Adaptive Receiver Beamforming for Diversity Coded OFDM Systems: Maximum SNR Design
Summary (2 min read)
Introduction
- Signal transmission in multi-input multi-output (MIMO) systems that employs more than one antennas at the transmitter and the receiver has shown to be effective in exploiting spatial diversified paths of wireless channels [1]-[2] and increasing both system capacity and error-rate performance.
- Their performance improvements are based on the assumption that the arriving multipath signals are sufficiently uncorrelated.
- The application of space-time coding to orthogonal frequency division multiplexing (OFDM) systems was first introduced in [8].
- With the effective use of beamforming at the multiantennas base station (BS) receiver, the optimal adaptive beam-mapping weights is applied to maximize the instantaneous SNR, and thus, system error-rate performance during uplink transmission in a singleinput multi-output (SIMO) channel is further enhanced.
- ‖ · ‖F is the Frobenius norm; √A stands for Hermitian square root of matrix A; det(·) denotes the determinant; E{·} is the expectation operator.
II. SYSTEM MODEL
- It is assumed that the channel coherent bandwidth is larger than the bandwidth of each subcharrier; the authors thus consider the corresponding subchannel to be frequency-flat.
- The normalized correlation matrix that specifies the correlation between antenna elements is Authorized licensed use limited to: RMIT University.
- Let us denote the correlated SIMO channel frequency response vector for the kth subcarrier as hk ∈ C1×Nr .
- ]T is the corresponding discrete Fourier transform coefficients.
- Furthermore, quasi-static fading is also assumed throughout the duration of one FTBC codeword length but fading may vary from one block to another.
A. Subchannel Grouping & Frequency-Time Encoding
- The concept of subchannel grouping, sometimes referred as subcarrier grouping, was originally used in adaptive modulation scheme in [10] to reduce processing complexity by grouping subcarriers or subchannels that are within one channel coherent bandwidth and having a similar fading gain.
- The authors utilize the concept of subchannel grouping in [12] by treating subcarriers that are having different fading gains as additional antennas at the MS.
- By doing so, the authors can then directly apply the spacetime codes in [3]-[5], [15] in their system by spreading symbol energy across OFDM frequencies instead of antennas.
- If the well-known Alamouti’s space-time block code in [3].
- Note that other STBC matrices in [4] and STTC technique in [5] can be applied in the same way, but with different subchannel grouping sizes.
C. Frequency-Time Decoding
- To recover original data, channel estimation results are also used for the FT decoding process.
- Since frequency subcarriers are treated as additional transmit antennas at the transmitter FT encoding, the decoding algorithm is divided into a combining stage and a maximum likelihood decoding (MLD) stage.
- The combining stage is simply adding the received signals in different subcarriers that are within the same subchannel group.
- Denote i(m) as the frequency index for subchannel group i.
- Thus, without the presumption that Alamouti’s space-time block code is used for the FT encoding, the combining process can be expressed as yi(n) = Nc/Ng∑ m=1 yi(m)(n).
III. OPTIMAL ANTENNA WEIGHTING MATRIX: MAXIMUM SNR DESIGN
- The objective of this Section is to maximize the received SNR in order to improve the system error-rate performance.
- Assume Note that their optimization problem has a similar form to that in [17].
- This shows that signal reception should be in the eigen-modes of the channel covariance matrix and effectively transforms the SIMO channel configuration into a set of Bk parallel and independent subchannels with the bth subchannel having a gain of |hk(b)|2δbµb,k.
- Without going to the extend of rewriting all (16)-(18) for this case, the authors can first re-arrange Nrσ 2 k εs|hk(j)|2δj ’s in a non-descending order.
IV. NUMERICAL RESULTS
- In this Section the authors provide bit-error-rate (BER) and symbolerror-rate (SER) curves for the proposed transmission schemes in broadband frequency-selective channels.
- Comparing the curves that correspond to these three schemes, it is clear that both ST-OFDM and FT-OFDM systems give significant error-rate improvement over the uncodedOFDM.
- It is observed that better performance curves can be obtained in channels with higher spatial correlations for FT-Beam structure.
V. CONCLUSIONS
- An adaptive transceiver structure that combines a new diversity coding scheme and receiver beamforming for uplink SIMO-OFDM transmission is investigated.
- By utilizing the concept of subchannel grouping, FT coding that provides frequency diversity in the broadband wireless channel has proven to be an effective means of signal transmission for MS with a single antenna.
- It is shown that adaptive eigenbeamforming at the receiver (to handle uplink signals in the eigen-modes of the correlation matrix) maximizes the received SNR and improves the system error-rate performance of the FT-coded OFDM system.
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"Adaptive Receiver Beamforming for D..." refers background in this paper
...The application of space-time coding to orthogonal frequency division multiplexing (OFDM) systems was first introduced in [8]....
[...]
501 citations
"Adaptive Receiver Beamforming for D..." refers background in this paper
...Motivated by the presence of additional multipath diversity offered by frequency-selectivity in broadband wireless channels, space-frequency (SF) [7] and space-timefrequency (STF) coding [9] were introduced....
[...]
...As a consequence, coherent deep fade between propagation signal paths is unavoidable and studies have shown that signal correlation can degrade the system performance significantly [6], [7]....
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401 citations
"Adaptive Receiver Beamforming for D..." refers background or methods in this paper
...Motivated by the presence of additional multipath diversity offered by frequency-selectivity in broadband wireless channels, space-frequency (SF) [7] and space-timefrequency (STF) coding [9] were introduced....
[...]
...In [9] and [12], subcarrier grouping is used for grouping frequencies that are approximately one coherent bandwidth apart to perform STF coding in OFDM systems to exploit both spatial and multipath diversity....
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