Iterative decoding architecture with HARQ combining and soft decision directed channel estimation

Certain aspects of the present disclosure relate to a method for iterative decoding with re-transmissions of data and to a method for iterative decoding with soft decision directed channel estimation.

BACKGROUND

Certain aspects of the present disclosure generally relate to wireless communications and, more particularly, to iterative decoding with re-transmissions and to iterative decoding with soft decision directed channel estimation.

Iterative demodulation-decoding structure can be employed at a wireless receiver side to enhance error rate performance. Channel estimates that are utilized for receiver processing can be typically obtained based on a known pilot signal, while actual data are not used. Therefore, further improvement of the error rate performance can be achieved by refining the channel estimates during the iterative demodulation-decoding algorithm by using available reliability information associated with transmitted data.

On the other hand, the Hybrid Automatic Repeat Request (HARQ) approach can be applied in a wireless communications system to improve its quality of service (QoS). The QoS improvement can be achieved by re-transmitting data if a current level of QoS is below a defined threshold value. It is proposed in the present disclosure to efficiently combine the HARQ approach with the iterative demodulation-decoding receiver structure.

SUMMARY

Certain aspects provide a method for wireless communications. The method generally includes receiving at least one data stream, de-mapping and decoding the received data stream in an iterative manner to compute a set of a posteriori log-likelihood ratios (LLRs) of bits of the received data stream, storing the computed set of a posteriori LLRs, if the decoding is performed in the iterative manner a defined number of times, receiving re-transmitted the data stream, and de-mapping and decoding the received re-transmitted data stream in the iterative manner using the stored set of LLRs.

Certain aspects provide an apparatus for wireless communications. The apparatus generally includes a receiver configured to receive at least one data stream, a de-mapper and a decoder configured to de-map and decode the received data stream in an iterative manner to compute a posteriori log-likelihood ratios (LLRs) of bits of the received data stream, and a buffer configured to store the computed a posteriori LLRs, if the decoding is performed in the iterative manner a defined number of times, wherein the receiver is also configured to receive re-transmitted data stream, and wherein the de-mapper and the decoder are also configured to de-map and decode the received re-transmitted data stream in the iterative manner using the stored set of LLRs.

Certain aspects provide an apparatus for wireless communications. The apparatus generally includes means for receiving at least one data stream, means for de-mapping and decoding the received data stream in an iterative manner to compute a posteriori log-likelihood ratios (LLRs) of bits of the received data stream, means for storing the computed a posteriori LLRs, if the decoding is performed in the iterative manner a defined number of times, means for receiving re-transmitted the data stream, and means for de-mapping and decoding the received re-transmitted data stream in the iterative manner using the stored set of LLRs.

Certain aspects provide a computer-program product for wireless communications. The computer-program product includes a computer-readable medium comprising instructions executable to receive at least one data stream, de-map and decode the received data stream in an iterative manner to compute a posteriori log-likelihood ratios (LLRs) of bits of the received data stream, store the computed a posteriori LLRs, if the decoding is performed in the iterative manner a defined number of times, receive re-transmitted data stream, and de-map and decode the received re-transmitted data stream in the iterative manner using the stored set of LLRs.

Certain aspects provide a wireless node. The wireless node generally includes at least one antenna, a receiver configured to receive at least one data stream via the at least one antenna, a de-mapper and a decoder configured to de-map and decode the received data stream in an iterative manner to compute a posteriori log-likelihood ratios (LLRs) of bits of the received data stream, and a buffer configured to store the computed a posteriori LLRs, if the decoding is performed in the iterative manner a defined number of times, wherein the receiver is also configured to receive re-transmitted data stream via the at least one antenna, and wherein the de-mapper and the decoder are also configured to de-map and decode the received re-transmitted data stream in the iterative manner using the stored set of LLRs.

Certain aspects provide a method for wireless communications. The method generally includes receiving a pilot signal and at least one data stream transmitted over a wireless channel, computing initial estimates of the wireless channel using the received pilot signal, de-mapping, de-rate matching and decoding the received data stream using the computed initial estimates of the wireless channel to compute a set of log-likelihood ratios (LLRs) of transmitted bits of the at least one data stream, updating estimates of the wireless channel using the computed set of LLRs and the computed initial estimates of the wireless channel, and de-mapping, de-rate matching and decoding the received data stream using the updated estimates of the wireless channel.

Certain aspects provide an apparatus for wireless communications. The apparatus generally includes a receiver configured to receive a pilot signal and at least one data stream transmitted over a wireless channel, an estimator configured to compute initial estimates of the wireless channel using the received pilot signal, and a de-mapper, a de-rate matching circuit and a decoder configured to de-map, de-rate match and decode the received data stream using the computed initial estimates of the wireless channel to compute a set of log-likelihood ratios (LLRs) of transmitted bits of the data stream, wherein the estimator is also configured to update estimates of the wireless channel using the computed set of LLRs and the computed initial estimates of the wireless channel, and wherein the de-mapper, the de-rate matching circuit and the decoder are also configured to de-map, de-rate match and decode the received data stream using the updated estimates of the wireless channel.

Certain aspects provide an apparatus for wireless communications. The apparatus generally includes means for receiving a pilot signal and at least one data stream transmitted over a wireless channel, means for computing initial estimates of the wireless channel using the received pilot signal, means for de-mapping, de-rate matching and decoding the received data stream using the computed initial estimates of the wireless channel to compute a set of log-likelihood ratios (LLRs) of transmitted bits of the data stream, means for updating estimates of the wireless channel using the computed set of LLRs and the computed initial estimates of the wireless channel, and means for de-mapping, de-rate matching and decoding the received data stream using the updated estimates of the wireless channel.

Certain aspects provide a computer-program product for wireless communications. The computer-program product includes a computer-readable medium comprising instructions executable to receive a pilot signal and at least one data stream transmitted over a wireless channel, compute initial estimates of the wireless channel using the received pilot signal, de-map, de-rate match and decode the received data stream using the computed initial estimates of the wireless channel to compute a set of log-likelihood ratios (LLRs) of transmitted bits of the data stream, update estimates of the wireless channel using the computed set of LLRs and the computed initial estimates of the wireless channel, and de-map, de-rate match and decode the received data stream using the updated estimates of the wireless channel.

Certain aspects provide a wireless node. The wireless node generally includes at least one antenna, a receiver configured to receive via the at least one antenna a pilot signal and at least one data stream transmitted over a wireless channel, an estimator configured to compute initial estimates of the wireless channel using the received pilot signal, and a de-mapper, a de-rate matching circuit and a decoder configured to de-map, de-rate match and decode the received data stream using the computed initial estimates of the wireless channel to compute a set of log-likelihood ratios (LLRs) of transmitted bits of the data stream, wherein the estimator is also configured to update estimates of the wireless channel using the computed set of LLRs and the computed initial estimates of the wireless channel, and wherein the de-mapper, the de-rate matching circuit and the decoder are also configured to de-map, de-rate match and decode the received data stream using the updated estimates of the wireless channel.

DETAILED DESCRIPTION

An Example Wireless Communication System

The techniques described herein may be used for various broadband wireless communication systems, including communication systems that are based on an orthogonal multiplexing scheme and a single carrier transmission. Examples of such communication systems include Orthogonal Frequency Division Multiple Access (OFDMA) systems, Single-Carrier Frequency Division Multiple Access (SC-FDMA) systems, Code Division Multiple Access (CDMA), and so forth. An OFDMA system utilizes orthogonal frequency division multiplexing (OFDM), which is a modulation technique that partitions the overall system bandwidth into multiple orthogonal sub-carriers. These sub-carriers may also be called tones, bins, etc. With OFDM, each sub-carrier may be independently modulated with data. An SC-FDMA system may utilize interleaved FDMA (IFDMA) to transmit on sub-carriers that are distributed across the system bandwidth, localized FDMA (LFDMA) to transmit on a block of adjacent sub-carriers, or enhanced FDMA (EFDMA) to transmit on multiple blocks of adjacent sub-carriers. In general, modulation symbols are sent in the frequency domain with OFDM and in the time domain with SC-FDMA. A CDMA system may utilize spread-spectrum technology and a coding scheme where each transmitter (i.e., user) is assigned a code in order to allow multiple users to be multiplexed over the same physical channel. The CDMA system may utilize, for example, Wideband Code Division Multiple Access (W-CDMA) protocol, High Speed Packet Access (HSPA) protocol, evolved Speed Packet Access (HSPA+) protocol, etc.

An access point (“AP”) may comprise, be implemented as, or known as NodeB, Radio Network Controller (“RNC”), eNodeB, Base Station Controller (“BSC”), Base Transceiver Station (“BTS”), Base Station (“BS”), Transceiver Function (“TF”), Radio Router, Radio Transceiver, Basic Service Set (“BSS”), Extended Service Set (“ESS”), Radio Base Station (“RBS”), or some other terminology.

FIG. 1illustrates an example of a wireless communication system100in which embodiments of the present disclosure may be employed. The wireless communication system100may be a broadband wireless communication system. The wireless communication system100may provide communication for a number of cells102, each of which is serviced by a base station104. A base station104may be a fixed station that communicates with user terminals106. The base station104may alternatively be referred to as an access point, a Node B or some other terminology.

FIG. 1depicts various user terminals106dispersed throughout the system100. The user terminals106may be fixed (i.e., stationary) or mobile. The user terminals106may alternatively be referred to as remote stations, access terminals, terminals, subscriber units, mobile stations, stations, user equipment, etc. The user terminals106may be wireless devices, such as cellular phones, personal digital assistants (PDAs), handheld devices, wireless modems, laptop computers, personal computers, etc.

A variety of algorithms and methods may be used for transmissions in the wireless communication system100between the base stations104and the user terminals106. For example, signals may be sent and received between the base stations104and the user terminals106in accordance with CDMA technique. If this is the case, the wireless communication system100may be referred to as a CDMA system.

A communication link that facilitates transmission from a base station104to a user terminal106may be referred to as a downlink (DL)108, and a communication link that facilitates transmission from a user terminal106to a base station104may be referred to as an uplink (UL)110. Alternatively, a downlink108may be referred to as a forward link or a forward channel, and an uplink110may be referred to as a reverse link or a reverse channel.

A cell102may be divided into multiple sectors112. A sector112is a physical coverage area within a cell102. Base stations104within a wireless communication system100may utilize antennas that concentrate the flow of power within a particular sector112of the cell102. Such antennas may be referred to as directional antennas.

FIG. 2illustrates various components that may be utilized in a wireless device202that may be employed within the wireless communication system100. The wireless device202is an example of a device that may be configured to implement the various methods described herein. The wireless device202may be a base station104or a user terminal106.

The wireless device202may also include a housing208that may include a transmitter210and a receiver212to allow transmission and reception of data between the wireless device202and a remote location. The transmitter210and receiver212may be combined into a transceiver214. A single or a plurality of transmit antennas216may be attached to the housing208and electrically coupled to the transceiver214. The wireless device202may also include (not shown) multiple transmitters, multiple receivers, and multiple transceivers.

The wireless device202may also include a signal detector218that may be used in an effort to detect and quantify the level of signals received by the transceiver214. The signal detector218may detect such signals as total energy, energy per subcarrier per symbol, power spectral density and other signals. The wireless device202may also include a digital signal processor (DSP)220for use in processing signals.

The various components of the wireless device202may be coupled together by a bus system222, which may include a power bus, a control signal bus, and a status signal bus in addition to a data bus.

FIG. 3illustrates an example of a transmitter300that may be used within a wireless communication system100that utilizes CDMA. Portions of the transmitter300may be implemented in the transmitter210of a wireless device202. The transmitter300may be implemented in a base station104for transmitting data302to a user terminal106on a downlink108. The transmitter300may also be implemented in a user terminal106for transmitting data302to a base station104on an uplink110.

Data302to be transmitted represent a plurality of signals dedicated to different user terminals106. Each signal from the plurality of signals may be spread in a spreading unit306by corresponding spreading code from a set of orthogonal spreading codes304. The plurality of spread signals dedicated to different user terminals106may be summed to generate a cumulative signal308. The cumulative signal308to be transmitted is shown being provided as input to a mapper310. The mapper310may map the data stream308onto constellation points. The mapping may be done using some modulation constellation, such as binary phase-shift keying (BPSK), quadrature phase-shift keying (QPSK),8phase-shift keying (8PSK), quadrature amplitude modulation (QAM), etc. Thus, the mapper310may output a symbol stream312, which may represent an input into a preamble insertion unit314.

The preamble insertion unit314may be configured for inserting a preamble sequence at the beginning of the input symbol stream312, and may generate a corresponding data stream316. The preamble may be known at the receiver and may be utilized for time and frequency synchronization, channel estimation, equalization and channel decoding. The output316of the preamble insertion unit314may then be up-converted to a desired transmit frequency band by a radio frequency (RF) front end318. At least one antenna320may then transmit a resulting signal322over a wireless channel.

Certain aspects of the present disclosure support an iterative decoding architecture with sophisticated channel estimation that may be implemented within the receiver212. The proposed iterative receiver structure may be also efficiently used at the receiver212for processing data re-transmissions in the case of Hybrid Automatic Repeat Request (HARQ) communication mode.

Iterative Receiver Structure

Iterative demodulation-decoding approach may be applied at a wireless receiver to enhance its error rate performance. The iterative receiver algorithm may comprise two steps that can be performed repeatedly in an interleaved fashion. In one step, a posteriori probability for every transmitted bit may be extracted. For example, a posteriori log likelihood ratio (LLR) information may be obtained after certain number of iterations of outer Turbo decoder on one or more data streams. In another step, the LLR of every transmitted bit may be generated.

In the very first iteration, LLRs may be generated directly from the received signal. For subsequent iterations, the extrinsic part of the a posteriori LLRs along with the received signal may be used to generate new LLRs for the next iteration.

FIG. 4illustrates an example receiver structure400based on iterative demodulation-decoding algorithm that may be used within a wireless communication system100. The iterative structure400may be an integral part of the receiver212fromFIG. 2. The proposed iterative structure400is based on LLR extraction jointly performed by a demapper406and a Turbo decoder420.

At least one data stream of symbols transmitted over a wireless channel may be received and stored in a write controller buffer (WCB)401. The iterative receiver structure400may comprise the demapper (i.e., demodulator)406and the Turbo decoder420that can be iteratively interfaced. A Turbo joint log-likelihood ratio (JLLR) demodulation unit404may generate a posteriori LLRs410of transmitted bits based on received samples402and based on a priori LLRs408. Extrinsic LLRs412may be obtained by subtracting the a priori LLRs408from the a posteriori LLRs410.

The extrinsic LLRs412may be processed by a de-rate matching (DRM) unit414to generate a priori LLRs416of an appropriate rate as input to the Turbo decoder420. A Turbo decoding (TD) unit418may provide hard values of decoded bits428. In order to improve error rate performance, outer feedback may be employed between the Turbo decoder420and the demapper406. The TD unit418may generate a posteriori LLRs422that represent soft values of transmitted bits of the at least one data stream, while extrinsic LLRs424may be obtained by subtracting the a priori LLRs416from the a posteriori LLRs422.

The extrinsic LLRs424may be processed by a rate matching (RM) unit426to obtain the a priori LLRs408of an appropriate rate. The a priori LLRs408may be utilized by the demodulator406in the next iteration. LLRs associated with a systematic portion of the transmitted bits and LLRs associated with a parity (i.e., redundant) portion of the transmitted bits may be extracted from the extrinsic LLRs424. The extracted LLRs related to the systematic bits may be utilized for updating the a priori LLRs408for the next processing iteration between the demapper406and the decoder420.

It can be noted that the proposed iterative decoder architecture400is different from the well-known hard/soft serial interference cancellation (SIC) architecture. The hard/soft SIC architecture may only be used for multiple-input multiple-output (MIMO) systems, while the proposed iterative decoding architecture may be used for both MIMO and single-input single-output (SISO) systems.

Important feature of the proposed iterative decoder400is that the extrinsic output424from the Turbo decoder420may become the a priori probability (APP) input408for the demapper406for the next iteration. Similarly, the extrinsic output412from the demapper406may become the APP input416for the Turbo decoder420. For the very first iteration, APP input may not be available to the demapper406, and the LLR output410of the demapper406may be equal to the extrinsic output412.

Computation of Extrinsic Log Likelihood Ratios

FIG. 5illustrates an example block diagram of the demapper406fromFIG. 4that may generate extrinsic LLRs in accordance with certain aspects of the present disclosure. A received signal500may be whitened and stored in a write controller buffer (WCB) unit502. The stored whitened received signal504may represent an input into the JLLR demodulator unit404fromFIG. 4. Another input in the demapper406may be a matrix506of MIMO channel coefficients, and yet another input may be a priori LLRs508from the Turbo decoder420fromFIG. 4. The JLLR demodulator unit404fromFIG. 4may generate a posteriori LLRs510of transmitted coded bits. Extrinsic LLRs512may be obtained by subtracting the a priori LLRs508from the a posteriori LLRs510.

The system model may be represented as:
y=H·x+n,(1)
where x is a vector of transmitted symbols from one or more transmit antennas, y is the whitened signal504, H is the matrix506of channel coefficients, and n is a noise vector. It can be assumed a MIMO wireless system, while a single stream wireless system and a single-input single-output (SISO) wireless system may be considered as special cases of the MIMO wireless system.

The LLR output510for the bit bkfrom the vector of transmitted modulated symbols x may be written as:

It can be observed from equation (2) that the a posteriori LLR output of the demodulator may be composed of two parts, the APP information and the extrinsic information. After combining equation (3) with equation (2), the extrinsic LLR for the bit bkmay be written as:

where σn2is a noise variance.

It can be observed from equation (4) that each term that represents a distance between a received symbol y and a transmitted hypothesis x may be shifted by adding APP LLRs. In addition, conversion of the APP LLRs into probabilities may not be required when utilizing the APP information.

The Max-Log MAP (MLM) solution may be obtained by replacing the sum operation in equation (4) by a maximum operation, as given by:

Iterative Decoding with HARQ Combining

FIG. 6illustrates an example iterative receiver600with Hybrid Automatic Repeat Request (HARQ) combining in accordance with certain aspects of the present disclosure. It can be observed that the receiver600is based on the iterative receiver400fromFIG. 4, where a pre-Turbo decoding (pre-TD) buffer632and a post-TD buffer636may be incorporated to efficiently support re-transmission of data in the case when the decoding is not successful.

For the first transmission of data, a structure and processing path may be identical as the structure400illustrated inFIG. 4. In particular, an extrinsic log-likelihood ratio (LLR) output624from a Turbo decoder620may become an a priori probability (APP) input608for a demapper606and for a Turbo JLLR unit604for the next processing iteration. Similarly, an extrinsic LLR output612from a demapper606may become an APP input616for the Turbo decoder620and for a Turbo decoding unit618.

At the last outer iteration between the demapper606and the Turbo decoder620of the first data transmission, the extrinsic LLR output634from the demapper606after being processed by a de-rate matching (DRM) unit614may be stored in the pre-TD buffer632. The stored LLRs may be utilized for possible HARQ combining during re-transmission of data in case when a cyclic redundancy check (CRC) at the output628of the Turbo decoder620fails after a defined number of outer iterations between the demapper606and the Turbo decoder620. Also, the Turbo decoder output LLRs622may be stored in the post-TD buffer636. The stored LLRs622may be then processed and used as APPs608for possible data re-transmission in the case when the CRC at the output628of the Turbo decoder620fails after the defined number of outer iterations of the first data transmission.

For the first iteration of the re-transmission, the LLRs622from the previous transmission stored in the post-TD buffer636may be directly utilized as APPs for the current re-transmission. On the other hand, the extrinsic LLR output634from the demapper606may be combined with the LLRs stored in the pre-TD buffer632(i.e., the LLRs saved during the previous transmission) as a part of the HARQ combining process. The output LLRs616may be then fed into the Turbo decoder620.

For the next iteration of the re-transmission, the extrinsic LLRs624from the Turbo decoder620may be first combined with the post-TD LLRs computed and stored during the previous data transmission. The combined LLRs638may be processed by a rate-matching (RM) unit626and then utilized as APPs608. The extrinsic output LLRs634from the demapper606may be combined with the LLRs stored in the pre-TD buffer632, and then fed again into the Turbo decoder620.

FIG. 7summarizes example operations700for iterative decoding with HARQ combining in accordance with certain aspects of the present disclosure. At710, at least one data stream may be received. At720, de-mapping and decoding of the received at least one data stream may be performed in an iterative manner. During the iterative process, a first set of LLRs of transmitted bits of the at least one data stream may be computed after each de-mapping step, while a second set of LLRs of the transmitted bits of the at least one data stream may be computed after each decoding step.

At730, the computed first set of LLRs may be saved for the next re-transmission of data, if the de-mapping has been performed a defined number of times. At740, the computed second set of LLRs may be saved for the next data re-transmission, if the decoding has been performed the defined number of times. At750, re-transmitted at least one data stream may be received. At760, de-mapping and decoding of the received re-transmitted at least one data stream may be performed in the iterative manner using the stored first and second set of LLRs.

FIG. 8illustrates another example of iterative receiver with HARQ combining in accordance with certain aspects of the present disclosure. The iterative receiver structure800may be utilized when considering HARQ with the purpose of saving a memory for storing LLRs from one data transmission to another. It can be observed fromFIG. 8that those LLRs822stored in the post-TD buffer832at the output of the Turbo decoder820may be used for both APP combining and for HARQ combining, as illustrated inFIG. 8by adders836and838, respectively. Therefore, the pre-TD buffer may not be required for HARQ combining In order to further save the memory, the post-TD buffer832may be utilized to save only systematic LLRs instead of all output LLRs822from the Turbo decoder820.

Soft Decision Directed Channel Estimation for Iterative Receiver

Certain aspects of the present disclosure support a soft decision directed channel estimation for the iterative receiver400fromFIG. 4.FIG. 9illustrates an example iterative receiver900with soft decision directed channel estimation in accordance with certain aspects of the present disclosure. The receiver structure900may comprise the iterative receiver structure400fromFIG. 4and a channel estimation block902.

For each data transmission, initial channel estimation may be obtained by processing a pilot signal transmitted over a pilot channel. In addition, at each iteration between the demapper406and the Turbo decoder420of the receiver400, rate-matched extrinsic LLRs408from the output of Turbo decoder420may be utilized to refine initial channel estimates. As illustrated inFIG. 9, the refined channel estimates904may be used in the next processing iteration by the Turbo JLLR404along with the received samples402.

FIG. 10illustrates example operations1000for iterative decoding with soft decision directed channel estimation in accordance with certain aspects of the present disclosure. At1010, a pilot signal and at least one data stream transmitted over a wireless channel may be received. At1020, initial estimates of the wireless channel may be computed using the received pilot signal. At1030, de-mapping and decoding of the at least one data stream may be performed using the computed initial estimates of the wireless channel, and a set of LLRs of transmitted bits of the at least one data stream may be computed during this process. At1040, estimates of the wireless channel may be updated using the computed set of LLRs and the previously computed initial channel estimates. At1050, de-mapping and decoding of the at least one data stream may be now performed using the updated estimates of the wireless channel. The process of updating the channel estimates may be repeated after de-mapping and decoding a defined number of times.

The soft decision directed channel estimation902is described below in greater detail. A MIMO-OFDM wireless system may be considered with M transmit antennas and N receive antennas. The total number of frequency tones (i.e., subcarriers) is denoted by K. The received signal at the arbitrary kthtone ykmay be expressed as:
yk=Hk·xk+nk, k=1,2, . . . ,K,(6)
where ykεCN×1, HkεCN×Mis a MIMO channel matrix associated with the kthtone, xkεCM×1represents transmitted symbols from all M transmit antennas at the kthtone, and nkεCN×1is a noise vector at the kthtone. Let hk,iεC1×M, iε1, 2, . . . , N denotes the ithrow of the MIMO channel matrix Hk. Then, equation (6) may be re-written as:

If all the K tones are grouped together in a matrix form, then equation (7) may be written as:

It can be noted that among the K tones, a portion of them may be training sequence used for channel estimation, while the rest may be used for actual data transmission. Let Xtdenotes the training portion of X constructed by removing all rows of X containing data, and ytdenotes the pilot tones among the received signal y. Then, the following may be written:
yt=Xt·h+nt.  (15)

For each transmitted sub-frame, the channel may be first estimated via the pilot channel using the received pilot signal. After the Turbo decoding is performed, the output soft LLR information on data tones may be utilized as extra information to refine the pilot-based channel estimates.

It can be assumed that E{h}=0. The linear minimum mean square error (LMMSE) channel estimator may be expressed as:
ĥ=A·yt.  (16)
By solving
E{(ĥ−h)·ytH}=0,  (17)
the LMMSE channel estimates may be obtained as:

h^=Rh⁢XtH⁡(Xt⁢Rh⁢XtH+Rnt)-1︸A·yt,(18)
where Rhand Rntare cross-correlation terms related to the channel vector h and to the noise vector nt. In addition, equation (18) may be written according to the matrix inversion lemma as:
ĥ=(XtHRnt−1Xt+Rh−1)−1XtHRut−1yt.  (19)

Equation (18) may have the computational advantage over equation (19) since the dimension of matrix inversion in the former may be in general smaller than the dimension of matrix inversion in the latter. As described later in greater detail, the pilot-based channel estimation obtained as in equation (18) may be set as the initial mean value in the following iterations, if an affine soft decision directed channel estimator is employed.

It can be noted from both equation (18) and equation (19) that:
E{ĥ}=0.  (20)
Thus, the covariance of the LMMSE channel estimator defined by equation (18) may be derived as:
Cov(ĥ)=E{ĥĥH}=AXtRhH.  (21)
Finally, the following may hold:
E{(ĥ−h) (ĥ−h)H}=AXtRhH+Rh−2Re{AXtRh}.  (22)
In the following iterations, the covariance matrix given by equation (21) may be set as the initial covariance matrix in the case when the affine soft decision directed channel estimator is utilized.

Certain aspects of the present disclosure support a linear soft decision directed channel estimation. This channel estimator may be written in the form:
ĥ=B·y.(23)
It can be still assumed that E{h}=0 for the iterative channel estimation process. The extrinsic LLRs obtained from the Turbo decoder may be utilized to construct soft symbols. The expectationsk,mand a variance σk,m2of a soft symbol corresponding to the arbitrary kth(k=1, . . . , K) tone and the arbitrary mth(m=1, . . . , M) transmit antenna may be readily obtained, while Gaussian approximation may be also used.

Let
X=X+{tilde over (X)},(24)
whereXrepresents the expectation of X, and
E{{tilde over (X)}H{tilde over (X)}}={tilde over (R)}  (25)
is a diagonal matrix. For pilot tones, the diagonal terms of matrix {tilde over (R)} may be equal to zero, and for data tones the diagonal terms may be equal to σk,m2. Therefore, the following may hold:

It can be assumed that:
z˜CN(0,Rz),  (27)
where Rzis a diagonal matrix. Then, the corresponding diagonal terms for pilot tones may be equal to zero, while the diagonal terms may be equal to σz2for data tones. Under this assumption, the following may be obtained:

σz2=1K⁢E⁢{zH⁢z}=1K⁢E⁢{tr⁡[X~⁢hhH⁢X~H]}=1K⁢tr⁡[Rh⁢R~].(28)
Thus, the linear soft decision directed channel estimator may be derived as:

It should be noted that for the OFDM system, elements of h (i.e., channel taps) may be strongly correlated implying that the approximation of Rzbeing diagonal may not be accurate. A simplified version of the estimator given by equation (29) may just ignore the term Rz.

Certain aspects of the present disclosure support the affine soft decision directed channel estimation. The affine channel estimator may have the form of:
ĥ=Cy+h,(30)
where a mean of the affine channel estimator may be set as the mean of the pilot-based LMMSE channel estimator given by equation (18). The system model may be written as:

The affine soft decision directed channel estimator may be expressed as:

It can be noted that the assumption that Rzis a diagonal matrix is reasonable since elements of {tilde over (h)} may not be strongly correlated. A simplified version of the affine estimator given by equation (34) may ignore either or both of the terms R{tilde over (z)}andHR{tilde over (x)}HHfrom equation (34). Also, it can be shown that:
E{ĥ}=h,  (36)
and
Cov(ĥ)=C·X·KhH.  (37)

In equation (34), an initial value of R{tilde over (h)}may be set to the value given by equation (22), which is obtained from the pilot-based channel estimation. In the following iterations, the R{tilde over (h)}term may be approximated by using equation (37).

The various operations of methods described above may be performed by any suitable means capable of performing the corresponding functions. The means may include various hardware and/or software component(s) and/or module(s), including, but not limited to a circuit, an application specific integrate circuit (ASIC), or processor. Generally, where there are operations illustrated in Figures, those operations may have corresponding counterpart means-plus-function components with similar numbering. For example, blocks710-760and1010-1050illustrated inFIGS. 7 and 10correspond to circuit blocks710A-760A and1010A-1050A illustrated inFIGS. 7A and 10A.

The techniques provided herein may be utilized in a variety of applications. For certain aspects, the techniques presented herein may be incorporated in an access point station, an access terminal, or other type of wireless device with processing logic and elements to perform the techniques provided herein.