Multiple-Differential Encoding for Multi-Hop Amplify-and-Forward IR-UWB Systems

Abstract

In this paper, we propose a novel multi-hop relaying scheme to improve the performance and coverage of impulseradio-based ultra-wideband (IR-UWB) systems. With regard to a simple practical realization, we focus on a non-coherent system setup in conjunction with amplify-and-forward (A&F) relaying. In particular, we propose to employ a multiple-differential encoding scheme at the source node and single differential decoding at each relay and at the destination node, respectively, so as to efficiently limit intersymbol-interference effects at the destination node. For a dual-hop system we derive a closed-form expression for the signal-to-noise ratio (SNR) at the destination node, and for the general multi-hop case we provide a simple recursive formula for SNR calculation. Based on these SNR results, we obtain a closed-form expression for the optimal transmit power allocation to the source node and the relay for a dual-hop system and a simple recursive suboptimal power allocation scheme for the multi-hop case, which permits a semi-distributed implementation with limited feedback between nodes. Simulation results illustrate the excellent performance of the proposed multiple-differential encoding scheme with A&F relaying for both uncoded and coded transmission compared to various alternative coherent and non-coherent schemes based on A&F relaying and decode-andforward (D&F) relaying. Furthermore, our simulations confirm the (near-)optimal performance of the proposed power allocation solutions.Index Terms-Ultra-wideband (UWB) communications, impulse radio (IR), amplify and forward (A&F) relaying, multiple hops, differential encoding, performance analysis, power allocation.

A cooperative approach for amplify-and-forward differential transmitted reference IR-UWB relay systems

“…We focus on the channel model CM1, considering a path loss exponent p = 3 and a standard deviation of the log-normal fading term σ fad = 2.5. The number of frames used to transmit each symbol is N f = 2, the bandwidth of bandpass filter is W = 5 GHz, and the integration time is Ti = 5.25 ns [10]. Let d sd , dsr and d rd be the source-destination, source-relay, and relay-destination distances.…”

“…In addition, even if SNRc depends on Eg/N0, we notice that the power allocation strategy is slightly affected by changes in this ratio. Figures 2 and 3 present a performance comparison between the direct transmission with single differential encoding, A&F noncooperative relaying with double differential encoding and the power allocation strategy described in [10], and the proposed cooperative approach with αs = 0.5 (equal power allocation) and αs given by Eq. (19).…”

“…In order to make the decision on the information bit a0[k], the existing non-cooperative method [10] takes into account only the S-R-D path, namely the decision variableã 0,srd [k]. Our proposal is to exploit the information coming from both the S-R-D and S-D paths, considering the three decision variablesã 1,sd [k],ã 1,sd [k + 1], and a 0,srd [k], which can be well approximated as Gaussian distributed and independent [4], [6].…”

“…If Et = N f Eg is the total transmitted energy associated to one information symbol and shared by source and relay, δ = W N f Ti N 2 0 /2 a second order noise term, and p l = G l · T i 0 w 2 rx,l (t)dt the percentage of power captured after the bandpass filter, it is possible to show that [10] (10), the independent Gaussian assumption and the fact that for i ∈ {−1, +1}…”

“…A possible solution to the problem consists in performing a multiple-differential encoding at the source node combined with a correlation operation with a noisy template at each intermediate relay. As a result, a significantly better bit error probability (BER) performance is obtained with respect to the direct transmission without extending guard intervals [10]. However, such a non-cooperative system shows its limits when source-relay, or relay-destination links are degraded.…”