1.  Field of Invention
This invention relates to communications systems.  Specifically, the present invention relates to systems and methods for calculating the log-likelihood ratio to facilitate optimal decoding in receivers employing pilot-assisted coherent demodulation. 
2.  Description of the Related Art
Cellular telecommunications systems are characterized by a plurality of mobile transceivers, such as mobile phones, in communication with one or more base stations.  Each transceiver includes a transmitter and a receiver. 
In a typical transceiver, an analog radio frequency (RF) signal is received by an antenna and downconverted by an RF section to an intermediate frequency (IF).  Signal processing circuits perform noise filtering and adjust the magnitude of the signal via analog automatic gain control (AGC) circuitry.  An IF section then mixes the signal down to baseband and converts the analog signal to a digital signal.  The digital signal is then input to a baseband processor for further signal processing to output voice or data. 
Similarly, the transmitter receives a digital input from the baseband processor and converts the input to an analog signal.  This signal is then filtered and upconverted by an IF stage to an intermediate frequency.  The gain of the transmit signal is adjusted and the IF signal is upconverted to RF in preparation for radio transmission. 
The link between a transmitter and a receiver is a channel.  One approach to increasing the information-carrying capacity of a channel between a base station and associated mobile stations is to enhance the signal-to-interference ratio (SIR).  The SIR is often expressed as a ratio of the energy per information bit received to the interference density of the received signal.  To increase system capacity, receivers in the mobile stations and base stations must effectively operate at lower signal-to-interference ratios (SIRs), or the SIR of the channel must be increased.  To increase the SIR, the power of the transmitted signal is often increased, which is costly, increases the interference to other mobiles, and, thus, is impractical in many applications.  Alternatively, special coding schemes are often employed in order to reduce the required SIR. 
Coding for communications signals involves the addition of redundant information to the signals.  By strategically adding redundancy to communications signals transmitted in noisy environments, errors introduced by a noisy channel are reduced to a desired level.  As shown by Shannon in 1948, if the information rate of the communications signals is less than the channel capacity, the desired noise level is attainable without a reduction of the information rate.  If redundancy is not employed in a noisy environment, error-free performance is difficult or impossible to obtain. 
Many encoding and decoding systems are designed to control noise and interference related errors that occur during transmission of information in a communications system.  Coding is an important consideration in the design of highly reliable modern digital communications systems. 
The ability to operate efficiently in noisy or faded environments is particularly important in code division multiple access (CDMA) wireless communications systems where Raleigh-faded signal environments and co-channel interference from other users are common.  Raleigh fading results from Doppler frequency shifts in the received signal due to mobile station movement.  Co-channel interference occurs when a CDMA communications system maintains multiple system users, with each additional user contributing incrementally to the co-channel interference.  Co-channel interference is typically larger than other forms of channel noise such as additive white Gaussian noise (AWGN). 
In a Raleigh-faded signal environment, the power levels of transmitted communications signals fluctuate in accordance with a Raleigh distribution.  The power typically fluctuates over a dynamic range of 10 dB to 50 dB. The duration of the fades is a function of the velocity of a mobile station, i.e., cellular telephone, the frequency channel assigned to the mobile station, and overall signal environment.  As the velocity of a mobile unit increases, fade duration decreases, leading to shorter error bursts.  As the velocity of the mobile unit decreases, fade duration increases, leading to longer error bursts. 
To improve the performance of a wireless communications system in a noisy and Raleigh-faded environment, interleavers following signal encoders are often employed.  An interleaver spreads the codewords output from an encoder so that individual bits of a given codeword are separated from each other and transmitted at different times.  As a result, individual bits of a given code experience independent fading, where the bits affected by an error burst belong to several codewords.  At the receiver, the received signal samples are deinterleaved before decoding.  Thus, the effect of the error burst is spread over the message so that it is possible to recover the data with the original error-correcting code.  Several types of interleavers exist, including diagonal, convolutional, interblock, and block interleavers. 
Turbo codes are serial or parallel concatenations of two or more constituent codes, separated by one or more code interleavers.  Turbo encoders and decoders are often employed to improve error control and to reduce the required SIR.  Turbo codes are often decoded with a relatively efficient iterative algorithm to achieve low error rates at signal-to-noise (SNR) ratios approaching the Shannon limit.  As an essential part of the Turbo code, code interleavers and deinterleavers must be inserted between the component code encoders and decoders, respectively.  The performance of turbo codes depends on the length and structure of the code interleavers.  Good turbo code performance can be achieved by using interleavers having pseudo random structures. 
Turbo decoders and convolutional decoders use the log-likelihood ratio (LLR) for the received signal to maximize decoder performance.  An LLR is a probability metric used by a decoder to determine whether a given symbol was transmitted given a particular received signal.  The LLR requires an accurate estimate of the channel coefficient, which is a measure of a complex scale factor applied to the transmitted signal by the channel.  Accurate LLR values are particularly important in turbo decoding applications where the LLR inputs are typically subjected to non-linear operations that can amplify inaccuracies in the LLR values and result in unacceptable decoder performance. 
Existing methods for calculating the LLR fail to properly account for uncertainty in the estimate of the channel coefficient, which results in sub-optimal detection and decoding.  Conventional receiver systems employing turbo codes achieve optimal decoding only when the channel coefficient is accurately known.  However, in practice, the channel coefficient is seldom known exactly, and only a channel estimate is available. 
To obtain an estimate of the channel, i.e., channel coefficient, which is typically subjected to Raleigh fading, a reference signal (i.e., a pilot signal) is often broadcast with a data signal.  The pilot signal is a predetermined sequence (typically a constant signal) broadcast by the transmitter over the channel to the receiver. 
A base station often broadcasts different data signals together with a common pilot signal to be sent to subscribers operating mobile stations within the coverage area of the base station.  The mobile stations use the pilot signal to establish the phase and magnitude of a channel estimate, which are necessary for performing coherent detection of the associated data signals.  The mobile station also transmits a pilot signal together with its traffic data signal.  The mobile's pilot signal is used by the base station to perform coherent demodulation in a similar manner as described above. 
The process of recovering a transmitted signal from a received modulated signal using a synchronized oscillator and pilot signal is called pilot assisted coherent demodulation.  To achieve effective coherent detection, pilot assisted coherent CDMA communications systems must generate accurate channel estimates from the received pilot signal. 
Theoretically, the channel equally impacts both the pilot signal and the data signal.  The receiver provides an estimate of the channel coefficient based on the known pilot signal and the received pilot signal and provides an estimate of the channel coefficient in response thereto.  The estimate of the channel coefficient is used to calculate the LLR value.  However, the channel estimate has an error factor.  The error factor may become unacceptably large when the channel is characterized by rapid or deep fades.  The resulting inaccuracies are particularly problematic for communications systems employing turbo codes, where inaccuracies in the LLR can result in significantly degraded performance. 
Currently, channel estimates are employed in LLR calculation circuits and corresponding methods.  Unfortunately, these circuits and methods typically fail to account for uncertainty in the estimate of the channel.  The channel is often subjected to deep and rapid Raleigh fading, which can result in erroneous channel estimates and poor decoding performance due sub-optimal log-likelihood ratios based on the channel estimates. 
Hence, a need exists in the art for an optimal method for decoding a received signal in systems employing pilot assisted coherent demodulation.  There is a further need for an efficient system that can accurately compute the log-likelihood ratio while taking into account uncertainty in the estimate of the channel.