Space-time bit-interleaved coded modulation for wideband transmission

[0001] 1. Field of the Invention

[0002] The present invention relates to data modulation and demodulation in a communication network, and, more particularly, to space-time coding and decoding techniques for wideband data channels.

[0003] 2. Description of the Related Art

[0004] Wireless channels exhibit a number of impairments, among which fading is one of the most severe. For narrowband channels, the fading can often be assumed to be flat, while for wideband channels the fading is typically frequency selective. In addition, additive noise and interference contribute significantly to signal degradation. Diversity is a method to improve transmission over fading channels. Time diversity uses encoding to duplicate and spread information through an encoded bit stream (e.g., convolutional encoding) and space diversity employs multiple transmit and/or receive links to duplicate and spread information over multiple signal paths.

[0005] Coded modulation systems employ methods that utilize time diversity. Encoded data is transmitted through the path between a single transmit antenna and a single receive antenna. Some methods efficiently utilize binary convolutional codes to obtain diversity gains with higher-order, non-binary modulation symbols (e.g., 16-QAM), such as bit-interleaved coded modulation (BICM) systems using multi-level coding methods (and corresponding multistage decoding at the receiver). For example, BICM systems provide diversity gains, and, for example, higher-order, coded modulation systems use well-known binary convolutional codes separated by interleaving to encode the data. Further improvements in system performance are obtained by iterative demapping (translation of symbols to bits) and decoding at the receiver. More recently, so-called space-time coding methods have been proposed to obtain both space and time diversity by using multiple transmit and/or receive antennas along with matching coding. For example, a space-time BICM scheme for narrowband radio channels employing multiple transmit antennas in flat fading cases is described in A. M. Tonello, “Space-Time Bit-Interleaved Coded Modulation With An Iterative Decoding Strategy,” Proceedings, VTC 2000 Fall, Boston, Mass., September 2000, pp. 473-478, which is incorporated herein in its entirety by reference.

[0006] Orthogonal Frequency Division Multiplexing (OFDM) is a form of data transmission in which a block of data is converted into a parallel form and mapped into frequency domain symbols. To generate a time domain signal for transmission over the antenna link between antennas, the inverse discrete Fourier transform (IDFT, or its fast version, the IFFT) of length F is applied to F frequency domain symbols to create F subchannels (also known as F subcarriers, since each channel is a separately modulated carrier). Each of the F subcarriers is orthogonal to each other while the frequency spectrum overlaps. The frequency spacing between the F subcarriers is minimum in OFDM, giving OFDM high spectral efficiency. At the receiver, the discrete Fourier transform (DFT, or its fast version, the FFT) is applied to the received signal over F subchannels to generate a sequence of values representing estimated frequency domain symbols. Demapping maps the estimated symbols back to the original block of user data (bits). OFDM allows for wideband transmission over frequency selective (radio) channels without adaptive equalizers. For wideband systems, OFDM has been proposed for a wide range of radio channel applications. One application is the wireless Local Area Network (LAN) system defined by the IEEE 802.11a standard. This standard adopts OFDM in packet-based communications operating in unlicensed 5-GHz bands.

[0007] In accordance with embodiments of the present invention, a system employs space-time coding characterized at the transmitter by coded modulation, such as bit-interleaved coded modulation (BICM), combined with Orthogonal Frequency Division Multiplexing (OFDM) over multiple transmit and/or receive antennas. A receiver demodulates the OFDM signal and applies multi-input, multi-output (MIMO) demapping to estimate the BICM encoded bitstream. After deinterleaving of the estimated BICM encoded bitstream, maximum a posteriori (MAP) decoding is applied to the resulting bit stream to generate soft output values for decoded user data. The MIMO demapping and MAP decoding processes exchange likelihood information to improve the bit error rate performance over several iterations of demapping/decoding.

[0008] In accordance with an exemplary embodiment of the present invention data is processed for transmission through a channel by (a) applying coded modulation to the data to generate an encoded bitstream; (b) forming at least two parallel streams from the encoded bitstream; (c) modulating each parallel stream to form a corresponding sequence of frequency domain symbols; and (d) transforming, for each parallel steam, F frequency domain symbols into F subchannels, wherein F is an integer greater than 1.

[0009] In accordance with another exemplary embodiment of the present invention, data is generated from two or more groups of F subchannels. A subchannel of each group is applied to a corresponding multi-input, multi-output (MIMO) demapper; and each MIMO demapper generates 1) a corresponding estimate of two or more parallel streams and 2) likelihood information based on extrinsic information. The estimates of the two or more parallel streams are combined into an estimate of an encoded bitstream that is decoded based on the likelihood information, wherein the decoding generates the extrinsic information.

[0015] FIG. 1 shows a coded modulation system 100 employing one or more embodiments of the present invention. Coded modulation system 100 is characterized by transmitter 200 applying space-time coding with bit-interleaved coded modulation that is combined with a multi-carrier OFDM modulation; and receiver 300 applying OFDM demodulation with iterative demapping and decoding. Such coded modulation systems in accordance with the present invention may be advantageously employed in wireless local/wide area network (LAN/WAN) applications.

[0016] FIG. 1 shows an example of a system with 3 transmit antennas and 2 receive antennas. In general, system 100 has N_t transmit antennas and N_r receive antennas. While the exemplary embodiment is described for space-time coding with bit-interleaved coded modulation, other types of coded modulation for space-time coding may be employed. In addition, the exemplary embodiments are described for a mapping of the bit-interleaved coded data into symbols using a modem constellation. Such modem constellation may be m-ary PSK or m-ary QAM with m constellation points, though the present invention is not limited to these constellations and may employ any multi-level signal point modulation. System 100 employs OFDM for wideband channels using F subcarriers rather than single carrier modems. The spectral efficiency of system 100 is R_C·N_t·log₂ m bits/s/Hz, where R_C is the rate of the convolutional code used.

[0017] FIG. 2 shows transmitter 200 for space-time coding with bit-interleaved coded modulation (BICM) with OFDM modulation for the case of wideband frequency selective channels. Transmitter 200 comprises convolutional encoder 201, bit interleaver 202, processing module 203, mapper modems 207(1)-207(N_t), inverse fast Fourier transform (IFFT) modules 208(1)-208(N_t), and transmit antennas 209(1)-209(N_t).

[0018] Applying BICM encoding to the data is as follows. Convolutional coder 201 applies a binary convolutional code with rate R_C to the input bits (input data). Bit interleaver 202 then interleaves the encoded bits from convolutional coder 201 to generate BICM encoded data. Bit interleaving by interleaver 202 de-correlates the fading channel, maximizes diversity, removes correlation in the sequence of convolutionally encoded bits from convolutional coder 201, and conditions the data for increased performance of iterative decoding. Convolutional coder 201 and bit interleaver 202 may typically operate on distinct blocks of input data, such as data packets.

[0019] Applying OFDM to the BICM encoded data is as follows. Processing module 203 includes serial-to-parallel converter 204 and optional framing module 206. Serial-to-parallel converter 204 receives the serial BICM encoded bitstream from bit interleaver 202, which bitstream may have framing information inserted in the bitstream by framing module 206. Optional framing information allows a receiver to synchronize its decoding on distinct blocks of information. Serial-to-parallel converter 204 generates a word of length N_t, with each element of the word provided to a corresponding one of mapper modems 207(1)-207(N_t). Elements of the word may be single-bit values or may be b-bit values where b is the number of bits represented by each modem constellation symbol.

[0020] Mapper modems 207(1)-207(N_t) each convert b bits to corresponding symbols (of the m-ary symbol space) in the sequence x_kⁱ of equation (5), described below. The output of the i^th modem mapper 207(i) is a symbol. Each IFFT module 208(i) each collects up to F symbols and then applies the IFFT operation of length F to the block of F symbols. Thus, each IFFT modules 208(i) generates F parallel subchannels that may be transmitted over a corresponding antenna 209(i). Each subchannel is a modulated subcarrier that is transmitted over the channel.

[0021] FIG. 3 shows receiver 300 as an iterative decoder for the space-time code for the OFDM system. Receiver 300 comprises receive antennas 301(1)-301(N_r), fast Fourier transform (FFT) modules 302(1)-302(N_r), demodulator/detector 303, parallel-to-serial converter 307, bit deinterleaver 308, maximum a posteriori (MAP) decoder 309, bit interleaver 310, and serial-to-parallel converter 311.

[0022] A system model may be defined for the general case of N_t transmit antennas (N_t an integer and N_t≧2) and N_r receive antennas (N_r an integer and N_r≧1). Each of the N_r receive antennas receives signals from the N_t transmit antennas. The output y_k,l^j at the kth subcarrier and at the lth time slot from the jth receive antenna matched filter after the discrete Fourier transform (DFT, or its fast version, the FFT) is given by equation (1):

[0023] $\begin{array}{cc}{y}_{k,l}^j=\sqrt{E_s}\sum _i^{N_i}{H}_{k,l}^{i,j}{x}_{k,l}^i+n_{k,l}^i\mathrm{for}j=1,2,\dots N_r& \left(1\right)\end{array}$
where x_k,lⁱ is the transmitted symbol (of a multi-level symbol constellation) at the ith transmit antenna at the kth subcarrier and at the lth time slot. The value E_s is defined as the symbol energy and H_k,l^i,j is defined as the equivalent channel frequency response of the link between the ith transmit antenna and jth receive antenna at the kth subcarrier and at the lth time slot. The quantity n_k,l^j represents the additive noise contribution, which is represented as a sequence of i.i.d. complex, zero-mean, Gaussian variables with variance N_o/2 per dimension (N_o being the noise power).

[0024] The time domain channel impulse response between the ith transmit and jth receive antenna may be a frequency selective channel that may be modeled as defined in equation (2):

[0025] $\begin{array}{cc}{h}^{i,j}\left(t,\tau \right)=\sum _{n=1}^K{\stackrel{\_}{h}}^{i,j}\left(n,t\right)\delta \left(\tau -{\tau }_n\right)& \left(2\right)\end{array}$
where the channel coefficients h^i,j (n,t) are complex Gaussian variables with zero mean (Rayleigh fading). The term δ(·) is defined as the Dirac delta function, t is the time base, τ is a delay and K denotes the number of channel (filter) taps.

[0026] The channel impulse responses of each of the antenna links are independent of one another. Both fast fading (i.e., uncorrelated fading coefficients in time) and block fading (i.e. static fading coefficients over a block of transmitted symbols, independent over blocks) may be present. For the described embodiments, the model is described using block fading typical of wireless LANs with slow movements. Consequently, the variables with respect to time indices l and t may be considered constant and these indices are omitted from the following description for clarity.

[0027] The channel frequency response in equation (1) may be expressed as given in equation (3):

[0028] $\begin{array}{cc}{H}_k^{i,j}=\sum _{n=1}^K{\stackrel{\_}{h}}^{i,j}\left(n\right)e^{-i2\pi k{\tau }_n/\mathrm{FT}}& \left(3\right)\end{array}$
where T denotes the sampling period. The absolute magnitude of the channel frequency response, |H_k^i,j|, is Rayleigh distributed.

[0029] The symbol constellation is normalized such that equation (4) holds true:
E{|x_kⁱ|²}=1 for i=1,2, . . . N_t  (4)

[0030] With vector notations, equation (2) may be expressed as in equation (5):

[0031] $\begin{array}{cc}{y}_k=\left[\begin{array}{c}{y}_k^1\\ ⋮\\ y_k^{N\tau }\end{array}\right]=\sqrt{E_s}\left[\begin{array}{ccc}{H}_k^{1,1}& \cdots & H_k^{N_i,1}\\ ⋮& ⋰& ⋮\\ H_k^{1,N_{\tau }}& \cdots & H_k^{N_i,N_{\tau }}\end{array}\right]\left[\begin{array}{c}{x}_k^1\\ ⋮\\ x_k^{N_i}\end{array}\right]+\left[\begin{array}{c}{n}_k^1\\ ⋮\\ n_k^{N_{\tau }}\end{array}\right]& \left(5\right)\end{array}$
or equivalently as in equation (5′):
y_k=√{square root over (E_s)}H_kx_k+n_k for k=1,2, . . . F  (5′)

[0032] Generally, receiver 300 includes circuitry that estimates the values for the elements in channel response matrix H_k, and such estimates may be generated using periodic test signals transmitted by transmitter 200 to receiver 300. Such a priori information of the channel impulse response may also be generated via simulations.

[0033] For a wideband system, receiver 300 performs OFDM demodulation for each of receive antennas 301(1)-301(N_r), where the demodulation and demapping is performed over F parallel subchannels. The jth receive antenna 301(j) senses a signal made up of various contributions of the signals transmitted from the N_t transmit antennas (i.e., contributions of the multiple F parallel, narrowband, flat fading subchannels transmitted over corresponding antennas 209(1)-209(N_t) of FIG. 2). Each FFT module 302(j) applies an F-point FFT to the signals from corresponding receive antenna 301(j). As such, the N_r FFT modules generate N_r parallel sets of F subchannels.

[0034] In accordance with embodiments of the present invention, demodulator/detector 303 estimates bits in each of the F subchannels (slowly varying with flat fading) rather than in only one subchannel as in the narrowband, flat fading systems of the prior art. Demodulator 304 demodulates F subchannel carriers to baseband for each of the N_r parallel sets of F subchannels. Multi-input multi-output (MIMO) demapper 305, based on the N_r parallel sets of F subchannels from FFT modules 302(1)-302(N_r) produces MAP estimates of the demapped bits (i.e, bits mapped from the constellation symbol) in each of the F subchannels from the N_t antennas in the transmitter. MIMO demapper 305 produces the MAP estimates of the demapped bits using reliability information generated by MAP decoder 309, which the MAP decodes the MAP estimates of the BICM values to generate either soft decisions during first and subsequent iterations or user data during the last iteration.

[0035] Estimation of bit values by MIMO demapper 305 is now described. MIMO demapper 305 computes soft values for bits transmitted on the overlapping F subchannels, along with an a posteriori probability of the soft value being correct. The a posteriori probability of the soft value is defined as an a posteriori log-likelihood ratio (LLR) for the soft value (bit). Defining d_k^i,m as the bit that is mapped at the kth subcarrier into the mth bit position (m=1, 2 . . . M, where M is the integer number of bits per symbol) of the constellation symbol of the ith transmit antenna, i=1, 2, . . . N_t, then the a posteriori LLR L (d_k^i,m) for the soft value corresponding to bit d_k^i,m is given as in equation (6):

[0036] $\begin{array}{cc}L\left(d_k^{i,m}\right)=\log \frac{P\left(d_k^{i,m}=+1\right)}{P\left(d_k^{i,m}=-1\right)}.& \left(6\right)\end{array}$

[0037] The set S_d^i,m, d=+1 or −1, is defined as the set of all symbol vectors with a +1 or −1 value for bit d_k^i,m, respectively. The number of elements in such a set is 2^N,M. The LLR in equation (6) conditioned on the channel state information H_k is given in equation (7):

[0038] $\begin{array}{cc}\log \frac{P\left(d_k^{i,m}=+1|y_k,H_k\right)}{P\left(d_k^{i,m}=-1|y_k,H_k\right)}=\log \frac{\sum _{x_k\in S_{+1}^{i,m}}^{}p\left(x_k,y_k,H_k\right)}{\sum _{x_k\in S_{-1}^{i,m}}^{}p\left(x_k,y_k,H_k\right)}& \left(7\right)\end{array}$

[0039] A MIMO demapper considers all 2^N,M combinations of overlapping bits in a subchannel and then evaluates the LLR for each combination. For system 100, the complexity (number of combinations evaluated) is approximately 2^N,M. Thus, assuming a transmitted vector of symbol bits x_k a vector of observations at the receiver y_k, and the known estimated channel function H_k, the soft output values for bits may be generated by calculating the LLR of equation (7) for all combinations.

[0040] MIMO demapper 305 in FIG. 3 is shown in FIG. 4. Each signal of the N_r receive antennas 302(1)-302(N_r) is divided into F subchannels (via demodulator 304, not shown in FIG. 4) by applying the FFT and sent to corresponding subchannel MIMO demappers 401(1)-401(F). The signal outputs of the kth subchannel for all N_r receive antennas are provided to the kth subchannel MIMO demapper 401(k), which computes the log likelihood ratio of equation (7) using extrinsic information (a likelihood ratio vector L_k^e) generated from the output of MAP decoder 309 of the previous iteration. Instead of the parallel structure shown in FIG. 4, it is possible to process the signals output from each of FFT modules 302(1)-302(N_r) sequentially by buffering the output and processing them one by one with only one MIMO demapper.

[0041] In order to generate a value for the LLR of equation (7), the joint probability density p(x_k,y_k,H_k) of equation (7) is evaluated. The joint probability density p(x_k,y_k,H_k) of equation (7) is proportional to (∝) the quantity of equation (8):

[0042] $\begin{array}{cc}p\left(x_k,y_k,H_k\right)\propto \exp \left(-\frac{1}{N_0}{y_k-H_k{x}_k}^2+\frac{1}{2}{d}_k^T{L}_k^e\right)& \left(8\right)\end{array}$
where d_k is a column vector comprising elements d_k^i,m and L_k^e is the extrinsic information column vector representing a priori log likelihood ratio (LLR) values for the bits from MAP decoder 309. The extrinsic information (the a priori LLR vector L_k^e) is exchanged between MIMO demapper 305 and MAP decoder 309 to improve the bit error rate performance for each iteration. The elements of the a priori LLR vector L_k^e may be independent variables in the interleaved bit stream.

[0043] For the first iteration (i.e., the first pass through the iterative detection and decoding process), the elements of the a priori LLR vector L_k^e are set to zero. For each subsequent iteration, the elements of the a priori LLR vector L_k^e are derived from the MAP decoding process of MAP decoder 309.

[0044] Returning to FIG. 3, the estimates of bits in F parallel streams from MIMO demapper 305 are provided to parallel-to-serial converter 307 which reconstitutes receiver 300's estimate of the BICM encoded bitstream generated by the transmitter. The estimated BICM encoded bitstream is then deinterleaved by bit deinterleaver 308 and applied to MAP decoder 309 to reverse the convolutional encoding applied by the transmitter.

[0045] The MAP decoding process generates soft output values for transmitted information bits. The MAP decoding process employs input a priori LLR values for decoding. The input a priori LLR values to MAP decoder 309 are extrinsic information from MIMO demapper 305, which is the difference between 1) the input LLR values L_k^e to MIMO demapper 305 for the encoded information bits and 2) the output LLR values L_k having elements L(d_k^l,m) calculated from equation (7) for the estimates for encoded information bits. For MAP decoding, the a posteriori log-likelihood ratio (LLR) value L(u_i) for a user's bit u_i at time i (for either a decoded or a new/improved encoded information bit) given an observation (channel output sample) y_i may be calculated as given in equation (9):

[0046] $\begin{array}{cc}L\left(u_i\right)=\log \left(\frac{p\left(u_i=+1|y_i\right)}{p\left(u_i=-1|y_i\right)}\right).& \left(9\right)\end{array}$

[0047] The a priori LLR vector L_k^e applied to the kth subchannel MIMO demapper 401(k) of FIG. 4 is formed from extrinsic information of MAP decoding. Extrinsic information for a bit is defined as the difference between 1) the input a priori LLR value to MAP decoder 309 for the encoded information bit (extrinsic information from the MIMO demapper) and 2) the output a posteriori LLR value for the encoded information bit (e.g., generated through equation (9)). However, after forming the difference, the extrinsic information from MAP decoder 309 is first applied to bit interleaver 310. Bit interleaving aligns elements of the extrinsic information with the interleaved estimated BICM encoded bitstream from MIMO demapper 305. In addition, the interleaved extrinsic information is applied to serial-to-parallel converter 311, which forms N_t parallel streams of extrinsic information corresponding to the parallel bit streams formed at the transmitter. Vector channel module 306 then forms the a priori LLR column vector L_k^e for each of the F subchannels from the N_t parallel streams of extrinsic information.

[0048] The extrinsic information is exchanged between MIMO demapper 305 and MAP decoder 309 to improve the bit error rate performance for each iteration. The elements of the a priori LLR vector L_k^e may be considered as independent variables in the interleaved bit stream.

[0049] However, for calculation of the LLR value of equation (7), the cardinality of the set S_d^i,m is 2^N,M. Thus, 2^N,M sequence evaluations are made. The number of evaluations grows exponentially with the product of the number of transmit antennas N_t and the number of bits per constellation symbol (signal point) M. To improve speed of decoding and decrease both circuit size and power consumption of an implementation, it is desirable to reduce the number of calculations during the evaluations. For a first level of complexity reduction without significant loss of performance, a Max-Log approximation for calculation of LLRs may be used in both a MIMO demapper and in a MAP decoder for the convolutional code. The Max-Log approximation for calculation of a posteriori LLR values may employ the max* term relationship of equation (10):
max*(x, y)=log(e^−x+e^−y)=max(x, y)+log(1+e^−|x−y|)  (10)
when calculating updated forward recursive, reverse recursive, and branch metrics sequences to calculate the value of equation (6). Each constituent MIMO demapper or MAP decoder thus calculates the max* term by separate calculation of a max term (max(x,y)) and a logarithmic correction term (log(1+e^−|x−y|)).

[0050] A system operating in accordance with an embodiment of the present invention may provide the following advantages. Space time bit-interleaved coded modulation (ST-BICM) in wireless LAN applications is flexible in various system configurations. Unlike other space-time coded systems of the prior art in which coding and modulation design was specified for each system setup, a single coder in a ST-BICM system operating in accordance with an exemplary embodiment of the present invention may support many different data rates. Support of multiple, varying data rates may be advantageous for wireless LAN system design where, for example, eight different data rate modes are defined in the 802.11a standard.

[0051] The present invention can be embodied in the form of methods and apparatuses for practicing those methods. The present invention can also be embodied in the form of program code embodied in tangible media, such as floppy diskettes, CD-ROMs, hard drives, or any other machine-readable storage medium, wherein, when the program code is loaded into and executed by a machine, such as a computer, the machine becomes an apparatus for practicing the invention. The present invention can also be embodied in the form of program code, for example, whether stored in a storage medium, loaded into and/or executed by a machine, or transmitted over some transmission medium or carrier, such as over electrical wiring or cabling, through fiber optics, or via electromagnetic radiation, wherein, when the program code is loaded into and executed by a machine, such as a computer, the machine becomes an apparatus for practicing the invention. When implemented on a general-purpose processor, the program code segments combine with the processor to provide a unique device that operates analogously to specific logic circuits.

[0052] It will be further understood that various changes in the details, materials, and arrangements of the parts which have been described and illustrated in order to explain the nature of this invention may be made by those skilled in the art without departing from the scope of the invention as expressed in the following claims.