Motivated by the fact that most existing research on multiuser CDMA capacity have focused on theoretical analysis with simplified system assumptions, in this work, we present a framework for capacity analysis of a WCDMA system with more realistic assumptions, which make the framework and results more valuable for the performance assessment of real cellular networks. Our main contributions are summarized as follows: − We provide a precise channel model reflecting practical operations of the uplink WCDMA physical (PHY) layer based on the 3GPP release 11 specification [
1]. Various realistic assumptions are included into the system such as: continuous-time waveform-transmitted signal and time-variant spreading and an asynchronous multi-code CDMA system with ISI over frequency-selective channels. It is worth noting that although the signal model is constructed based on a WCDMA system, the approach and framework can be extended or transferred to other wireless standards. − We derive sufficient statistics for decoding the transmitted symbols based on the continuous-time-received signal, which provides us an equivalent discrete-time signal model. A matrix representation of channel model is provided for which the equivalent additional noise is shown to be a Gaussian distributed random vector. − Since sufficient statistics preserve the mutual information ([
25], Chap. 2), the capacity is then derived using the equivalent discrete-time signal model. In particular, we characterize the capacity region when the input signal is fixed to finite constellations, e.g., PSK, QAM, and so on, with a uniform input distribution, which are widely used in current real cellular networks. Additionally, we provide the capacity region when the input signal follows a Gaussian distribution, which is the optimal input distribution for additive Gaussian noise channels. Accordingly, the Gaussian capacity offers a capacity outer bound for the real WCDMA cellular networks using finite constellation input. − Due to the data-processing inequality ([
25], Chap. 2), the mutual information between input and output cannot increase through any post-processing at the receiver. Given the capacity bounds measured directly at the receive antenna of a real system, we can now assess the capacity loss due to a specific post-processing at the receiver. Therewith, we investigate the capacity loss due to sampling, which is a traditional discretization approach in practical systems. Note that in the real cellular networks, since the sampling window is finite, perfect reconstruction of a band-limited signal is not guaranteed even if the sampling rate is equal to Nyquist rate ([
26], Chap. 8). The assessment of such impact on the capacity is also considered in this work. − We analyze the asymptotic sum-capacity when the signal-to-noise ratio (SNR) goes to infinity, for which we derive the conditions on the signature waveform space so that on every link to the base station, the individual capacities are achieved simultaneously. To this end, we first derive the
sufficient condition, which holds for all kinds of input signals including signals based on finite and infinite constellations. Next, once again, we motivate our study from a practical perspective by focusing on the finite constellation input signal. Accordingly, a
necessary condition to simultaneously achieve the individual capacities with a finite constellation input signal, which takes the signal constellation structure into account, is derived. Those results are particularly useful for spreading sequence design in a real WCDMA cellular network.
The rest of the paper is organized as follows: Section
2 presents the signal model where sufficient statistics and an equivalent matrix representation are derived. In Section
3, the capacity analysis is provided considering finite constellations and Gaussian-distributed input signals. The capacity employing sampling is also investigated in this section. The asymptotic capacity when the SNR goes to infinity is analyzed and discussed in Section
4. Finally, Section
5 concludes the paper.