properties and a period much larger than the signal duration. It has been suggested that a non-spreading signature sequence be used in wireless LAN systems, where one can expect to encounter multipath interference.

In U.S. patent number 5,809,060, Cafarella and Fischer claim that the cyclic nature of CCSK could cause problems in the presence of multipath interference because a delayed version of a symbol would correlate well with the wrong signal. This should not be the case, though, because of the signature sequence. Examining the validity of the claim is one reason for investigating the performance of CCSK with a signature sequence across a multipath channel.

The performance measure of interest is the probability of a symbol error. The probability of error is a function of E_b/N_0, which is the ratio of the energy per bit to the one-sided noise spectral density, and the interference level, which is the voltage ratio of the direct-path signal to the reflected-path signal. The non-orthogonal signal set makes it difficult to compute the probability of error, so simulations were used instead. The probabilities of error for the orthogonal signal set, used for comparison, come from the formula for the probability of error of 32-ary orthogonal signaling with a coherent receiver.

The effectiveness of an alternate CCSK receiver relative to the standard matched-filter bank receiver is also of interest. The alternate receiver consists of three filters, each matched to the first 63 chips of two periods of the base CCSK signal. The input to the receiver is sent to one of the three filters for the duration of a symbol. The kth received symbol is sent to filter k mod 3, where the filters are numbered zero through two. The inputs to the filters are gated so that each filter processes a waveform of duration T followed by a blank interval of duration 2T, where T is the duration of a CCSK symbol. The output of each filter is sampled at 32 evenly spaced time offsets starting at T and ending at 2T - Tc, where Tc is the duration of a chip. The 32 samples become the decision statistics, and the largest sample designates the estimate of the transmitted symbol. The properties of this receiver are examined analytically rather than experimentally.

The simulations were performed in MATLAB using Simulink models. The models use discrete-time sequences to simulate the continuous-time signals in the actual system. The discrete-time sequences have 10 samples per chip of the continuous-time symbols, which was verified to be adequate.

The signal set consists of the 32 CCSK signals, each scaled to have unit energy. For the multipath and multiple-access simulations, each signal in the set is multiplied by the current 32-chip segment of a signature sequence. The sequence used is a period 1023 maximal-length linear feedback shift register sequence (m-sequence) generated by the polynomial .

Symbols for the data signal are chosen randomly from the set for transmission across the channel, which adds Gaussian white noise and, for multipath and multiple access channels, an interfering signal to the transmitted signal. Multipath interference is generated by adding an attenuated, delayed copy of the transmitted signal prior to adding the noise. The delays are multiples of the chip duration. The multiple access interference is generated by attenuating randomly selected signals from an alternate set, consisting of the same symbols with a different m-sequence mask. The polynomial generates the sequence used for the interference set. The multiple access interference and the data signal are chip synchronous.

Time-synchronization is assumed in the receiver, which has a bank of filters matched to the CCSK signals. The signals in the set have already been multiplied by the appropriate segment of the m-sequence, which is equivalent to multiplying only the received signal by the m-sequence segment. The receiver multiplies the received signal by each signal in the set and passes each output to an integrate-and-dump filter, which is sampled at the end of each symbol period to produce the decision statistics. The decision is determined by choosing the largest sample, which indicates the symbol that correlates best with the received symbol.

The system was simulated for a fixed number of symbol transmissions, and the errors were counted. This process was then repeated until a minimum number of errors had occurred, after which the error rate was calculated. The final data was collected using 100 transmissions per run and minimum of 1000 errors.

The simulation methods were verified for correctness in two ways. The noise-only model was used for verification because it contained all of the components that needed to be checked. The signal set was replaced by an orthogonal signal set and the simulation was run with various values of . The probability of error for 32-ary orthogonal signaling is much less complex to compute than for CCSK, so the simulation results could be compared to the theoretical values.

The signal set was also replaced by one with only two of the CCSK signals. The results of the simulation were then compared with the theoretical values for the pairwise probability of error. These tests verify that the noise process and receiver behave as desired.

In a noise-only environment, CCSK yields error rates close to the theoretical values for 32-ary orthogonal signaling (Figure 1). The performance is judged according to the degradation, which is the amount E_b/N_0 must be adjusted in order to maintain a given error rate, measured relative to a base case. For CCSK across a noisy channel, orthogonal signaling is used for comparison. The degradation worsens as the error rate decreases, but maintaining a rate of 0.001 errors/transmission with CCSK only requires increasing E_b/N_0 by 0.04 dB compared to orthogonal signaling.

The error rates with multipath interference are shown in Figure 2. The reflected-path delays are fixed, and each curve shows a different direct-path to reflected-path power ratio. At an error rate of 0.001, the 4 dB, 6 dB, and 12 dB cases require E_b/N_0 increases of 2.1 dB, 1.21 dB, and 0.3 dB over the noise-only case, respectively. The degradation is illustrated better in Figure 3. The reflected-path delay does not appear to have an effect on the performance of the system. CCSK performance with multiple-access interference is the same as with multipath interference.

Analysis of the CCSK-specific receiver shows that, when implemented with three filters and the time-gating, it performs the same as the traditional receiver. The gating causes the input to be correlated with only one CCSK signal at each sample time. In practice a system might encounter sample timing errors, but the comparison of the two receivers in the presence of timing errors is beyond the scope of this project.

Analysis of the effects of timing errors on the two receivers would give a more realistic picture of their behavior in a system. Specifically, the alternate CCSK receiver might not perform as well as the standard matched-filter bank receiver, which might outweigh the reduced hardware required. Also, a practical system might use a non-coherent receiver instead of a coherent one, so the performance of CCSK with this type of receiver would be important.

For multipath environments, the performance of a rake receiver could be investigated. The one-to-one data to signature chip ratio protects against interference, but it might reduce the ability of a rake receiver to identify and use multipath components. A higher chip rate signature sequence might allow the reflected-path delay to be determined more easily, which would be important for wireless LAN systems.