Direct Sequence CDMA

Prerequisites:

Given:

A direct sequence signal. The spreading factor is 7. Rectangular bit pulses and chip waveforms are chosen. The modulation is antipodal: a "1" and a "0" use opposite phases of transmit signal. The transmit power is 1 watt.
The radio channel has (baseband equivalent) impulse response

      h(t) = A [d(t) + 0.5 j d(t- 1 msec) + 0.25 d(t- 2msec)]

The path attenuation A is such that the power received over the first path (thus over Ad(t) ) is 10-10 watt. The noise floor of the system is N0 = 10-16 watt/Hz.

Problems:

How many resolvable paths has this channel at maximum?

What is the minimum required chip rate rc to resolve all possible paths? What is the user bit rate in this case? In the next questions, we will further use this chip rate and user data rate.

Design a rake receiver. In particular, what should be the weight factors for the different fingers?

What is the SNR in each of the fingers and at the output of the rake?

What would be the SNR expressed in received power divided by the total noise in the transmit bandwidth? Assume that the transmit bandwidth is approximately equal to the chip rate.

What is the BER? Which SNR should you use to calculate ther BER?

If non-spread, narrowband transmission were used, depending on the carrier frequency chosen, the received signal power would vary between 0.25 10-10 and 1.75 10-10 watt.
What SNR's correspond to this range? How does it compare to the performance DS-CDMA with rake receiver?

Assume that the channel is Rayleigh fading. The local-mean signal-to-noise ratios in the fingers of the rake are equal to the (fixed) values computed above for the rake receiver.

The next questions address the selection of the spreading code.

For the spreading codes 1110010 or 1110100, show that both are maximal length Linear Feedback Shift Register (LFSR) sequences. For each code, determine a LFSR that generates the code.

What is the autocorrelation for these codes?

Show that in this DS-CDMA link, intersymbol interference (ISI) can occur due to the channel dispersion.

Which code has the least ISI?